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A knowledge-intensive machine-learning approach to the principal- agent problem

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A knowledge-intensive machine-learning approach to the principal- agent problem
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Garimella, Kiran K
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xvi, 220 leaves : ill. ; 29 cm.

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Correlations ( jstor )
Entropy ( jstor )
Knowledge bases ( jstor )
Learning ( jstor )
Machine learning ( jstor )
Modeling ( jstor )
Motivation ( jstor )
Signals ( jstor )
Simulations ( jstor )
Statistics ( jstor )
Agency Theory / Expertensystem / Lernprozess / Theorie
Decision and Information Sciences thesis Ph. D
Decision making ( lcsh )
Dissertations, Academic -- Decision and Information Sciences -- UF
Machine learning ( lcsh )
City of Gainesville ( local )
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Thesis (Ph. D.)--University of Florida, 1993.
Bibliography:
Includes bibliographical references (leaves 206-218).
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Also available online.
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Typescript.
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Vita.
Statement of Responsibility:
by Kiran K. Garimella.

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Full Text









A KNOWLEDGE-INTENSIVE MACHINE-LEARNING APPROACH
TO THE PRINCIPAL-AGENT PROBLEM
















By

KIRAN K. GARIMELLA


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA
1993
































To my mother, Dr. Seeta Garimella













ACKNOWLEDGMENTS


I thank Prof. Gary Koehler, chairman of the DIS department, a guru to me in the

deepest sense of the word who made it possible for me to grow intellectually and

experience the richness and fulfillment of an active mind.

I also want to thank Prof. Selcuk Erenguc for encouraging me at all times; Prof.

Harold Benson who taught me care, caution, and clarity in thinking by patiently teaching

me proof techniques in mathematics; Prof. David E.M. Sappington for giving me

invaluable lessons, by his teaching and example, on research techniques, for writing

papers and books that are replete with elegance and clarity, and for ensuring that my

research is meaningful and interesting from an economist's perspective; Prof. Sanford

V. Berg, for providing valuable suggestions in agency theory; and Prof. Richard Elnicki,

Prof. Antal Majthay, and Prof. Ira Horowitz for their advice and help with the research.

I thank Prof. Malay Ghosh, Department of Statistics, and Prof. Scott

McCullough, Department of Mathematics, for their guidance in statistics and

mathematics.

I also thank the administrative staff of the DIS department for helping me in

numerous ways and making my work extremely pleasant.

I thank my wife, Raji, for her patience and understanding while I put in long and

erratic hours.








I cannot conclude without expressing my deepest sense of gratitude to my mother,

Dr. Seeta Garimella, who constantly encouraged me in ways too numerous to recount

and made it possible for me to pursue my studies in the land of my dreams.













TABLE OF CONTENTS


ACKNOWLEDGMENTS ................................... iii

LIST OF TABLES ...................................... viii

ABSTRACT ........................................... xv

1 OVERVIEW ...................................... 1

2 EXPERT SYSTEMS AND MACHINE LEARNING ............... 6

2.1 Introduction ............ .... .. .. ...... ..... ... 6
2.2 Expert Systems ..................................... 8
2.3 Machine Learning ................................. 10
2.3.1 Introduction ................................. 10
2.3.2 Definitions and Paradigms ....................... 14
2.3.3 Probably Approximately Close Learning ............. 21

3 GENETIC ALGORITHMS .............................. 23

3.1 Introduction ................................... 23
3.2 The Michigan Approach ............................ 26
3.3 The Pitt Approach ................................ 27

4 THE MAXIMUM ENTROPY PRINCIPLE ................... 28

4.1 Historical Introduction .............................. 28
4.2 Examples ..................................... 34

5 THE PRINCIPAL-AGENT PROBLEM .................... 38

5.1 Introduction ............ ............................38
5.1.1 The Agency Relationship ....................... 38
5.1.2 The Technology Component of Agency ............. 40
5.1.3 The Information Component of Agency ............. 40
5.1.4 The Timing Component of Agency .................. 42








5.1.5 Limited Observability, Moral Hazard, and Monitoring . . 44
5.1.6 Informational Asymmetry, Adverse Selection, and Screening 45
5.1.7 Efficiency of Cooperation and Incentive Compatibility . . 47
5.1.8 Agency Costs . . . . . . . . . . . . . ... .. 47
5.2 Formulation of the Principal-Agent Problem . . . . . . ... .. 48
5.3 Main Results in the Literature . . . . . . . . . . ... .. 62
5.3.1 Model 1: The Linear-Exponential-Normal Model . . . .. ..63
5.3.2 M odel 2 . . . . . . . . . . . . . . . ... .. 68
5.3.3 Model 3 . . .................................. 72
5.3.4 Model 4: Communication under Asymmetry . . . . ... ..77
5.3.5 Model G: Some General Results . . . . . . . . ... .. 80

6 METHODOLOGICAL ANALYSIS . . . . . . . . . . ... .. 82

7 MOTIVATION THEORY . . . . . . . . . . . . . ... .. 87

8 RESEARCH FRAMEWORK . . . . . . . . . . . . ... .. 92

9 M ODEL 3 ........................................ 97

9.1 Introduction .................................... 97
9.2 An Implementation and Study ......................... 101
9.3 Details of Experiments ............................ 106
9.3.1 Rule Representation .......................... 106
9.3.2 Inference Method .............................. 110
9.3.3 Calculation of Satisfaction ....................... 111
9.3.4 Genetic Learning Details . . . . . . . . . . ... .. 114
9.3.5 Statistics Captured for Analysis . . . . . . . . ... .. 115
9.4 Results . . . . . . . . . . . . . . . . . . . 116
9.5 Analysis of Results ................................ 118

10 REALISTIC AGENCY MODELS ......................... 149

10.1 Characteristics of Agents ......................... 157
10.2 Learning with Specialization and Generalization .......... 158
10.3 Notation and Conventions ...................... 160
10.4 Model 4: Discussion of Results ................... 161
10.5 Model 5: Discussion of Results ................... 163
10.6 Model 6: Discussion of Results ................... 164
10.7 Model 7: Discussion of Results ................... 165
10.8 Comparison of the Models ........................ 167
10.9 Examination of Learning ......................... 172

11 CONCLUSION . . . . . . . . . . . . . . . . . . 194








12 FUTURE RESEARCH ................................. 198

12.1 Nature of the Agency . . . . . . . . . . . ... .. 198
12.2 Behavior and Motivation Theory . . . . . . . . ... ..199
12.3 Machine Learning . . . . . . . . . . . . ... .. 200
12.4 Maximum Entropy . . . . . . . . . . . . ... ..203

APPENDIX FACTOR ANALYSIS . . . . . . . . . . . ... ..204

REFERENCES . . . . . . . . . . . . . . . . . . . . 206

BIOGRAPHICAL SKETCH ................................. 219













LIST OF TABLES


Table page

9.1: Characterization of Agents . . . . . . . . . . . . . . ... .. 125

9.2: Iteration of First Occurrence of Maximum Fitness . . . . . . ... ..126

9.3: Learning Statistics for Fitness of Final Knowledge Bases . . . . .. ..126

9.4: Entropy of Final Knowledge Bases and Closeness to the Maximum . . . 126

9.5: Frequency (as Percentage) of Values of Compensation Variables in the Final
Knowledge Base in Experiment 1 . . . . . . . . . . . ... .. 127

9.6: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 1 . . . . . . . ... ..127

9.7: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 1 . . . . . . . . . . . ... .. 128

9.8: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 1 . . . . . . . . . . . . . . ... .. 128

9.9: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 1 Factor Pattern . . . . . . . . . ... ..129

9.10: Experiment 1 Varimax Rotation . . . . . . . . . . . ... .. 130

9.11: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 2 . . . . . . . . . ... ..131

9.12: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 2 . . . . . . . ... ..131

9.13: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 2 . . . . . . . . . . . ... ..131


viii








9.14: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 2 Eigenvalues of the Correlation Matrix ....... ..132

9.15: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 2 Factor Pattern . . . . . . . . . ... ..133

9.16: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 2 -Varimax Rotated Factor Pattern . . . . .. ..134

9.17: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 3 . . . . . . . . . ... ..135

9.18: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 3 . . . . . . . ... ..135

9.19: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 3 . . . . . . . . . . . ... .. 135

9.20: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 3 Eigenvalues of the Correlation Matrix ....... ..136

9.21: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 3 Factor Pattern . . . . . . . . . ... ..137

9.22: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 3 Varimax Rotated Factor Pattern . . . . ... ..138

9.23: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 4 . . . . . . . . . ... ..139

9.24: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 4 . . . . . . . ... ..139

9.25: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 4 . . . . . . . . . . . ... .. 139

9.26: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 4 Eigenvalues of the Correlation Matrix ....... ..140

9.27: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 4 Factor Pattern . . . . . . . . . ... .. 141

9.28: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 4 Varimax Rotated Factor Pattern . . . . ... ..143








9.29: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 5 . . . . . . . . . ... ..144

9.30: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 5 . . . . . . . ... ..144

9.31: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 5 . . . . . . . . . . . ... ..144

9.32: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 5 Eigenvalues of the Correlation Matrix ....... ..145

9.33: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 5 Factor Pattern . . . . . . . . . ... ..145

9.34: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 5 Varimax Rotated Factor Pattern . . . . ... ..146

9.35: Summary of Factor Analytic Results for the Five Experiments . . ... ..146

9.36: Expected Factor Identification of Compensation Variables for the Five
Experiments Derived from the Direct Factor Analytic Solution ....... ..147

9.37: Expected Factor Identification of Compensation Variables for the Five
Experiments Derived from the Varimax Rotated Factor Analytic
Solution . . . . . . . . . . . . . . . . . . . . 147

9.38: Expected Factor Identification of Behavioral and Risk Variables for the
Five Experiments Derived from the Direct Factor Pattern . . . ... ..148

9.39: Expected Factor Identification of Behavioral and Risk Variables for the
Five Experiments Derived from Varimax Rotated Factor Analytic
Solution . . . . . . . . . . . . . . . . . . . . 148

10.1: Correlation of LP and CP with Simulation Statistics (Model 4) . . ... ..174

10.2: Correlation of LP and CP with Compensation Offered to Agents (Model
4) . . . . . . . . . . . . . . . . . . . . . . 174

10.3: Correlation of LP and CP with Compensation in the Principal's Final KB
(M odel 4) . . . . . . . . . . . . . . . . . . . 174

10.4: Correlation of LP and CP with the Movement of Agents (Model 44 . . 174








10.5: Correlation of LP with Agent Factors (Model 4) . . . . . . ... ..174

10.6: Correlation of LP and CP with Agents' Satisfaction (Model 4) . . ... ..175

10.7: Correlation of LP and CP with Agents' Satisfaction at Termination (Model
4) . . . . . . . . . . . . . . . . . . . . . . 175

10.8: Correlation of LP and CP with Agency Interactions (Model 4) . . ... ..175

10.9: Correlation of LP with Rule Activation (Model 4) . . . . . . ... .. 175

10.10: Correlation of LP with Rule Activation in the Final Iteration (Model 4) . 175

10.11: Correlation of LP and CP with Principal's Satisfaction and Least Squares
(M odel 4) . . . . . . . . . . . . . . . . . . . 175

10.12: Correlation of Agent Factors with Agent Satisfaction (Model 4) . . . 176

10.13: Correlation of Principal's Satisfaction with Agent Factors (Model 4) . 176

10.14: Correlation of Principal's Satisfaction with Agents' Satisfaction (Model
4) . . . . . . . . . . . . . . . . . . . . . . 176

10.15: Correlation of Principal's Last Satisfaction with Agents' Last Satisfaction
(M odel 4) . . . . . . . . . . . . . . . . . . . 176

10.16: Correlation of Principal's Factor with Agent Factors (Model 4) . . . 177

10.17: Correlation of LP and CP with Simulation Statistics (Model 5) ....... ..177

10.18: Correlation of LP and CP with Compensation Offered to Agents (Model
5) . . . . . . . . . . . . . . . . . . . . . . 177

10.19: Correlation of LP and CP with Compensation in the Principal's Final
Knowledge Base (Model 5) . . . . . . . . . . . . . ... ..177

10.20: Correlation of LP and CP with the Movement of Agents (Model 5) . .. 177

10.21: Correlation of LP with Agent Factors (Model 5) . . . . . . ... ..178

10.22: Correlation of LP and CP with Agents' Satisfaction (Model 5) ....... ..178

10.23: Correlation of LP and CP with Agents' Satisfaction at Termination (Model
5) . . . . . . . . . . . . . . . . . . . . . . 178








10.24: Correlation of LP and CP with Agency Interactions (Model 5) ....... ..178

10.25: Correlation of LP with Rule Activation (Model 5) . . . . . . ... ..178

10.26: Correlation of LP with Rule Activation in the Final Iteration (Model 5 . 179

10.27: Correlation of LP and CP with Payoffs from Agents (Model 5) . . .. ..179

10.28: Correlation of LP and CP with Principal's Satisfaction, Principal's Factor
and Least Squares (Model 5) . . . . . . . . . . . . ... ..179

10.29: Correlation of Agent Factors with Agent Satisfaction (Model 5) . . . 179

10.30: Correlation of Principal's Satisfaction with Agent Factors (Model 5) . 180

10.31: Correlation of Principal's Satisfaction with Agents' Satisfaction (Model
5) . . . . . . . . . . . . . . . . . . . . . . 180

10.32: Correlation of Principal's Last Satisfaction with Agents' Last Satisfaction
(M odel 5) . . . . . . . . . . . . . . . . . . . 180

10.33: Correlation of Principal's Satisfaction with Outcomes from Agents (Model
5) . . . . . . . . . . . . . . . . . . . . . . 18 1

10.34: Correlation of Principal's Factor with Agents' Factors (Model 5) . . . 181

10.35: Correlation of LP and CP with Simulation Statistics (Model 6) ....... ..181

10.36: Correlation of LP and CP with Compensation Offered to Agents (Model
6) . . . . . . . . . . . . . . . . . . . . . . 18 1

10.37: Correlation of LP and CP with Compensation in the Principal's Final
Knowledge Base (Model 6) . . . . . . . . . . . . . ... ..182

10.38: Correlation of LP and CP with the Movement of Agents (Model 6) . . 182

10.39: Correlation of LP and CP with Agent Factors (Model 6) . . . . .. .. 182

10.40: Correlation of LP and CP with Agents' Satisfaction (Model 6) ....... ..182

10.41: Correlation of LP and CP with Agents' Satisfaction at Termination (Model
6) . . . . . . . . . . . . . . . . . . . . . . 183

10.42: Correlation of LP and CP with Agency Interactions (Model 6) ....... ..183

xii








10.43: Correlation of LP and CP with Rule Activation (Model 6) . . . .. ..183

10.44: Correlation of LP and CP with Rule Activation in the Final Iteration
(M odel 6) . . . . . . . . . . . . . . . . . . . 183

10.45: Correlation of LP and CP with Principal's Satisfaction and Least Squares
(M odel 6) . . . . . . . . . . . . . . . . . . . 184

10.46: Correlation of Agents' Factors with Agents' Satisfaction (Model 6) . . 184

10.47: Correlation of Principal's Satisfaction with Agents' Factors and Agents'
Satisfaction (M odel 6) . . . . . . . . . . . . . . ... .. 185

10.48: Correlation of Principal's Factor with Agents' Factor (Model 6) . . . 185

10.49: Correlation of LP and CP with Simulation Statistics (Model 7) ....... ..185

10.50: Correlation of LP and CP with Compensation Offered to Agents (Model
7) . . . . . . . . . . . . . . . . . . . . . . 185

10.51: Correlation of LP and CP with Compensation in the Principal's Final


Knowledge Base (Model 7) . .


186


Correlation

Correlation

Correlation

Correlation
7) . . .

Correlation

Correlation

Correlation

Correlation

Correlation

Correlation


of LP and CP with the Movement of Agents (Model 7) . . 186

of LP with Agent Factors (Model 7) . . . . . . ... ..186

of LP and CP with Agents' Satisfaction (Model 7) ....... ..186

of LP and CP with Agents' Satisfaction at Termination (Model
. . . . . . . . . . . . . . . . . . . . 187

of LP and CP with Agency Interactions (Model 7) ....... ..187

of LP and CP with Rule Activation (Model 7) . . . .. ..187

of LP with Rule Activation in the Final Iteration (Model 7) . 187

of LP and CP with Payoffs from Agents (Model 7) ....... .188

of LP and CP with Principal's Satisfaction (Model 7) . . 188

of Agent Factors with Agent Satisfaction (Model 7) . . . 188


xiii


10.52:

10.53:

10.54:

10.55:


10.56:

10.57:

10.58:

10.59:

10.60:

10.61:








10.62: Correlation of Principal's Satisfaction with Agent Factors (Model 7) . 188

10.63: Correlation of Principal's Satisfaction with Agents' Satisfaction (Model
7) . . . . . . . . . . . . . . . . . . . . . . 189

10.64: Correlation of Principal's Last Satisfaction with Agents' Last Satisfaction
(M odel 7) . . . . . . . . . . . . . . . . . . . 189

10.65: Correlation of Principal's Satisfaction with Outcomes from Agents (Model
7) . . . . . . . . . . . . . . . . . . . . . . 189

10.66: Correlation of Principal's Factor with Agents' Factor (Model 7) . . . 189

10.67: Comparison of Models . . . . . . . . . . . . . . ... .. 190

10.68: Probability Distributions for Models 4, 5, 6, and 7 . . . . . .. .. 193


xiv













Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

A KNOWLEDGE-INTENSIVE MACHINE-LEARNING APPROACH
TO THE PRINCIPAL-AGENT PROBLEM

By

Kiran K. Garimella

August 1993

Chairperson: Gary J. Koehler
Major Department: Decision and Information Sciences

The objective of the research is to explore an alternative approach to the solution

of the principal-agent problem, which is extremely important since it is applicable in

almost all business environments. It has been traditionally addressed by the optimization-

analytical framework. However, there is a clearly recognized need for techniques that

allow the incorporation of behavioral and motivational characteristics of the agent and

the principal that influence their selection of effort and payment levels.

The alternative proposed is a knowledge-intensive, machine-learning approach,

where all the relevant knowledge and the constraints of the problem are taken into

account in the form of knowledge-bases.

Genetic algorithms are employed for learning, supplemented in later models by

specialization and generalization operators. A number of models are studied in order of

increasing complexity and realism. Initial studies are presented that provide counter-







examples to traditional agency theory and that emphasize the need for going beyond the

traditional framework. The new framework is more robust, easily extensible in a

modular manner, and yields contracts tailored to the behavioral characteristics of

individual agents.

Factor analysis of final knowledge bases after extensive learning shows that

elements of compensation besides basic pay and share of output play a greater role in

characterizing good contracts. The learning algorithms tailor contracts to the behavioral

and motivational characteristics of individual agents. Further, neither did perfect

information yield the highest satisfaction nor did the complete absence of information

yield the least satisfaction. This calls into question the traditional agency wisdom that

more information is always desirable.

Studies of other models study the effect of two different policies of evaluating

agents' performance by the principal-individualized (discriminatory) evaluation versus the

relative (nondiscriminatory) evaluation. The results suggest guidelines for employing

different types of models to simulate different agency environments.













CHAPTER 1
OVERVIEW





The basic research addressed by this dissertation is the theory and application of

machine learning to assist in the solution of decision problems in business. Much of the

earlier research in machine learning was devoted to addressing specific and ad-hoc

problems or to fill a gap or make up for some deficiency in an existing framework,

usually motivated by developments in expert systems and statistical pattern recognition.

The first applications were to technical problems such as knowledge acquisition, coping

with a changing environment and filtering of noise (where filtering and optimal control

were considered inadequate because of poorly understood domains), data or knowledge

reduction (where the usual statistical theory is inadequate to express the symbolic

richness of the underlying domain), and scene and pattern analysis (where the classical

statistical techniques fail to take into account pertinent prior information; see for

example, Jaynes, 1986a).

The initial research was concerned with gaining an understanding of learning in

extremely simple toy world models, such as checkers (Samuel, 1963), SHRDLU blocks

world (Winograd, 1972), and various discovery systems. The insights gained by such

research soon influenced serious applications.








2
The underlying domains of most of the early applications were relatively well

structured, whether they were the stylized rules of checkers and chess or the digitized

images of visual sensors. Our research focus is on importing these ideas into the area

of business decisionmaking.

Genetic algorithms, a relatively new paradigm of machine learning, deals with

adaptive processes modeled on ideas from natural genetics. Genetic algorithms use the

ideas of parallelism, randomized search, fitness criteria for individuals, and the formation

of new exploratory solutions using reproduction, survival and mutation. The concept is

extremely elegant, powerful, and easy to work with from the viewpoint of the amount

of knowledge necessary to start the search for solutions.

A related issue is maximum entropy. The Maximum Entropy Principle is an

extension of Bayesian theory and is founded on two other principles: the Desideratum of

Consistency and Maximal-Noncommitment. While Bayesian analysis begins by assuming

a prior, the Maximum Entropy Principle seeks distributions that maximize the Shannon

entropy and at the same time satisfy whatever constraints may apply. The justification

for using Shannon entropy comes from the works of Bernoulli, Laplace, Jeffreys, and

Cox on the one hand, and from the works of Maxwell, Boltzmann, Gibbs, and Shannon

on the other; the principle has been extensively championed by Jaynes and is only just

now penetrating into economic analysis.

Under the maximum entropy technique, the task of updating priors based on data

is now subsumed under the general goal of maximizing entropy of distributions given any

and all applicable constraints, where the data (or sufficient statistics on the data) play the








3
role of constraints. Maximum entropy is related to machine learning by the fact that the

initial distributions (or assumptions) used in a learning framework, such as genetic

algorithms, may be maximum entropy distributions. A topic of research interest is the

development of machine learning algorithms or frameworks that are robust with respect

to maximum entropy. In other words, deviation of initial distributions from maximum

entropy distributions should not have any significant effect on the learning algorithms (in

the sense of departure from good solutions).

The overall goal of the research is to present an integrated methodology involving

machine learning with genetic algorithms in knowledge bases and to illustrate its use by

application to an important problem in business. The principal-agent problem was

chosen for the following reasons: it is widespread, important, nontrivial, and fairly

general so that different models of the problem can be investigated, and information-

theoretic considerations play a crucial role in the problem. Moreover, a fair amount of

interest over the problem has been generated among researchers in economics, finance,

accounting, and game theory, whose predominant approach to the problem is that of

constrained optimization. Several analytical insights have been generated, which should

serve as points of comparison to results that are expected from our new methodology.

The most important component of the new proposed methodology is information

in the form of knowledge bases, coupled with strength of performance of the individual

pieces of knowledge. These knowledge bases, the associated strengths, their relation to

one another, and their role in the scheme of things are derived from the individuals' prior

knowledge and from the theory of human behavior and motivation. These knowledge








4
bases contain, for example, information about the agent's characteristics and pattern of

behavior under different compensation schemes; in other words, they deal with the issues

of hidden characteristics and induced effort or behavior. Given the expected behavior

pattern of an agent, a related research issue is the study of the effect of using

distributions that have maximum entropy with respect to the expected behavior.

Trial compensation schemes, which come from the specified knowledge bases, are

presented to the agentss. Upon acceptance of the contract and realization of the output,

the actual performance of the agent (in terms of output or the total welfare) is evaluated,

and the associated compensation schemes are assigned proportional credit. Periodically,

iterations of the genetic algorithm will be used to create a new knowledge base that

enriches the current one.

Chapter 2 begins with an introduction to artificial intelligence, expert systems,

and machine learning. Chapter 3 describes genetic algorithms. Chapter 4 covers the

origin of the Maximum Entropy Principle and its formulation. Chapter 5 deals with a

survey of the principal-agent problem, where a few basic models are presented, along

with some of the main results of the research.

Chapter 6 examines the traditional methodology used in attacking the principal-

agent problem, and measures to cover the inadequacies are proposed. One of the basic

assumptions of the economic theory--the assumption of risk attitudes and utility--is

circumvented by directly dealing with the knowledge-based models of the agent and the

principal. To this end, a brief look at some of the ideas from behavior and motivation

theory is taken in Chapter 7.








5
Chapter 8 describes the basic research model. Elements of behavior and

motivation theory and knowledge bases are incorporated. A research strategy to study

agency problems is proposed. The use of genetic algorithms periodically to enrich the

knowledge bases and to carry out learning is suggested. An overview of the research

models, all of which incorporate many features of the basic model, is presented.

Chapter 9 describes Model 3 in detail. Chapter 10 introduces Models 4 through

7 and describes each in detail. Chapter 11 provides a summary of the results of Chapters

9 and 10. Directions for future research are covered in Chapter 12.













CHAPTER 2
EXPERT SYSTEMS AND MACHINE LEARNING


2.1 Introduction


The use of artificial intelligence in a computerized world is as revolutionary as

the use of computers is in a manual world. One can make computers intelligent in the

same sense as man is intelligent. The various techniques of doing this compose the body

of the subject of artificial intelligence. At the present state of the art, computers are at

last being designed to compete with man on his own ground on something like equal

terms. To put it in another way, computers have traditionally acted as convenient tools

in areas where man is known to be deficient or inefficient, namely, doing complicated

arithmetic very quickly, or making many copies of data (i.e., files, reports, etc.).

Learning new things, discovering facts, conjecturing, evaluating and judging

complex issues (for example, consulting), using natural languages, analyzing and

understanding complex sensory inputs such as sound and light, and planning for future

action are mental processes that are peculiar to man (and to a lesser extent, to some

animals). Artificial intelligence is the science of simulating or mimicking these mental

processes in a computer.

The benefits are immediately obvious. First, computers already fill some of the

gaps in human skills; second, artificial intelligence fills some of the gaps that computers








7
themselves suffer (i.e., human mental processes). While the full simulation of the human

brain is a distant dream, limited application of this idea has already produced favorable

results.

Speech-understanding problems were investigated with the help of the HEARSAY

system (Erman et al., 1980, 1981; and Hayes-Roth and Lesser, 1977). The faculty of

vision relates to pattern recognition and classification and analysis of scenes. These

problems are especially encountered in robotics (Paul, 1981). Speech recognition

coupled with natural language understanding as in the limited system SHRDLU

(Winograd, 1973) can find immediate uses in intelligent secretary systems that can help

in data management and correspondence associated with business.

An area that is commercially viable in large business environments that involve

manufacturing and any other physical treatment of objects is robotics. This is a proven

area of artificial intelligence application, but is not yet cost effective for small business.

Several robot manufacturers have a good order book position. For a detailed survey see

for example, Engelberger, 1980.

An interesting viewpoint to the application of artificial intelligence to industry and

business is that presented by decision analysis theory. Decision analysis helps managers

to decide between alternative options and assess risk and uncertainty in a better way than

before, and to carry out conflict management when there are conflicts among objectives.

Certain operations research techniques are also incorporated, as for example, fair

allocation of resources that optimize returns. Decision analysis is treated in Fishburn

(1981), Lindley (1971), Keeney (1984) and Keeney and Raiffa (1976). In most








8
applications of expert systems, concepts of decision analysis find expression (Phillips,

1986). Manual application of these techniques is not cost effective, whereas their use

in certain expert systems, which go by the generic name of Decision Analysis Expert

Systems, leads to quick solutions of what were previously thought to be intractable

problems (Conway, 1986). Several systems have been proposed that range from

scheduling to strategy planning. See for example, Williams (1986).


2.2 Expert Systems


The most fascinating and economically justifiable area of artificial intelligence is

the development of expert systems. These are computer systems that are designed to

provide expert advice in any area. The kind of information that distinguishes an expert

from a nonexpert forms the central idea in any expert system. This is perhaps the only

area that provides concrete and conclusive proof of the power of artificial intelligence

techniques. Many expert systems are commercially viable and motivate diverse sources

of funding for research into artificial intelligence. An expert system incorporates many

of the techniques of artificial intelligence, and a positive response to artificial intelligence

depends on the reception of expert systems by informed laymen.

To construct an expert system, the knowledge engineer works with an expert in

the domain and extracts knowledge of relevant facts, rules, rules-of-thumb, exceptions

to standard theory, and so on. This is a difficult task and is known variously as

knowledge acquisition or mining. Because of the complex nature of the knowledge and

the ways humans store knowledge, this is bound to be a bottleneck to the development








9

of the expert system. This knowledge is codified in the form of several rules and

heuristics. Validation and verification runs are conducted on problems of sufficient

complexity to see that the expert system does indeed model the thinking of the expert.

In the task of building expert systems, the knowledge engineer is helped by several tools,

such as EMYCIN, EXPERT, OPS5, ROSIE, GURU, etc.

The net result of the activity of knowledge mining is a knowledge base. An

inference system or engine acts on this knowledge base to solve problems in the domain

of the expert system. An important characteristic of expert systems is the ability to

justify and explain their line of reasoning. This is to create credibility during their use.

In order to do this, they must have a reasonably sophisticated input/output system.

Some of the typical problems handled by expert systems in the areas of business,

industry, and technology are presented in Feigenbaum and McCorduck (1983) and Mitra

(1986). Important cases where expert systems are brought in to handle the problems are

1. Capturing, replicating, and distributing expertise.

2. Fusing the knowledge of many experts.

3. Managing complex problems and amplifying expertise.

4. Managing knowledge.

5. Gaining a competitive edge.

As examples of successful expert systems, one can consider MYCIN, designed

to diagnose infectious diseases (Shortliffe, 1976); DENDRAL, for interpretation of

molecular spectra (Buchanan and Feigenbaum, 1978); PROSPECTOR, for geological

studies (Duda et al., 1979; Hart, 1978); and WHY, for teaching geography (Stevens and








10

Collins, 1977). For a more exhaustive treatment, see, for example Stefik et al. (1982),

Barr and Feigenbaum (1981, 1982), Cohen and Feigenbaum (1982), and Barr et al.

(1989).


2.3 Machine Learning


2.3.1 Introduction


One of the key limitations of computers as envisaged by early researchers is the

fact that they must be told in explicit detail how to solve every problem. In other words,

they lack the capacity to learn from experience and improve their performance with time.

Even in most expert systems today, there is only some weak form of implicit learning,

such as learning by being told, rote memorizing, and checking for logical consistency.

The task of machine learning research is to make up for this inadequacy by incorporating

learning techniques into computers.

The abstract goals of machine learning research are broadly

1. To construct learning algorithms that enable computers to learn.

2. To construct learning algorithms that enable computers to learn in the same way

as humans learn.

In both cases, the functional goals of machine learning research are as follows:

1. To use the learning algorithms in application domains to solve nontrivial

problems.

2. To gain a better understanding of how humans learn, and the details of human

cognitive processes.








11

When the goal is to come up with paradigms that can be used to solve problems,

several subsidiary goals can be proposed:

1. To see if the learning algorithms do indeed perform better than humans do in

similar situations.

2. To see if the learning algorithms come up with solutions that are intuitively

meaningful for humans.

3. To see if the learning algorithms come up with solutions that are in some way

better or less expensive than some alternative methodology.

It is undeniable that humans possess cognitive skills that are superior not only to

other animals but also to most learning algorithms that are in existence today. It is true

that some of these algorithms perform better than humans in some limited and highly

formalized situations involving carefully modeled problems, just as the simplex method

consistently produces solutions superior to those possible by a human being. However,

and this is the crucial issue, humans are quick to adopt different strategies and solve

problems that are ill-structured, ill-defined, and not well understood, for which there

does not exist any extensive domain theory, and that are characterized by uncertainty,

noise, or randomness. Moreover, in many cases, it seems more important to humans to

find solutions to problems that satisfy some constraints rather than to optimize some

"function." At the present state of the art, we do not have a consistent, coherent and

systematic theory of what these constraints are. These constraints are usually understood

to be behavioral or motivational in nature.








12

Recent research has shown that it is also undeniable that humans perform very poorly in

the following respects:

* they do not solve problems in probability theory correctly ;

* while they are good at deciding cogency of information, they are poor at judging

relevance (see Raiffa, accident witnesses, etc.);

* they lack statistical sophistication;

* they find it difficult to detect contradictions in long chains of reasoning;

* they find it difficult to avoid bias in inference and in fact may not be able to

identify it.

(See for example, Einhomrn, 1982; Kahneman and Tversky, 1982a, 1982b, 1982c, 1982d;

Lichtenstein et al., 1982; Nisbett et al., 1982; Tversky and Kahneman, 1982a, 1982b,

1982c, 1982d.)

Tversky and Kahneman (1982a) classify, for example, several misconceptions in

probability theory as follows:

* insensitivity to prior probability of outcomes;

* insensitivity to sample size;

* misconceptions of chance;

* insensitivity to predictability;

* the illusion of validity;

* misconceptions of regression.








13

The above inadequacies on the part of humans pertain to higher cognitive

thinking. It goes without saying that humans are poor at manipulating numbers quickly,

and are subject to physical fatigue and lack of concentration when involved in mental

activity for a long time. Computers are, of course, subject to no such limitations.

It is important to note that these inadequacies usually do not lead to disastrous

consequences in most everyday circumstances. However, the complexity of the modem

world gives rise to intricate and substantial problems, solutions to which forbid

inadequacies of the above type.

Machine learning must be viewed as an integrated research area that seeks to

understand the learning strategies employed by humans, incorporate them into learning

algorithms, remove any cognitive inadequacies faced by humans, investigate the

possibility of better learning strategies, and characterize the solutions yielded by such

research in terms of proof of correctness, convergence to optimality (where meaningful),

robustness, graceful degradation, intelligibility, credibility, and plausibility.

Such an integrated view does not see the different goals of machine learning

research as separate and clashing; insights in one area have implications for another.

For example, insights into how humans learn help spot their strengths and weaknesses,

which motivates research into how to incorporate the strengths into algorithms and how

to cover up the weaknesses; similarly, discovering solutions from machine learning

algorithms that are at first nonintuitive to humans motivates deeper analysis of the

domain theory and of the human cognitive processes in order to come up with at least

plausible explanations.












2.3.2 Definitions and Paradigms


Any activity that improves performance or skills with time may be defined as

learning. This includes motor skills and general problem-solving skills. This is a highly

functional definition of learning and may be objected to on the grounds that humans learn

even in a context that does not demand action or performance. However, the functional

definition may be justified by noting that performance can be understood as improvement

in knowledge and acquisition of new knowledge or cognitive skills that are potentially

usable in some context to improve actions or enable better decisions to be taken.

Learning may be characterized by several criteria. Most paradigms fall under

more than one category. Some of these are

1. Involvement of the learner.

2. Sources of knowledge.

3. Presence and role of a teacher.

4. Access to an oracle (learning from internally generated examples).

5. Learning "richness."

6. Activation of learning:

(a) systematic;

(b) continuous;

(c) periodic or random;

(d) background;

(e) explicit or external (also known as intentional);









(f) implicit (also known as incidental);

(g) call on success; and

(h) call on failure.

When classified by the criterion of the learner's involvement, the standard is the

degree of activity or passivity of the learner. The following paradigms of learning are

classified by this criterion, in increasing order of learner control:

1. Learning by being told (learner only needs to memorize by rote);

2. Learning by instruction (learner needs to abstract, induce, or integrate to some

extent, and then store it);

3. Learning by examples (learner needs to induce to a great extent the correct

concept, examples of which are supplied by the instructor);

4. Learning by analogy (learner needs to abstract and induce to a greater degree in

order to learn or solve a problem by drawing the analogy. This implies that the

learner already has a store of cases against which he can compare the analogy and

that he knows how to abstract and induce knowledge);

5. Learning by observation and discovery (here the role of the learner is greatest;

the learner needs to focus on only the relevant observations, use principles of

logic and evidence, apply some value judgments, and discover new knowledge

either by using induction or deduction).

The above learning paradigms may also be classified on the basis of richness of

knowledge. Under this criterion, the focus is on the richness of the resulting knowledge,

which may be independent of the involvement of the learner. The spectrum of learning








16

is from "raw data" to simple functions, complicated functions, simple rules, complex

knowledge bases, semantic nets, scripts, and so on.

One fundamental distinction can be made from observation of human learning.

The most widespread form of human learning is incidental learning. The learning

process is incidental to some other cognitive process. Perception of the world, for

example, leads to formation of concepts, classification of objects in classes or primitives,

the discovery of the abstract concepts of number, similarity, and so on (see for example,

Rand 1967). These activities are not indulged in deliberately. As opposed to incidental

learning, we have intentional learning, where there is a deliberate and explicit effort to

learn. The study of human learning processes from the standpoint of implicit or explicit

cognition is the main subject of research in psychological learning. (See for example,

Anderson, 1980; Craik and Tulving, 1975; Glass and Holyoak, 1986; Hasher and Zacks,

1979; Hebb, 1961; Mandler, 1967; Reber, 1967; Reber, 1976; Reber and Allen, 1978;

Reber et al., 1980).

A useful paradigm for the area of expert systems might be learning through

failure. The explanation facility ensures that the expert system knows why it is correct

when it is correct, but it needs to know why it is wrong when it is wrong, if it must

improve performance with time. Failure analysis helps in focussing on deficient areas

of knowledge.

Research in machine learning raises several wider epistemological issues such as

hierarchy of knowledge, contextuality, integration, conditionality, abstraction, and

reduction. The issue of hierarchy arises in induction of decision trees (see for example,







17

Quinlan, 1979; Quinlan, 1986; Quinlan, 1990); contextuality arises in learning semantics,

as in conceptual dependency (see for example, Schank, 1972; Schank and Colby, 1973),

learning by analogy (see for example, Buchanan et al., 1977; Dietterich and Michalski,

1979), and case-based reasoning (Riesbeck and Schank, 1989); integration is fundamental

to forming relationships, as in semantic nets (Quillian, 1968; Anderson and Bower, 1973;

Anderson, 1976; Norman, et al., 1975; Schank and Abelson, 1977), and frame-based

learning (see for example, Minsky, 1975); abstraction deals with formation of universals

or classes, as in classification (see for example, Holland, 1975), and induction of

concepts (see for example, Mitchell, 1977; Mitchell, 1979; Valiant, 1984; Haussler,

1988); reduction arises in the context of deductive learning (see for example, Newell

and Simon, 1956; Lenat, 1977), conflict resolution (see for example, McDermott and

Forgy, 1978), and theorem-proving (see for example, Nilsson, 1980). For an excellent

treatment of these issues from a purely epistemological viewpoint, see for example Rand

(1967) and Peikoff (1991).

In discussing real-world examples of learning, it is difficult or meaningless to look

for one single paradigm or knowledge representation scheme as far as learning is

concerned. Similarly, there could be multiple teachers: humans, oracles, and an

accumulated knowledge that acts as an internal generator of examples.

In analyzing learning paradigms, it is useful to look at least three aspects, since

they each have a role in making the others possible:

1. Knowledge representation scheme.

2. Knowledge acquisition scheme.










3. Learning scheme.

At the present time, we do not yet have a comprehensive classification of learning

paradigms and their systematic integration into a theory. One of the first attempts in this

direction was taken by Michalski, Carbonell, and Mitchell (1983).

An extremely interesting area of research in machine learning that will have far-

reaching consequences for such a theory of learning is multistrategy systems, which try

to combine one or more paradigms or types of learning based on domain problem

characteristics or to try a different paradigm when one fails. See for example Kodratoff

and Michalski (1990). One may call this type of research meta-learning research,

because the focus is not simply on rules and heuristics for learning, but on rules and

heuristics for learning paradigms. Here are some simple learning heuristics, for

example:

LH1: Given several "isa" relationships, find out about relations between the properties.

(For example, the observation that "Socrates is a man" motivates us to find out

why Socrates should indeed be classified as a man, i.e., to discover that the

common properties are "rational animal" and several physical properties.)

LH2: When an instance causes an existing heuristic with certainty to be revised

downwards, ask for causes.

LH3: When an instance that was thought to belong to a concept or class but later turns

out not to belong to it, find out what it does belong to.

LH4: If X isa Yl and X isa Y2, then find the relationship between Yl and Y2, and

check for consistency. (This arises in learning by using semantic nets).










LH5: Given an implication, find out if it is also an equivalence.

LH6: Find out if any two or more properties are semantically the same, the opposite,

or unrelated.

LH7: If an object possesses two or more properties simultaneously from the same class

or similar classes, check for contradictions, or rearrange classes hierarchically.

LH8: An isa-tree in a semantic net creates an isa-tree with the object as a parent; find

out in which isa-tree the parent object occurs as a child.

We can contrast these with meta-rules or meta-heuristics. A meta-rule is also a

rule which says something about another rule. It is understood that meta-rules are watch-

dog rules that supervise the firing of other rules. Each learning paradigm has a set of

rules that will lead to learning under that paradigm. We can have a set of meta-rules for

learning if we have a learning system that has access to several paradigms of learning

and if we are concerned with what paradigm to select at any given time. Learning meta-

rules help the learner to pick a particular paradigm because the learner has knowledge

of the applicability of particular paradigms given the nature and state of a domain or

given the underlying knowledge-base representation schema.

The following are examples of meta-rules in learning:

ML1: If several instances of a domain-event occur,

then use generalization techniques.

ML2: If an event or class of events occur a number of times with little or no change on

each occurrence,

then use induction techniques.








20

ML3: If a problem description similar to the problem on hand exists in a different

domain or situation and that problem has a known solution,

then use learning-by-analogy techniques.

ML4: If several facts are known about a domain including axioms and production rules,

then use deductive learning techniques.

ML5: If undefined variables or unknown variables are present and no other learning rule

was successful,

then use the learning-from-instruction paradigm.

In all cases of learning, meta-rules dictate learning strategies, whether explicitly as in a

multi-strategy system, or implicitly as when the researcher or user selects a paradigm.

Just as in expert systems, the learning strategy may be either goal directed or

knowledge directed. Goal-directed learning proceeds as follows:

1. Meta-rules select learning paradigm(s).

2. Learner imposes the learning paradigm on the knowledge base.

3. The structure of the knowledge base and the characteristics of the paradigm

determine the representation scheme.

4. The learning algorithm(s) of the paradigm(s) execute(s).

Knowledge directed learning, on the other hand, proceeds as follows:

1. The learner examines the available knowledge base.

2. The structure of the knowledge base limits the extent and type of learning, which

is determined by the meta-rules.

3. The learner chooses an appropriate representation scheme.









4. The learning algorithm(s) of the chosen learning paradigm(s) execute(s).


2.3.3 Probably Approximately Close Learning


Early research on inductive inference dealt with supervised learning from

examples (see for example, Michalski, 1983; Michalski, Carbonell, and Mitchell, 1983).

The goal was to learn the correct concept by looking at both positive and negative

examples of the concept in question. These examples were provided in one of two ways:

either the learner obtained them by observation, or they were provided to the learner by

some external instructor. In both cases, the class to which each example belonged was

conveyed to the learner by the instructor (supervisor, or oracle). The examples provided

to the learner were drawn from a population of examples or instances. This is the

framework underlying early research in inductive inference (see for example, Quinlan,

1979; Quinlan, 1986: Angluin and Smith 1983).

Probably Approximately Close Identification (or PAC-ID for short) is a powerful

machine-learning methodology that seeks inductive solutions in a supervised

nonincremental learning environment. It may be viewed as a multiple-criteria learning

problem in which there are at least three major objectives:

(1) to derive (or induce) the correct solution, concept or rule, which is as close as we

please to the optimal (which is unknown);

(2) to achieve as high a degree of confidence as we please that the solution so derived

above is in fact as close to the optimal as we intended;

(3) to ensure that the "cost" of achieving the above two objectives is "reasonable."








22

PAC-ID therefore replaces the original research direction in inductive machine

learning (seeking the true solution) by the more practical goal of seeking solutions close

to the true one in polynomial time. The technique has been applied to certain classes of

concepts, such as conjunctive normal forms (CNF). Estimates of necessary distribution

independent sample sizes are derived based on the error and confidence criteria; the

sample sizes are found to be polynomial in some factor such as the number of attributes.

Applications to science and engineering have been demonstrated.

The pioneering work on PAC-ID was by Valiant (1984, 1985) who proposed the

idea of finding approximate solutions in polynomial time. The ideas of characterizing

the notion of approximation by using the concept of functional complexity of the

underlying hypothesis spaces, introducing confidence in the closeness to optimality, and

obtaining results that are independent of the underlying probability distribution with

which the supervisory examples are generated (by nature or by the supervisor), compose

the direction of the latest research. (See for example, Haussler, 1988; Haussler, 1990a;

Haussler, 1990b; Angluin, 1987; Angluin, 1988; Angluin and Laird, 1988; Blumer,

Ehrenfeucht, Haussler, and Warmuth, 1989; Pitt and Valiant, 1988; and Rivest, 1987).

The theoretical foundations for the mathematical ideas of learning convergence

with high confidence are mainly derived from ideas in statistics, probability, statistical

decision theory, and fractal theory. (See for example, Vapnik, 1982; Vapnik and

Chervonenkis, 1971; Dudley, 1978; Dudley, 1984; Dudley, 1987; Kolmogorov and

Tihomirov, 1961; Kullback, 1959; Mandelbrot, 1982; Pollard, 1984; Weiss and

Kulikowski, 1991).













CHAPTER 3
GENETIC ALGORITHMS


3.1 Introduction


Genetic classification algorithms are learning algorithms that are modeled on the

lines of natural genetics (Holland, 1975). Specifically, they use operators such as

reproduction, crossover, mutation, and fitness functions. Genetic algorithms make use

of inherent parallelism of chromosome populations and search for better solutions through

randomized exchange of chromosome material and mutation. The goal is to improve the

gene pool with respect to the fitness criterion from generation to generation.

In order to use the idea of genetic algorithms, problems must be appropriately

modeled. The parameters or attributes that constitute an individual of the population

must be specified. These parameters are then coded. The simulation begins with a

random generation of an initial population of chromosomes, and the fitness of each is

calculated. Depending on the problem and the type of convergence desired, it may be

decided to keep the population size constant or varying across iterations of the

simulation.

Using the population of an iteration, individuals are selected randomly according

to their fitness level to survive intact or to mate with other similarly selected individuals.

For mating members, a crossover point is randomly determined (an individual with n








24

attributes has n-1 crossover points), and the individuals exchange their "strings," thus

forming new individuals. It may so happen that the new individuals are exactly the same

as the parents. In order to introduce a certain amount of richness into the population,

a mutation operator with extremely low probability is applied to the bits in the individual

strings, which randomly changes each bit. After mating, survival, and mutation, the

fitness of each individual in the new population is calculated. Since the probability of

survival and mating is dependent on the fitness level, more fit individuals have a higher

probability of passing on their genetic material.

Another factor plays a role in determining the average fitness of the population.

Portions of the chromosome, called genes or features, act as determinants of qualities of

the individual. Since in mating, the crossover point is chosen randomly, those genes that

are shorter in length are more likely to survive a crossover and thus be carried from

generation to generation. This has important implications for modeling a problem and

will be mentioned in the chapter on research directions.

The power of genetic algorithms (henceforth, GAs) derives from the following

features:

1. It is only necessary to know enough about the problem to identify the

essential attributes of the solution (or "individual"); the researcher can work

in comparative ignorance of the actual combinations of attribute values that

may denote qualities of the individual.

2. Excessive knowledge cannot harm the algorithm; the simulation may be

started with any extra knowledge the researcher may have about the problem,








25

such as his beliefs about which combinations play an important role. In such

cases, the simulation may start with the researcher's population and not a

random population; if it turns out that the whole or some part of this

knowledge is incorrect or irrelevant, then the corresponding individuals get

low fitness values and hence have a high probability of eventually

disappearing from the population.

3. The remarks in point 2 above apply in the case of mutation also. If mutation

gives rise to a useless feature, that individual gets a low fitness value and

hence has a low probability of remaining in the population for a long time.

4. Since GAs use many individuals, the probability of getting stuck at local

optima is minimized.

According to Holland (1975), there are essentially four ways in which genetic

algorithms differ from optimization techniques:

1. GAs manipulate codings of attributes directly.

2. They conduct search from a population and not from a single point.

3. It is not necessary to know or assume extra simplifications in order to

conduct the search; GAs conduct the search "blindly." It must be noted

however, that randomized search does not imply directionless search.

4. The search is conducted using stochastic operators (random selection

according to fitness) and not by using deterministic rules.








26

There are two important models for GAs in learning. One is the Pitt approach,

and the other is the Michigan approach. The approaches differ in the way they define

individuals and the goals of the search process.


3.2 The Michigan Approach


The knowledge base of the researcher or the user constitutes the genetic

population, in which each rule is an individual. The antecedents and consequents of each

rule form the chromosome. Each rule denotes a classifier or detector of a particular

signal from the environment. Upon receipt of a signal, one or more rules fire,

depending on the signal satisfying the antecedent clauses. Depending on the success of

the action taken or the consequent value realized, those rules that contributed to the

success are rewarded, and those rules that supported a different consequent value or

action are punished. This process of assigning reward or punishment is called credit

assignment.

Eventually, rules that are correct classifiers get high reward values, and their

proposed action when fired carries more weight in the overall decision of selecting an

action. The credit assignment problem is the problem of how to allocate credit (reward

or punishment). One approach is the bucket-brigade algorithm (Holland, 1986).

The Michigan approach may be combined with the usual genetic operators to

investigate other rules that may not have been considered by the researcher.









3.3 The Pitt Approach


The Pitt Approach, by De Jong (see for example, De Jong, 1988), considers the

whole knowledge base as one individual. The simulation starts with a collection of

knowledge bases. The operation of crossover works by randomly dichotomizing two

parent knowledge bases (selected at random) and mixing the dichotomized portions across

the parents to obtain two new knowledge bases. The Pitt approach may be used when

the researcher has available to him a panel of experts or professionals, each of whom

provides one knowledge base for some decision problem at hand. The crossover operator

therefore enables one to consider combinations of the knowledge of the individuals, a

process that resembles a brainstorming session. This is similar to a group decision-

making approach. The final knowledge base or bases that perform well empirically

would then constitute a collection of rules obtained from the best rules of the original

expertise, along with some additional rules that the expert panel did not consider before.

The Michigan approach will be used in this research to simulate learning on one

knowledge base.













CHAPTER 4
THE MAXIMUM ENTROPY PRINCIPLE


4.1 Historical Introduction


The principle of maximum entropy was championed by E.T. Jaynes in the 1950s

and has gained many adherents since. There are a number of excellent papers by E.T.

Jaynes explaining the rationale and philosophy of the maximum entropy principle. The

discussion of the principle essentially follows Jaynes (1982, 1983, 1986a, 1986b, and

1991).

The maximum entropy principle may be viewed as "a natural extension and

unification of two separate lines of development . The first line is identified with the

names Bernoulli, Laplace, Jeffreys, Cox; the second with Maxwell, Boltzmann, Gibbs,

Shannon." (Jaynes, 1983).

The question of approaching any decision problem with some form of prior

information is historically known as the Principle of Insufficient Reason (so named by

James Bernoulli in 1713). Jaynes (1983) suggests the name Desideratum of Consistency,

which may be formally stated as follows:

(1) a probability assignment is a way of describing a certain state of knowledge;

i.e., probability is an epistemological concept, not a metaphysical one;








29
(2) when the available evidence does not favor any one alternative among others,

then the state of knowledge is described correctly by assigning equal

probabilities to all the alternatives;

(3) suppose A is an event or occurrence for which some favorable cases out of

some set of possible cases exist. Suppose also that all the cases are equally

likely. Then, the probability that A will occur is the ratio of the number of

cases favorable to A to the total number of equally possible cases. This idea

is formally expressed as


Pr[A] = M Number of cases favorable to A
N Number of equally possible cases"

In cases where Pr[] is difficult to estimate (such as when the number of cases is

infinite or impossible to find out), Bernoulli's weak law of large numbers may be

applied, where


Pr [A] = M = Number of cases favorable to A
N Total number of equally likely cases


Number of times A occurs
Number of trials


m
n

Limit theorems in statistics show that given (M,N) as the true state of nature, the

observed frequency f(m,n) = m/n approaches Pr[A] = P(M,N) = M/N as the number

of trials increase.







30

The reverse problem consists of estimating P(M,N) by f(m,n). For example, the

probability of seeing m successes in n trials when each trial is independent with

probability of success p, is given by the binomial distribution:


P(m I n,-) = P(m I n,p) (= )p(I -p)"- m.


The inverse problem would then consist of finding Pr[M] given (m,N,n). This problem

was given a solution by Bayes in 1763 as follows: Given (m,n), then

Pr[p < M < p + dp] = P(dp rm, n)
N

: (n + 1) M p (I p) n -w dp.
m! (n m)

which is the Beta distribution.

These ideas were generalized and put into the form they are today, known as the

Bayes' theorem, by Laplace as follows: When there is an event E with possible causes

C1, and given prior information I and the observation E, the probability that a particular

cause Ci caused the event E is given by


P(Ci[E,) = 1 ^
EP(El C1) P(CI|J)
S_, p (EI C ) P (Cjl- 1T

which result has been called "learning by experience" (Jaynes, 1978).

The contributions of Laplace were rediscovered by Jeffreys around 1939 and in

1946 by Cox who, for the first time, set out to study the "possibility of constructing a

consistent set of mathematical rules for carrying out plausible, rather than deductive,

reasoning." (Jaynes, 1983).







31

According to Cox, the fundamental result of mathematical inference may be

described as follows: Suppose A, B, and C represent propositions, AB the proposition

"Both A and B are true", and -'A the negation of A. Then, the consistent rules of

combination are:

P(ABIC) = P(A|BC) P(BIC), and

P(AIB) + P(-,AIB) = 1.

Thus, "Cox proved that any method of inference in which we represent degrees of

plausibility by real numbers, is necessarily either equivalent to Laplace's, or

inconsistent." (Jaynes, 1983).

The second line of development starts with James Clerk Maxwell in the 1850s

who, in trying to find the probability distribution for the velocity direction of spherical

molecules after impact, realized that knowledge of the meaning of the physical

parameters of any system constituted extremely relevant prior information. The

development of the concept of entropy maximization started with Boltzmann who

investigated the distribution of molecules in a conservative force field in a closed system.

Given that there are N molecules in the closed system, the total energy E remains

constant irrespective of the distribution of the molecules inside the system. All positions

and velocities are not equally likely. The problem is to find the most probable

distribution of the molecules. Boltzmann partitioned the phase space of position and

momentum into a discrete number of cells Rk, where 1 k < s. These cells were

assumed to be such that the k-th cell is a region which is small enough so that the energy

of a molecule as it moves inside that region does not change significantly, but which is








32

also so large that a large number Nk of molecules can be accommodated in it. The

problem of Boltzmann then reduces to the problem of finding the best prediction of Nk

for any given k in 1,...,s.

The numbers Nk are called the occupation numbers. The number of ways a given

set of occupation numbers will be realized is given by the multinomial coefficient


W(Nk) N= N!. ... N
N1 N2 N,!


The constraints are given by


S
E = E Nk Ek, and
k =1


N = Nk.
k= 1

Since each set {NJ} of occupation numbers represents a possible distribution, the

problem is equivalently expressed as finding the most probable set of occupation numbers

from the many possible sets. Using Stirling's approximation of factorials


n! V- -/nn (n) n
ej

in equation (1) yields
logW = -N^ ) 1og I. (2)
k=1\N \N

The right hand side of (2) is the familiar Shannon entropy formula for the

distribution specified by probabilities which are approximated by the frequencies Nk/N,

k = 1, ..., s. In fact, in the limit as N goes to infinity,











li N log 10 -E N log ( N) = H.
N- 00 N.


Distributions of higher entropy therefore have higher multiplicity. In other words,

Nature is likely to realize them in more ways. If W, and W2 are two distributions, with

corresponding entropies of H, and H2, then the ratio W2/W1 is the relative preference of

W2 over W,. Since W2/W, exp[N(H2 H,)], when N becomes large (such as the

Avogadro number), the relative preference "becomes so overwhelming that exceptions

to it are never seen; and we call it the Second Law of Thermodynamics." (Jaynes, 1982).

The problem may now be expressed in terms of constrained optimization as

follows:

Maximize log W = -N -k 1o04-I
{Nkl ki \N/ N/


subject to

s
E Nk Ek = E, and
k= 1


SNk = N.
k = I
k=1

The solution yields surprisingly rich results which would not be attainable even

if the individual trajectories of all the molecules in the closed spaces were calculated.

The efficiency of the method reveals that in fact, such voluminous calculations would

have canceled each other out, and were actually irrelevant to the problem. A similar

idea is seen in the chapter on genetic algorithms, where ignorance can be seemingly








34

exploited and irrelevant information, even if assumed, would be eliminated from the

solution.

The technique has been used in artificial intelligence (see for example, [Lippman,

1988; Jaynes, 1991; Kane, 1991]), and in solving problems in business and economics

(see for example, [Jaynes, 1991; Grandy, 1991; Zellner, 1991]).


4.2 Examples


We will see how the principle is used in solving problems involving some type

of prior information which is used as a constraint on the problem. For simplicity, we

will deal with problems involving one random variable 0 having n values, and call the

associated probabilities pi. For all the problems, the goal is to choose a probability

distribution from among many possible ones which has the maximum entropy.

No prior information whatsoever. The problem may be formulated using the

Lagrange multiplier X for the single constraint as:


n n
Max g({pi}) = p1 in p + P 1 .
{Pi} i = i i

The solution is obtained as follows:Hence, pi = 1/n, i = l,...,n is the MaxEnt

assignment, which confirms the intuition on the non-informative prior.

Suppose the expected value of 0 is 10. We have two constraints in this problem:

the first is the usual constraint on the probabilities summing to one; the second is the

given information expected value of 0 is 1. We use the Lagrange multipliers X, and

\2 for the two constraints respectively. The problem statement follows:












= 1 lnp, + I = 0


= X -i

= e&-1 V i = 1,...,n,


= 1


n
e- 1
= E eX-i = 1
i=1


= n el-1 = 1

= n p,= 1


Pi = 1 V i = 1,. .,n.
n


- f Piln Pi + x1iE Pi-1 + ;2[L (OiPi2.L ]
j=-1 ,


This can be solved in the usual way by taking partial derivatives of gO w.r.t. p,, X,, and

X2, and equating them to zero. We obtain:
Pi = e21, and

n n
Sie-2 = VI e 2(I.
=-1 1i1


Writing


x = e


ag
api


- in pi


Pi


n
= Pi
i=1


Maxg({pi}) =
(PI}










we get

i Qx8 I.Le
n n
i =i i =i1


(Oi =6) x0 = 0
i =i


which is a polynomial in x, whose roots can be determined numerically.

For example, let n = 3, 0 take values {1,2,3}, lo = 1.25. Solving as above and

taking the appropriate roots, we obtain

X, 2.2752509, X2 -1.5132312, giving

p, 0.7882, p2 = 0.1671, and p3 0.0382.

Partial knowledge of probabilities. Suppose we know p,, i = l,...,k. Since we

have n-1 degrees of freedom in choosing pi, assume k < n-2 to make the example non-

trivial. Then, the problem may be formulated as:
n n
max g(pi}) = E Pi in pi + I pi + q- 1 ,
{Pj} i = k+1 i = kk1

k
where q = Pi.
i =1


Solving, we obtain
S-- V i = k+l,...n.
Pi-n A"'


This is again fairly intuitive: the remaining probability 1-q is distributed non-

informatively over the rest of the probability space. For example, if n = 4, p, = 0.5,

and P2 = 0.3, then k = 2, q = 0.8, and P3 = p4 = (1 0.8)/(4 2) = 0.2/2 = 0.1.

Note that the first case is a special case of the last one, with q = k = 0.







37
The technique can be extended to cover prior knowledge expressed in the form

of probabilistic knowledge bases by using two key MaxEnt solutions: non-informativeness

(as covered in the last example above), and statistical independence of two random

variables given no knowledge to the contrary (in other words, given two probability

distributions f and g over two random variables X and Y respectively, and no further

information, the MaxEnt joint probability distribution h over X*Y is obtained as h =

f*g).













CHAPTER 5
THE PRINCIPAL-AGENT PROBLEM


5.1 Introduction


5.1.1 The Agency Relationship


The principal-agent problem arises in the context of the agency relationship in

social interaction. The agency relationship occurs when one party, the agent, contracts

to act as a representative of another party, the principal, in a particular domain of

decision problems.

The principal-agent problem is a special case of a dynamic two-person game. The

principal has available to her a set of possible compensation schemes, out of which she

must select one that both motivates the agent and maximizes her welfare. The agent also

must choose a compensation scheme which maximizes his welfare, and he does so by

accepting or rejecting the compensation schemes presented to him by the principal. Each

compensation package he considers implicitly influences him to choose a particular

(possibly complex) action or level of effort. Every action has associated with it certain

disutilities to the agent, in that he must expend a certain amount of effort and/or expense.

It is reasonable to assume that the agent will reject outright any compensation package

which yields less than that which can be obtained elsewhere in the market. This

assumption is in turn based on the assumptions that the agent is knowledgeable about his








39
"reservation constraint", and that he is free to act in a rational manner. The assumption

of rationality also applies to the principal. After agreeing to a contract, the agent

proceeds to act on behalf of the principal, which in due course yields a certain outcome.

The outcome is not only dependent on the agent's actions but also on exogenous factors.

Finally the outcome, when expressed in monetary terms, is shared between the principal

and the agent in the manner decided upon by the selected compensation plan.

The specific ways in which the agency relationship differs from the usual

employer-employee relationship are (Simon, 1951):

(1) The agent does not recognize the authority of the principal over specific tasks the

agent must do to realize the output.

(2) The agent does not inform the principal about his "area of acceptance" of

desirable work behavior.

(3) The work behavior of the agent is not directly (or costlessly) observable by the

principal.

Some of the first contributions to the analysis of principal-agent problems can be

found in Simon (1951), Alchian & Demsetz (1972), Ross (1973), Sitglitz (1974), Jensen

& Meckling (1976), Shavell (1979a, 1979b), Holmstrom (1979, 1982), Grossman & Hart

(1983), Rees (1985), Pratt & Zeckhauser (1985), and Arrow (1986).

There are three critical components in the principal-agent model: the technology,

the informational assumptions, and the timing. Each of these three components is

described below.









5.1.2 The Technology Component of Agency


The technology component deals with the type and number of variables involved

(for example, production variables, technology parameters, factor prices, etc.), the type

and the nature of functions defined on these variables (for example, the type of utility

functions, the presence of uncertainty and hence the existence of probability distribution

functions, continuity, differentiability, boundedness, etc.), the objective function and the

type of optimization (maximization or minimization), the decision criteria on which

optimization is carried out (expected utility, weighted welfare measures, etc.), the nature

of the constraints, and so on.


5.1.3 The Information Component of Agency


The information component deals with the private information sources of the

principal and the agent, and information which is public (i.e. known to both the parties

and costlessly verifiable by a third party, such as a court). This component of the model

addresses the question, "who knows what?". The role of the informational assumption

in agency is as follows:

(a) it determines how the parties act and make decisions (such as offer payment

schemes or choose effort levels),

(b) it makes it possible to identify or design communication structures,

(c) it determines what additional information is necessary or desirable for

improved decision making, and








41

(d) it enables the computation of the cost of maintaining or establishing

communication structures, or the cost of obtaining additional information.

For example, one usual assumption in the principal-agent literature is that the

agent's reservation level is known to both parties. As another example of the way in

which additional information affects the decisions of the principal, note that the principal,

in choosing a set of compensation schemes for presenting to the agent, wishes to

maximize her welfare. It is in her interest, therefore, to make the agent accept a payment

scheme which induces him to choose an effort level that will yield a desired level of

output (taking into consideration exogenous risk). The principal would be greatly

assisted in her decision making if she had knowledge of the "function" which induces the

agent to choose an effort level based on the compensation scheme, and also knowledge

of the hidden characteristics of the agent such as his utility of income, disutility of effort,

risk attitude, reservation constraint, etc. Similarly, the agent would be able to take better

decisions if he were more aware of his risk attitude, disutility of effort and exogenous

factors. Any information, even if imperfect, would reduce either the magnitude or the

variance of risk or both. However, better information for the agent does not always

imply that the agent will choose an act or effort level that is also optimal for the

principal. In some cases, the total welfare of the agency may be reduced as a result

(Christensen, 1981).

The gap in information may be reduced by employing a system of messages from

the agent to the principal. This system of messages may be termed a "communication

structure" (Christensen, 1981). The agent chooses his action by observing a signal from








42
his private information system after he accepts a particular compensation scheme from

the principal subject to its satisfying the reservation constraint. This signal is caused by

the combination of the compensation scheme, an estimate of exogenous risk by the agent

based on his prior information or experience, and the agent's knowledge of his risk

attitude and disutility of action. The communication structure agreed upon by both the

principal and the agent allows the agent to send a message to the principal. It is to be

noted that the agency contract can be made contingent on the message, which is jointly

observable by both the parties. The compensation scheme considers the messages) as

one (some) of the factors in the computation of the payment to the agent, the other of

course being the output caused by the agent's action. Usually, formal communication

is not essential, as the principal can just offer the agent a menu of compensation

schemes, and allow the agent to choose one element of the menu.


5.1.4 The Timing Component of Agency


Timing deals with the sequence of actions taken by the principal and the agent,

and the time when they commit themselves to specific decisions (for example, the agent

may choose an effort level before or after observing some signal about exogenous risk).

Below is one example of timing (T denotes time):

T1. The principal selects a particular compensation scheme from a set of possible

compensation schemes.

T2. The agent accepts or rejects the suggested compensation scheme depending on

whether it satisfies his reservation constraint or not.








43
T3. The agent chooses an action or effort level from a set of possible actions or effort

levels.

T4. The outcome occurs as a function of the agent's actions and exogenous factors

which are unknown or known only with uncertainty.

Another example of timing is when a communication structure with signals and

messages is involved (Christensen, 1981):

Tl. The principal designs a compensation scheme.

T2. Formation of the agency contract.

T3. The agent observes a signal.

T4. The agent chooses an act and sends a message to the principal.

T5. The output occurs from the agent's act and exogenous factors.

Variations in the principal-agent problems are caused by changes in one or more

of these components. For example, some principal-agent problems are characterized by

the fact that the agent may not be able to enforce the payment commitments of the

principal. This situation occurs in some of the relationships in the context of regulation.

Another is the possibility of renegotiation or review of the contract at some future date.

Agency theory, dealing with the above market structure, gives rise to a variety

of problems caused by the presence of factors such as the influence of externalities,

limited observability, asymmetric information, and uncertainty (Gjesdal, 1982).









5.1.5 Limited Observability. Moral Hazard, and Monitoring


An important characteristic of principal-agent problems limited observability of

the agent's actions gives rise to moral hazard. Moral hazard is a situation in which one

party (say, the agent) may take actions detrimental to the principal and which cannot be

perfectly and/or costlessly observed by the principal (see for example, [Holmstrom,

1979]). Formally, perfect observation might very well impose "infinite" costs on the

principal. The problem of unobservability is usually addressed by designing monitoring

systems or signals which act as estimators of the agent's effort. The selection of

monitoring signals and their value is discussed for the case of costless signals in Harris

and Raviv (1979), Holmstrom (1979), Shavell (1979), Gjesdal (1982), Singh (1985), and

Blickle (1987). Costly signals are discussed for three cases in Blickle (1987).

On determining the appropriate monitoring signals, the principal invites the agent

to select a compensation scheme from a class of compensation schemes which she, the

principal, compiles. Suppose the principal determines monitoring signals s,, ..., s,,, and

has a compensation scheme c(q, s,, ..., sj, where q is the output, which the agent

accepts. There is no agreement between the principal and the agent as to the level of the

effort e. Since the signals si, i = 1, ..., n determine the payoff and the effort level e of

the agent (assuming the signals have been chosen carefully), the agent is thereby induced

to an effort level which maximizes the expected utility of his payoff (or some other

decision criterion). The only decision still in the agent's control is the choice of how

much payoff he wants; the assumption is that the agent is rational in an economic sense.

The principal's residuum is the output q less the compensation c(-). The principal








45

structures the compensation scheme c(.) in such a way as to maximize the expected

utility of her residuum (or some other decision criterion). In this manner, the principal

induces desirable work behavior in the agent.

It has been observed that "the source of moral hazard is not unobservability but

the fact that the contract cannot be conditioned on effort. Effort is noncontractible."

(Rasmusen, 1989). This is true when the principal observes shirking on the part of the

agent but is unable to prove it in a court of law. However, this only implies that a

contract on effort is imperfectly enforceable. Moral hazard may be alleviated in cases

where effort is contracted, and where both limited observability and a positive probability

of proving non-compliance exist.


5.1.6 Informational Asymmetry. Adverse Selection, and Screening


Adverse selection arises in the presence of informational asymmetry which causes

the two parties to act on different sets of information. When perfect sharing of

information is present and certain other conditions are satisfied, first-best solutions are

feasible (Sappington and Stiglitz, 1987). Typically however, adverse-selection exists.

While the effect of moral hazard makes itself felt when the agent is taking actions

(say, production or sales), adverse selection affects the formation of the relationship, and

may give rise to inefficient (in the second-best sense) contracts. In the information-

theoretic approach, we can think of both being caused by lack of information. This is

variously referred to as the dissimilarity between private information systems of the agent








46
and the firm, or the unobservability or ignorance of "hidden characteristics" (in the latter

sense, moral hazard is caused by "hidden effort or actions").

In the theory of agency, the hidden characteristic problem is addressed by

designing various sorting and screening mechanisms, or communication systems that pass

signals or messages about the hidden characteristics (of course, the latter can also be used

to solve the moral hazard problem).

On the one hand, the screening mechanisms can be so arranged as to induce the

target party to select by itself one of the several alternative contracts (or "packages").

The selection would then reveal some particular hidden characteristic of the party. In

such cases, these mechanisms are called "self-selection" devices. See, for example,

Spremann (1987) for a discussion of self-selection contracts designed to reveal the agent's

risk attitude. On the other hand, the screening mechanisms may be used as indirect

estimators of the hidden characteristics, as when aptitude tests and interviews are used

to select agents.

The significance of the problem caused by the asymmetry of information is related

to the degree of lack of trust between the parties to the agency contract which, however,

may be compensated for by observation of effort. However, most real life situations

involving an agency relationship of any complexity are characterized not only by a lack

of trust but also by a lack of observability of the agent's effort. The full context to the

concept of information asymmetry is the fact that each party in the agency relationship

is either unaware or has only imperfect knowledge of certain factors which are better

known to the other party.









5.1.7 Efficiency of Cooperation and Incentive Compatibility


In the absence of asymmetry of information, both principal and agent would

cooperatively determine both the payoff and the effort or work behavior of the agent.

Subsequently, the "game" would be played cooperatively between the principal and the

agent. This would lead to an efficient agreement termed the first-best design of

cooperation. First-best solutions are often absent not merely because of the presence of

externalities but mainly because of adverse selection and moral hazard (Spremann, 1987).

Let F = { (c,e) }, where compensation c and effort e satisfy the principal's and

the agent's decision criteria respectively. In other words, F is the set of first-best

designs of cooperation, also called efficient designs with respect to the principal-agent

decision criteria. Now, suppose that the agent's action e is induced as above by a

function I: I(c) = e. Let S = { (c,I(c)) } -- i.e. S denotes the set of designs feasible

under information asymmetry. If it were not the case that F n S = 0, then efficient

designs of cooperation would be easily induced by the principal. Situations where this

occurs are said to be incentive compatible. In all other cases, the principal has available

to her only second-best designs of cooperation, which are defined as those schemes that

arise in the presence of information asymmetry.


5.1.8 Agency Costs


There are three types of agency costs (Schneider, 1987):

(1) the cost of monitoring the hidden effort of the agent,

(2) the bonding costs of the agent, and








48
(3) the residual loss, defined as the monetary equivalent of the loss in welfare of the

principal caused by the actions taken by the agent which are non-optimal with

respect to the principal.

Agency costs may be interpreted in the following two ways:

(1) they may be used to measure the "distance" between the first-best and the second-

best designs;

(2) they may be looked upon as the value of information necessary to achieve second-

best designs which are arbitrarily close to the first-best designs.

Obviously, the value of perfect information should be considered as an upper

bound on the agency costs (see for example, [Jensen and Meckling, 1976]).


5.2 Formulation of the Principal-Agent Problem


The following notation and definitions will be used throughout:

D: the set of decision criteria, such as {maximin, minimax, maximax, minimin,

minimax regret, expected value, expected loss,...}. We use A E D.

Ap: the decision criterion of the principal.

AA: the decision criterion of the agent.

Up: the principal's utility function.

UA: the agent's utility function.

C: the set of all compensation schemes. We use c E C.

E: the set of actions or effort levels of the agent. We use e E E.

0: a random variable denoting the true state of nature.








49
Op: a random variable denoting the principal's estimate of the state of nature.

O^: a random variable denoting the agent's estimate of the state of nature.

q: output realized from the agent's actions (and possibly the state of nature).

qp: monetary equivalent of the principal's residuum. Note that qp = q c(.),

where c may depend on the output and possibly other variables.

Output/outcome. The goal or purpose of the agency relationship, such as sales,

services or production, is called the output or the outcome.

Public knowledge/information. Knowledge or information known to both the

principal and the agent, and also a third enforcement party, is termed public knowledge

or information. A contract in agency can be based only on public knowledge (i.e.

observable output or signals).

Private knowledge/information. Knowledge or information known to either the

principal or the agent but not both is termed private knowledge or information.

State of nature. Any events, happenings, occurrences or information which are

not in the control of the principal or the agent and which affect the output of the agency

directly through the technology constitute the state of nature.

Compensation. The economic incentive to the agent to induce him to participate

in the agency is called the compensation. This is also called wage, payment or reward.

Compensation scheme. The package of benefits and output sharing rules or

functions that provide compensation to the agent is called the compensation scheme.

Also called contract, payment function or compensation function.







50

The word "scheme" is used here instead of "function" since complicated

compensation packages will be considered as an extension later on. In the literature, the

word "scheme" may be seen, but it is used in the sense of "function", and several nice

properties are assumed for the function (such as continuity, differentiability, and so on).

Depending on the contract, the compensation may be negative a penalty for the agent.

Typical components of the compensation functions considered in the literature are rent

(fixed and possibly negative), and share of the output.

The principal's residuum. The economic incentive to the principal to engage in

the agency is the principal's residuum. The residuum is the output (expressed in

monetary terms) less the compensation to the agent. Hence, the principal is sometimes

called the residual claimant.

Payoff. Both the agent's compensation and the principal's residuum are called

the payoffs.

Reservation welfare (of the agent). The monetary equivalent of the best of the

alternative opportunities (with other competing principals, if any) available to the agent

is known as the reservation welfare of the agent. Accordingly, it is the minimum

compensation that induces an agent to accept the contract, but not necessarily induce him

to his best effort level. Also known as reservation utility or individual utility, it is

variously denoted in the literature as m or U.

Disutility of effort. The cost of inputs which the agent must supply himself when

he expends effort contributes to disutility, and hence is called the disutility of effort.








51

Individual rationality constraint (IRC). The agent's (expected) utility of net

compensation (compensation from the principal less his disutility of effort) must be at

least as high as his reservation welfare. This constraint is also called the participation

constraint.

When a contract violates the individual rationality constraint, the agent rejects it

and prefers unemployment instead. Such a contract is not necessarily "bad", since

different individuals have different levels of reservation welfare. For example,

financially independent individuals may have higher than usual reservation welfare levels,

and might very well prefer leisure to work even when contracts are attractive to most

other people.

Incentive compatibility constraint (ICC). A contract will be acceptable to the

agent if it satisfies his decision criterion on compensation, such as maximization of

expected utility of net compensation. This constraint is called the incentive compatibility

constraint.



Development of the problem: Model 1. We develop the problem from simple

cases involving the least possible assumptions on the technology and informational

constraints, to those having sophisticated assumptions. Corresponding models from the

literature are reviewed briefly in section 1.3.



A. Technology:

(a) fixed compensation, C set of fixed compensations, U E C;










output q q(e); assume q(0) = 0;

existence of nonseparable utility functions;

decision criterion: maximization of utility;

no uncertainty in the state of nature.


B. Public information:

(a) compensation scheme, c;

(b) range of possible outputs, Q;

(c) U.


Information


private to the principal: Up


Information private to the agent:

(a) U^;

(b) disutility of effort, d;

(c) range of effort levels, e.



C. Timing:

(1) the principal makes an offer of fixed wage c;

(2) the agent either rejects or accepts the offer;

(3) if he accepts it, exerts effort level e;

(4) output q(e) results;










(5) sharing of output according to contract.


D. Payoffs:

Case 1:

7p

7A

Case 2:


rp
1rA


Agent rejects contract, i.e. e = 0;

= Up[q(e)] = Up[q(0)] = Up[0].

= UA[U].

Agent accepts contract;

= Up[q(e) c].

= UA[c d(e)].


E. The principal's problem:

(MI.P1) Max, c c maxq E Q Up[q c]

such that

c > U. (IRC)

Suppose C* c C is the solution set of Ml.P1. The principal picks c* E C* and offers

it to the agent.



The agent's problem:

(M1.A1) For a given c*,

Max, E E U^[c d(e)].

Suppose E* c E is the solution set of M1.A1. The agent selects e* E E*.









F. The solution:

(a) the principal offers c* E C* to the agent;

(b) the agent accepts the contract;

(c) the agent exerts effort e'(c') E E';

(d) output q(e*(c)) occurs;

(e) payoffs:

rp = Up[q(e'(c4)) c'];

7A = UA[c" d(e'(c'))].

Notes:

1. The agent accepts the contract in F.b since IRC is present in Ml.PI, and C*

is nonempty since U E C.

2. Effort of the agent is a function of the offered compensation.

3. Since one of the informational assumptions was that the principal does not

know the agent's utility function, U is a compensation rather than the agent's

utility of compensation, so UA(U) is meaningful.



G. Variations:

1. The principal offers C to the agent instead of a c* E C*. The agent's problem

then becomes:

(M1.A2) Maxc. E c. max, E E UA[c d(e)].

The first three steps in the solution then become:

(a) the principal offers C* to the agent;









(b) the agent accepts the contract;

(c) the agent picks an effort level e* which is a solution to M1.A2 and reports

the corresponding c" (or its index if appropriate) to the principal.



2. The agent may decide to solve an additional problem: from among two or more

competing optimal effort levels, he may wish to select a minimum effort level.

Then, his problem would be:

(M1.A3) Min e- d(e)

such that

e* E argmax, E E UA[c* d(e)].

Example:

Let E = {e,, e2, e3},

C* = {c,,c2,c3}.

Suppose,

c1(q(e,)) = 5, d(e,) = 2;

c2(q(e2)) = 6, d(e2) = 3;

c3(q(e3)) = 6, d(e,) = 4;

The net compensation to the agent in choosing the three effort levels is 3, 3, and

2 respectively. Assuming d(e) is monotone increasing in e, the agent chooses e,

to e2, and so prefers compensation c, to C2.








56
3. We assumed U is public knowledge. If this were not so, then the agent has to

test all offers to see it they are at least as high as the utility of his reservation

welfare. The two problems then become:

(M1.P2) Maxc C maxq E Q Up[q c]

and

(M1.A4) Max, E UA[c" d(e)]

such that

c* > UA[U], (IRC)

c* E argmax M1.P2.

In this case, there is a distinct possibility of the agent rejecting an offer of the

principal.



4. Note that in most realistic situations, a distinction must be made between the

reservation welfare and the agent's utility of the reservation welfare. Otherwise,

merely using IRC with the reservation welfare in Ml.P1 may not satisfy the

agent's constraint. On the other hand, U = UA(U) implies knowledge of UA by

the principal, a complication which yields a completely different model.

When U UA(U), the following two problems occur:

(M 1.P3) Max c C maXq E Q Up(q c)

such that

c > U.

(M1.A5) Max, E E UA(C d(e))









such that

c. > UA(U), (IRC)

c* E argmax M1.P3.

In other words, the principal solves her problem the best way she can, and hopes

the solution is acceptable to the agent.



5. Negotiation. Negotiation of a contract can occur in two contexts:

(a) when there is no solution to the initial problem, the agent may communicate

to the principal his reservation welfare, and the principal may design new

compensation schemes or revise her old schemes so that a solution may be

found. This type of negotiation also occurs in the case of problems M1.P3

and M1.A5.

(b) The principal may offer c* E argmax, c c Ml .P1. The agent either accepts

it or does not; if he does not, then the principal may offer another optimal

contract, if any. This interaction may continue until either the agent accepts

some compensation scheme or the principal runs out of optimal

compensations.



Development of the problem: Model 2. This model differs from the first by

incorporating uncertainty in the state of nature, and conditioning the compensation

functions on the output.









A. Technology:

(a) presence of uncertainty in the state of nature;

(b) compensation scheme c = c(q);

(c) output q = q(e,O);

(d) existence of known utility functions for the agent and the principal;

(e) disutility of effort for the agent is monotone increasing in effort e;



B. Public information:

(a) presence of uncertainty, and range of 0;

(b) output function q;

(c) payment functions c;

(d) range of effort levels of the agent.



Information private to the principal:

(a) the principal's utility function;

(b) the principal's estimate of the state of nature.



Information private to the agent:

(a) the agent's utility function;

(b) the agent's estimate of the state of nature;

(c) disutility of effort;

(d) reservation welfare;










C. Timing:

(a) the principal determines the set of all compensation schemes that maximize

her expected utility;

(b) the principal presents this set to the agent as the set of offered contracts;

(c) the agent picks from this set of compensation schemes a compensation

scheme that maximizes his net compensation, and a corresponding effort

level;

(d) a state of nature occurs;

(e) an output results;

(f) sharing of the output takes place as contracted.



D. Payoffs:

Case 1: Agent rejects contract, i.e. e = 0;

rp = Up[q(e,0)] = Up[q(0,0)].

7KA = UA[U].


Case 2:

Ir.

7rA


Agent accepts contract;

= Up[q(e,0) c(q)].

= UA[c(q) d(e)].









E. The principal's problem:
(M2.P) MaxCEC MaxoE EP Up [q(e, 0) c(q(e,Q))]

where the expectation E(.) is given by (assuming the usual regularity conditions)

0
f Up[q(e,0) c(q(e,0))] f- (0) dO
fo ep

where


0 E [0, U], and

f(O) is the distribution assigned by the principal.



The agent's problem:
(M2.A) Maxcec MaxeE E@A UA[c(q(e,O) ) d(e)]


subject to

EeA[c(q(e,O)) d(e)] >U, (IRC)

c e argmax(M2.P).
where the expectation E(.) is given as usual by

U
f UA[q(e,0) c(q(e,O))] f- (0) dO.
0 0,









F. The solution:

(a) The agent selects c* E C, and a corresponding effort e* which is a solution

to M2.A;

(b) a state of nature 0 occurs;

(c) output q(e*,0) is generated;

(d) payoffs:

,rp = Up[q(e',0) c'(q(e*,0))];

7rA = UA[c'(q(e',0)) d(e*)].



Development of the problem: Model 3. In this model, the strongest possible

assumption is made about information available to the principal: the principal has

complete knowledge of the utility function of the agent, his disutility of effort, and his

reservation welfare. Accordingly, the principal is able to make an offer of compensation

which satisfies the decision criterion of the agent and his constraints. In other words,

the two problems are treated as one. The assumptions are as in model 2, so only the

statement of the problem will be given below.



The problem:
MaxEc, e-e E Up[q(e*',Q) c(q(e*,O))]


subject to

E UA[c(q(e*,O)) d(e*)] > U, (IRC)

e* E argmax {MaxEE, cEc E U[c(q(e,O) ) d(e)] } (ICC)











5.3 Main Results in the Literature


Several results from basic agency models will be presented using the framework

established in the development of the problem. The following will be presented for each

model:

Technology,

Information,

Timing,

Payoffs, and

Results.

It must be noted that the literature rarely presents such an explicit format; rather,

several assumptions are often buried within the results, or implied or just not stated.

Only by trying an algorithmic formulation is it possible to unearth unspecified

assumptions. In many cases, some of the factors are assumed for the sake of formal

completeness, even though the original paper neither mentions nor uses those factors in

its results. This type of modeling is essential when the algorithms are implemented

subsequently using a knowledge-intensive methodology.

One recurrent example of incomplete specification is the treatment of the agent's

individual rationality constraint (IRC). The principal has to pick a compensation which

satisfies IRC. However, some consistency in using IRC is necessary. The agent's

reservation welfare U is also a compensation (albeit a default one). The agent must








63
check one of two constraints to verify that the offered compensation indeed meets his

reservation welfare:

c > U or UA(c) -- UA(U).

If the principal picks a compensation which satisfies c > U, it is not necessary that

UA(C) -> UA(U) be also satisfied. However, using UA(C) > U for the IRC, where

U is treated "as if" it were UA(U), implies knowledge of the agent's utility on the part

of the principal.

The difference between the two situations is of enormous significance if the

purpose of analysis is to devise solutions to real-world problems. In the literature, this

distinction is conveniently overlooked. If all such vagueness in the technological,

informational and temporal assumptions was to be systematically eliminated, the analysis

might change in a way not intended in the original literature. Hence, the main results

in the literature will be presented as they are.


5.3.1 Model 1: The Linear-Exponential-Normal Model


This name of the model (Spremann, 1987) derives from the nature of three crucial

parameters: the payoff functions are linear, the utility functions are exponential, and the

exogenous risk has a normal distribution. Below is a full description.



Technology:

(a) compensation is the sum of a fixed rent r and a share s of the output q: c(q)

= r + sq;








64
(b) presence of uncertainty in the state of nature, denoted by 9, where 0 -

N(O,o2);

(c) the set of effort levels of the agent, E = [O,1]; effort is induced by

compensation;

(d) output q =- q(e,O) =- e + 0;

(e) the agent's disutility of effort is d d(e) e2;

(f) the principal's utility Up is linear (the principal is risk neutral);

(g) the agent has constant risk aversion ca > 0, and his utility is

UA(W) = -exp(-uw), where w is his net compensation (also called the

wealth);

(h) the certainty equivalent of wealth, denoted V, is defined as:

V(w) = U-[E(U(w))], where U denotes the utility function, E0 is the

expectation with respect to 0; as usual, subscripts P or A on V denote the

principal or the agent respectively;

(i) the decision criterion is maximization of expected utility.



Public information:

(a) compensation scheme c(q; r,s);

(b) output q;

(c) distribution of 0;

(d) agent's reservation welfare U;

(e) agent's risk aversion a.









Information private to the principal:

Utility of residuum, Up.

Information private to the agent:

(a) selection of effort given the compensation;

(b) utility of welfare;

(c) disutility of effort.



Timing:

(a) the principal offers a contract (r,s) to the agent;

(b) the agent's effort e is induced by the compensation scheme;

(c) a state of nature occurs;

(d) the agent's effort and the state of nature give rise to output;

(e) sharing of the output takes place.



Payoffs:

-p = Up[q (r + sq)]

= Up[e(r,s) + 0 (r + s(e(r,s) + 0o))]

7rA = UA[r + sq d(e(r,s))]

= U^[r + s(e(r,s) + 0) d(e(r,s))],

where e(r,s) is the function which induces effort based on compensation, and 0o

is the realized state of nature.








66

Results:

Result 1.1: The optimal effort level of the agent given a compensation scheme

(r,s) is denoted e*, and is obtained by straightforward maximization to yield:

e* = e*(r,s) = s/2.

This shows that the rent r and the reservation welfare U have no impact on the selection

of the agent's effort.

Result 1.2: A necessary and sufficient condition for IRC to be satisfied for a

given compensation scheme (r,s) is:


j S2 (1 2a(12)
r U S( 00
4




Result 1.3: The optimal compensation scheme for the principal is c* = (r*,s*),

where


s* = 1and
1 + 2ao*


= 1 2go2
4s *2




Corollary 1.3: The agent's optimal effort given a compensation scheme (r*,s")

is (using result 1.1):
e 1
2 (1 + 2ao2)








67

Result 1.4: Suppose 2ao? > 1. Then, an increase in share s requires an increase

in rent r (in order to satisfy IRC).

To see this, suppose we increase the share s by 5,

o= s + 5, 0 < 6 < 1-s. From Result 1.2, for IRC to hold we need,


so2(1 2xo2)
4



= (s + 8)2(1 2a02)
4


(1 2go02)[S2 + 2s8 + 82]
4


S (1 2 ~ 2) 2 (2S6 + 82)(1 2aO2)
4 4



= (2S8 + 82)(1 2a02)
4


r ( 1 < 2ao 2).





Result 1.5: The welfare attained by the agent is U, while the principal's welfare

is given by:
1
S -U.
45s*








68
Result 1.6: The principal prefers agents with lower risk aversion. This is

immediate from the fact that the principal's welfare is decreasing in the agent's risk

aversion for a given o2 and U.

Result 1.7: Fixed fee arrangements are non-optimal, no matter how large the

agent's risk aversion. This is immediate from the fact that


s* =- 1 > 0 Va > 0.
1 + 2aco2



Result 1.8: It is the connection between unobservability of the agent's effort and

his risk aversion that excludes first-best solutions.


5.3.2 Model 2


This model (Gjesdal, 1982) deals with two problems:

(a) choosing an information system, and

(b) designing a sharing rule based on the information system.



Technology:

(a) presence of uncertainty, 0;

(b) finite effort set of the agent; effort has several components, and is hence

treated as a vector;

(c) output q is a function of the agent's effort and the state of nature 0; the

range of output levels is finite;









(d) presence of a finite number of public signals;

(e) presence of a set of public information systems (i.e. signals), including non-

informative and randomized systems, the output being treated as one of the

informative information systems;

(f) costlessness of public information systems;

(g) compensation schemes are based on signals about effort or output or both.



Public information:

(a) distribution of the state of nature, 0;

(b) output levels;

(c) common information systems which are non-informative and randomizing;

(d) UA.

Information private to the principal: utility function, Up.

Information private to the agent: disutility of effort.



Timing:

(a) principal offers contract based on observable public information systems,

including the output;

(b) agent chooses action;

(c) signals from the specified public information systems are observed;

(d) agent gets paid on the basis of the signal;

(e) a state of nature occurs;










(f) output is observed;

(g) principal keeps the residuum.



Special technological assumptions: Some of these assumptions are used in only some of

the results; other results are obtained by relaxing them.

(a) The joint probability distribution function on output, signals, and actions is

twice-differentiable in effort, and the marginal effects on this distribution of

the different components of effort are independent.

(b) The principal's utility function Up is trice differentiable, increasing, and

concave.

(c) The agent's utility function UA is separable, with the function on the

compensation scheme (or sharing rule as it is known) being increasing and

concave, and the function on the effort being concave.



Results:

Result 2.1: There exists a marginal incentive informativeness condition which is

essentially sufficient for marginal value given a signal information system Y. When

information about the output is replaced by signals about the output and/or the agent's

effort, marginal incentive informativeness is no longer a necessary condition for marginal

value since an additional information system Z may be valuable as information about

both the output and the effort.








71

Result 2.2: Information systems having no marginal insurance value but having

marginal incentive informativeness may be used to improve risk sharing, as for example,

when the signals which are perfectly correlated with output on the agent's effort are

completely observable.

Result 2.3: Under the assumptions of result 2.2, when the output alone is

observed, it must be used for both incentives and insurance. If the effort is observed as

well, then a contract may consist of two parts: one part is based on the effort, and takes

care of incentives; the other part is based on output, and so takes care of risk-sharing.

For example, consider auto insurance. The principal (the insurer) cannot observe

the actions taken by the driver (such as care, caution and good driving habits) to avoid

collisions. However, any positive signals of effort can be the basis of discounts on

insurance premiums, as for example when the driver has proof of regular maintenance

and safety check up for the vehicle or undergoes safe driving courses. Also factors such

as age, marital status and expected usage are taken into account. The "output" in this

case is the driving history, which can be used for risk- sharing; another indicator of risk

which may be used is the locale of usage (country lanes or heavy city traffic). This

example motivates result 2.4, a corollary to results 2.2 and 2.3.

Result 2.4: Information systems having no marginal incentive informativeness

but having marginal insurance value may be used to offer improved incentives.

Result 2.5: If the uncertainty in the informative signal system is influenced by

the choices of the principal and the agent, then such information systems may be used

for control in decentralized decision-making.









5.3.3 Model 3


Holmstrom's model (Holmstrom, 1979) examines the role of imperfect

information under two conditions: (i) when the compensation scheme is based on output

alone, and (ii) when additional information is used. The assumptions about technology,

information and timing are more or less standard, as in the earlier models. The model

specifically uses the following:

(a) In the first part of the model, almost all information is public; in the second

part, asymmetry is brought in by assuming extra knowledge on the part of

the agent.

(b) output is a function of the agent's effort and state of nature: q q(e,0), and

aq/ae > 0.

(c) The agent's utility function is separable in compensation and effort, where

UA(c) is defined on compensation, and d(e) is the disutility defined on effort.

(d) Disutility of effort d(e) is increasing in effort.

(e) The agent is risk averse, so that UA" < 0.

(f) The principal is weakly risk neutral, so that Up" < 0.

(g) Compensation is based on output alone.

(h) Knowledge of the probability distribution on the state of nature 0 is public.

(i) Timing: The agent chooses effort before the state of nature is observed.



The problem:

(P) MaxEC c EE E[Up(q c(q))]









such that

E[UA(c(q),e)] > U, (IRC)

e E argmax,.EE E[UA(C(q), e')]. (ICC)

To obtain a workable formulation, two further assumptions are made:

(a) There exists a distribution induced on output and effort by the state of

nature, denoted F(q,e), where q q(e,0). Since aq/ae > 0 by assumption,

it implies aF(q,e)/ae < 0. For a given e, assume aF(q,e)/ae < 0 for some

range of values q.

(b) F has density function f(q,e), where (denoting fe = af/ae) f, and fe are well

defined for all (q,e).

The ICC constraint in (P) is replaced by its first order condition using f, and the

following formulation is obtained:

(P') MaxEC ,cEE I Up(q c(q)) f(q,e) dq

such that

I [UA(c(q)) d(e)] f(q,e) dq U, (IRC')

SUA(c(q)) fQ(q,e) dq = d'(e). (ICC')



Results:

Result 3.1: Let X and /A be the Lagrange multipliers for IRC' and ICC' in (P')

respectively. Then, the optimal compensation schemes are characterized as follows:










U(q c(q)) f.(qe)
-- ; ----__ = X + IL. -^ ]
Uc(q)) fq,e)



where c is the agent's wealth, and c is the principal's wealth plus the output (these form

the lower and upper bounds). If the equality in the above characterization does not hold,

then c(q) = c or c depending on the direction of inequality.

Result 3.2: Under the given assumptions and the characterization in result 3.1,

1A > 0; this is equivalent to saying that the principal prefers the agent increase his effort

given a second-best compensation scheme as in the above result 3.1. The second-best

solution is strictly inferior to a first-best solution.

Result 3.3: f I /f is interpreted as a benefit-cost ratio for deviation from optimal

risk sharing. Result 3.1 states that such deviation must be proportional to this ratio

taking individual risk aversion into account. From Result 3.2, incentives for increased

effort are preferable to the principal. The following compensation scheme accomplishes

this (where cF(q) denotes the first-best solution for a given X):

c(q) > cF(q), if the marginal return on effort is positive to the agent;

c(q) < cF(q), otherwise.

Result 3.4: Intuitively, the agent carries excess responsibility for the output. This

is implied by result 3.3 and the assumptions on the induced distribution f.

A previous assumption is now modified as follows: Compensation c is a function

of output and some other signal y which is public knowledge. Associated with this is a

joint distribution F(q,y,e) (as above), with f(q,y,e) the corresponding density function.








75

Result 3.5: An extension of result 3.1 on the characterization of optimal

compensation schemes is as follows:


U(q c(q,y)) f(q,y,e)
U(c(q,y)) W

where X and /x are as in result 3.1.

Result 3.6: Any informative signal, no matter how noisy it is, has a positive value

if costlessly obtained and administered into the contract.

Note: This result is based on rigorous definitions of value and informativeness of signals

(Holmstrom, 1979).

In the second part of this model, an assumption is made about additional

knowledge of the state of nature revealed to the agent alone, denoted z. This introduces

asymmetry into the model. The timing is as follows:

(a) the principal offers a contract c based on the output and an observed signal

y;

(b) the agent accepts the contract;

(c) the agent observes a signal z about 0;

(d) the agent chooses an effort level;

(e) a state of nature occurs;

(f) agent's effort and state of nature yield an output;

(g) sharing of output takes place.







76
We can think of the signal y as information about the state of nature which both

parties share and agree upon, and the signal z as special post-contract information about

the state of nature received by the agent alone.

For example, a salesman's compensation may be some combination of percentage

of orders and a fixed fee. If both the salesman and his manager agree that the economy

is in a recession, the manager may offer a year-long contract which does not penalize the

salesman for poor sales, but offers above subsistence level fixed fee to motivate loyalty

to the firm on the part of the salesman, and a clause thrown in which transfers a larger

share of output than normal to the agent (i.e. incentives for extra effort in a time of

recession).

Now suppose the salesman, as he sets out on his rounds, discovers that the

economy is in an upswing, and that his orders are being filled with little effort on his

part. Then the agent may continue to exert little effort, realize high output, get a higher

share of output in addition to a higher initial fixed fee as his compensation.

In the case of asymmetric information, the problem is formulated as follows:

(PA) Maxc(qy)Ec,e(z)EE I Up(q c(q,y))f(q,y I z,e(z))p(z)dqdydz

such that

I UA(c(q,y))f(q,y I z,e(z))p(z)dqdydz- J d(e(z))pzdz > U, (IRC)

e(z) E argmax.gE I UA(c(q,y))f(q,yIz,e')dqdy- d(e') V z (ICC)

where p(z) is the marginal density of z, d(e(z)) is the disutility of effort e(z).

Let X and 1t(z)p(z) be the Lagrange multipliers for (IRC) and (ICC) in (PA) respectively.







77
Result 3.7: The extension of result 3.1 on the characterization of optimal

compensation schemes to the problem (PA) is:


U'(q c(qy)) I fpL(z).f(q,y Iz,e(z))p(z)dz
Uq-------)- = A. + -------

U(c(q,y)) fftq,y Iz,e(z))p(z)dz



The interpretation of result 3.7 is similar to that of result 3.1. Analogous to result 3.2,

p(z) 4 0, and /z(z) < 0 for some z and )(z) > 0 for other z, which implies, as in

result 3.2, that result 3.7 characterizes solutions which are second-best.


5.3.4 Model 4: Communication under Asymmetry


This model (Christensen, 1981) attempts an analysis similar to model 3, and

includes communication structures in the agency. The special assumptions are as

follows:

(a) There is a set of messages M that the agent uses to communicate with the

principal; compensation is based on the output and the message picked by

the agent; hence, the message is public knowledge.

(b) There is a set of signals about the environment; the agent chooses his effort

level based on the signal he observes; the agent also selects his compensation

scheme at this time by selecting an appropriate message to communicate to

the principal; selection of the message is based on the effort.








78
(c) Uncertainty is with respect to the signals observed by the agent; the

distribution characterizing this uncertainty is public knowledge; the joint

density is defined on output and signal conditioned on the effort:

f(qtle) = f(ql|,e)'f().

(d) Both parties are Savage(1954)-rational.

(e) The principal's utility of wealth is Up, with weak risk-aversion; in particular,

Up' > 0 and U" < 0.

(f) The agent's utility of wealth is separable into UA defined on compensation

and disutility of effort. The agent has positive marginal utility for money,

and he is strictly risk-averse; i.e. UA' > 0, UA" < 0, and d' > 0.



Timing:

(a) The principal and the agent determine the set compensation schemes, based

on the output and the message sent to the principal by the agent; the

principal is committed to this set of compensation schemes;

(b) the agent accepts the compensation scheme if it satisfies his reservation

welfare;

(c) the agent observes a signal ;

(d) the agent picks an effort level based on ;

(e) the agent sends a message m to the principal; this causes a compensation

scheme from the contracted set to be chosen;

(f) output occurs;









(g) sharing of output takes place.

Note that in the timing, (d) and (e) could be interchanged in this model without affecting

anything.



The following is the principal's problem:

(P) Find (c*(q,m),e'(,m),m*()) such that c* E C, e* E E, and

m* E M solves:

Maxq,n,),mi) E[Up(q c(q,m))]

such that

E[UA(c(q,m)) d(e)] U, (IRC)

e(Q) E argmaxo.'E E[UA(c(q,m())) d(e') (self-selection of action),

m(Q) argmaxm.eM E[UA(c(q,m'))-d(e(Q,m')) f] (self-selection of

message),

where e(Q,m) is the optimal act given that is observed and m is reported.



The following assumptions are used for analyzing the problem in the above formulation:

(a) Up(.) and U^(*) d(.) are concave and twice continuously differentiable in

all arguments.

(b) Compensation functions are piecewise continuous and differentiable a.e.(Q).

(c) The density function f is twice differentiable a.e.

(d) Regularity conditions enable differentiation under the integral sign.

(e) Existence of an optimal solution is assumed.









Result:

Result 4.1: The following is a characterization of optimal functions:



Up,(q-c "(q,&)) = e .-( l--)) p(tq,E le(E))
= I *
U (c *(q,E)) Aq,E le *(E)) f(q,E le *(E)



where X, 1(Q), and p(Q) are Lagrange multipliers for the three constraints in (P)

respectively.


5.3.5 Model G: Some General Results


Result G. 1 (Wilson. 1968). Suppose that both the principal and the agent are risk

averse having linear risk tolerance functions with the same slope, and the disutility of the

agent's effort is constant. Then the optimal sharing rule is a non-constant function of the

output.

Result G.2. In addition to the assumptions of result G. 1, also suppose that the

agent's effort has negative marginal utility. Let cl(q) be a sharing rule (or compensation

scheme) which is linear in the output q, and let c2(q) = k be a constant sharing rule.

Then, c, dominates c2.

The two results above deal with conditions when observation of the output is

useful. Suppose Y is a public information system that conveys information about the

output. So, compensation schemes can be based on Y alone. The value of Y, denoted

W(Y) (following model 1), is defined as: W(Y) = maxcEc EUp[q c(y)], subject to IRC







81

and ICC. Let Y' denote a non-informative signal. Then, the two results yield a ranking

of informativeness: W(Y) > W(Y). When Q is an information system denoting perfect

observability of the output q, and the timing of the agency relationship is as in model 1

(i.e. payment is made to the agent after observing the output), then W(Q) > W(Y) as

well.













CHAPTER 6
METHODOLOGICAL ANALYSIS





The solution to the principal-agent problem is influenced by the way the model

itself is setup in the literature. Highly specialized assumptions, which are necessary in

order to use the optimization technique, contribute a certain amount of bias. As an

analogy, one may note that a linear regression model assumes implicit bias by seeking

solutions only among linear relationships between the variables; a correlation coefficient

of zero therefore implies only that the variables are not linearly correlated, not that they

are not correlated. Examples of such specialized assumptions abound in the literature,

a small but typical sample of which are detailed in the models presented in Chapter 5.

The consequences of using the optimization methodology are primarily of two.

Firstly, much of the pertinent information that is available to the principal, the agent and

the researcher must be ignored, since this information deals with variables which are not

easily quantifiable, or which can only be ranked nominally, such as those that deal with

behavioral and motivational characteristics of the agent and the prior beliefs of the agent

and principal (regarding the task at hand, the environment, and other exogenous

variables). Most of this knowledge takes the form of rules linking antecedents and

consequents, and which have associated certainty factors.








83

Secondly, a certain amount of bias is introduced into the model by requiring that

the functions involved in the constraints satisfy some properties, such as differentiability,

monotone likelihood ratio, and so on. It must be noted that many of these properties are

reasonable and meaningful from the standpoint of accepted economic theory. However,

standard economic theory itself relies heavily on concepts such as utility and risk

aversion in order to explain the behavior of economic agents. Such assumptions have

been criticized on the grounds that individuals violate them; for example, it is known that

individuals sometimes violate properties of the Neumann-Morgenstemrn utility functions.

Decision theory addressing economic problems also uses concepts such as utility, risk,

loss, and regret, and relies on classical statistical inference procedures. However, real

life individuals are rarely consistent in their inference, lacking in statistical sophistication,

and unreliable on probability calculations. Several references to support this view are

cited in Chapter 2. If the term "rational man" as used in economic theory means that

individuals act as if they were sophisticated and infallible (in terms of method and not

merely content), then economic analysis might very well yield erroneous solutions.

Consider, as an example, the treatment of compensation schemes in the literature.

They are assumed to be quite simple, either being linear in the output, or involving a

fixed element called the rent. (See chapter 5 for details). In practice, compensation

schemes are fairly comprehensive and involved. They cover as many contingencies as

possible, provide for a variety of payment and reward criteria, specify grievance

procedures, termination, promotion, varieties of fringe benefits, support services, access

to company resources, and so on.








84
The set of all compensation schemes is in fact a set of knowledge bases consisting

of the following components (B.R. Ellig, 1982):

(1) Compensation policies/strategies of the principal;

(2) Knowledge of the structure of the compensation plans, which means specific rules

concerning short-term incentives linked to partial realization of expected output,

long-term incentives linked to full realization of expected output, bonus plans

linked to realizing more than the expected output, disutilities linked to

underachievement, and rules specifying injunctions to the agent to restrain from

activities that may result in disutilities to the principal (if any).

There are various elements in a compensation scheme, which can be classified as

financial and non-financial:

Financial elements of compensation

1. Base Pay (periodic).

2. Commission or Share of Output.

3. Bonus (annual or on special occasions).

4. Long Term Income (lump sum payments at termination).

5. Benefits (insurance, etc.).

6. Stock Participation.

7. Non-taxable or tax-sheltered values.

Nonfinancial elements of compensation

1. Company Environment.

2. Work Environment.




Full Text
60
E. The principals problem:
(M2.P) Maxcec MaxeE E9p Up[q(e,e) -c(q(e,Q))]
where the expectation E( ) is given by (assuming the usual regularity conditions)
0
Up[q(e,d) c(g(e, 0) ) ] f- (0) c?0
0p
where
/
0 6 [0, 0] and
f(0) is the distribution assigned by the principal.
The agents problem:
(M2.A) Maxcec MaxeeE Ee* UA[c(q(e,d) ) d(e) ]
subject to
E**[c(q(e,Q)) -d(e)] Z, (IRC)
c e argmax(M2. P) .
where the expectation E( ) is given as usual by
UA[q(e,Q) c(g(e,0))] £ (0) d0.
e,
/


63
check one of two constraints to verify that the offered compensation indeed meets his
reservation welfare:
c > U or UA(c) > UA(U).
If the principal picks a compensation which satisfies c > U, it is not necessary that
UA(c) > UA(U) be also satisfied. However, using UA(c) > U for the IRC, where
is treated "as if it were UA(), implies knowledge of the agents utility on the part
of the principal.
The difference between the two situations is of enormous significance if the
purpose of analysis is to devise solutions to real-world problems. In the literature, this
distinction is conveniently overlooked. If all such vagueness in the technological,
informational and temporal assumptions was to be systematically eliminated, the analysis
might change in a way not intended in the original literature. Hence, the main results
in the literature will be presented as they are.
5.3.1 Model 1: The Linear-Exponential-Normal Model
This name of the model (Spremann, 1987) derives from the nature of three crucial
parameters: the payoff functions are linear, the utility functions are exponential, and the
exogenous risk has a normal distribution. Below is a full description.
Technology:
(a) compensation is the sum of a fixed rent r and a share s of the output q: c(q)
= r + sq;


61
F. The solution:
(a) The agent selects c E C\ and a corresponding effort e* which is a solution
to M2.A;
(b) a state of nature 6 occurs;
(c) output q(e*,0) is generated;
(d) payoffs:
tp = UP[q(e*,0) c*(q(e\0))];
= UA[c*(q(e*,0)) d(e*)].
Development of the problem: Model 3. In this model, the strongest possible
assumption is made about information available to the principal: the principal has
complete knowledge of the utility function of the agent, his disutility of effort, and his
reservation welfare. Accordingly, the principal is able to make an offer of compensation
which satisfies the decision criterion of the agent and his constraints. In other words,
the two problems are treated as one. The assumptions are as in model 2, so only the
statement of the problem will be given below.
The problem:
Marcee, e-E E Up[q(e*,Q) c(g(e\0) ) ]
subject to
E UA[c(q(e\0) ) d(e') ] ^ U, (IRC)
e* e argmax {MaxeeE¡ c6C E UA[c (q(e, 6) ) -d(e)]). (ICC)


24
attributes has n-1 crossover points), and the individuals exchange their "strings," thus
forming new individuals. It may so happen that the new individuals are exactly the same
as the parents. In order to introduce a certain amount of richness into the population,
a mutation operator with extremely low probability is applied to the bits in the individual
strings, which randomly changes each bit. After mating, survival, and mutation, the
fitness of each individual in the new population is calculated. Since the probability of
survival and mating is dependent on the fitness level, more fit individuals have a higher
probability of passing on their genetic material.
Another factor plays a role in determining the average fitness of the population.
Portions of the chromosome, called genes or features, act as determinants of qualities of
the individual. Since in mating, the crossover point is chosen randomly, those genes that
are shorter in length are more likely to survive a crossover and thus be carried from
generation to generation. This has important implications for modeling a problem and
will be mentioned in the chapter on research directions.
The power of genetic algorithms (henceforth, GAs) derives from the following
features:
1. It is only necessary to know enough about the problem to identify the
essential attributes of the solution (or "individual"); the researcher can work
in comparative ignorance of the actual combinations of attribute values that
may denote qualities of the individual.
2. Excessive knowledge cannot harm the algorithm; the simulation may be
started with any extra knowledge the researcher may have about the problem,


157
least squares computation between the antecedents of the principals
knowledge base and the agents true characteristics, and also between the
antecedents and the principals estimate of the agents true characteristics.
Whenever some statistic distinguishes between the three types of agents, a statistic
that includes all the agents is also computed. These statistics enable one to study the
behavior and performance of the agency along several parameters. These statistics are
used to study the appropriate correlations.
10.1 Characteristics of Agents
For the purpose of the simulation, the characteristics of the agents are generated
randomly from probability distributions. These distributions capture the composition of
the agent pool. Other distributions may be used in another agency context. For these
studies, some of the characteristics are generated independently of others, while some are
generated from conditional distributions. Education, experience and general social skills
are conditional on the age of the agent, while office and managerial skills are conditional
on the education of the agent. Each agent is an "object" consisting of the following:
1. Nine behavioral characteristics.
2. Three elements of private information.
3. Index of risk aversion, generated randomly from the uniform (0,1)
distribution.
4. A vector which plays a role in effort selection by the agent.


128
TABLE 9.7: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 1
(Spearman Correlation Coefficients in the first row for each variable,
Prob> j R j under Ho: Rho=0 in the second)
BP
S
BO
TP
B
SP
BP
1.00000
0.04942
0.11030
0.11728
-0.07280
0.02989
0.0
0.4882
0.1209
0.0990
0.3068
0.6752
S
0.04942
1.00000
0.03915
-0.04413
0.00558
-0.09337
0.4882
0.0
0.5830
0.5360
0.9377
0.1896
BO
0.11030
0.03915
1.00000
-0.03333
0.00579
-0.03130
0.1209
0.5830
0.0
0.6402
0.9354
0.6607
TP
0.11728
-0.04413
-0.03333
1.00000
0.02864
-0.00110
0.0990
0.5360
0.6402
0.0
0.6880
0.9877
B
-0.07280
0.00558
0.00579
0.02864
1.00000
-0.04710
0.3068
0.9377
0.9354
0.6880
0.0
0.5089
SP
0.02989
-0.09337
-0.03130
-0.00110
-0.04710
1.00000
0.6752
0.1896
0.6607
0.9877
0.5089
0.0
TABLE 9.8: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 1
(Eigenvalues of the Correlation Matrix)
Total = 11 Average = 0.6875
1
2
3
4
5
6
Eigenvalue
1.494645
1.352410
1.160236
1.116413
1.051618
1.012871
Difference
0.142235
0.192174
0.043823
0.064795
0.038747
0.080984
Proportion
0.1359
0.1229
0.1055
0.1015
0.0956
0.0921
Cumulative
0.1359
0.2588
0.3643
0.4658
0.5614
0.6535
7
8
9
10
11
12
Eigenvalue
0.931887
0.823970
0.757124
0.714118
0.584709
0.000000
Difference
0.107916
0.066847
0.043006
0.129409
0.584709
0.000000
Proportion
0.0847
0.0749
0.0688
0.0649
0.0532
0.0000
Cumulative
0.7382
0.8131
0.8819
0.9468
1.0000
1.0000
13
14
15
16
Eigenvalue
0.000000
0.000000
0.000000
0.000000
Difference
0.000000
0.000000
0.000000
0.000000
Proportion
0.0000
0.0000
0.0000
0.0000
Cumulative
1.0000
1.0000
1.0000
1.0000


69
(d) presence of a finite number of public signals;
(e) presence of a set of public information systems (i.e. signals), including non-
informative and randomized systems, the output being treated as one of the
informative information systems;
(f) costlessness of public information systems;
(g) compensation schemes are based on signals about effort or output or both.
Public information:
(a) distribution of the state of nature, 9;
(b) output levels;
(c) common information systems which are non-informative and randomizing;
(d) UA.
Information private to the principal: utility function, UP.
Information private to the agent: disutility of effort.
Timing:
(a) principal offers contract based on observable public information systems,
including the output;
(b) agent chooses action;
(c) signals from the specified public information systems are observed;
(d) agent gets paid on the basis of the signal;
(e) a state of nature occurs;


173
positive correlation with number of learning periods, but not at the 0.1 level of
significance. In all other cases, the correlation was negative, but not at the 0.1 level of
significance (except for Model 6, which showed significance). This suggests that the
models may be GA-deceptive. Further study is necessary to verify this, and suggestions
are made in Chapter 12 (Future Research). Another reason for this behavior may be due
to the fact that the functions which calculate fitness of rules do not cover all the factors
that cause the fitness to change. Of necessity, the agents private information must
remain unknown to the principals learning mechanism. Further, the index of risk
aversion of the agents is uniformly distributed in the interval (0,1). Computation of
fitness is hence not only probabilistic, but also "incomplete".


31
According to Cox, the fundamental result of mathematical inference may be
described as follows: Suppose A, B, and C represent propositions, AB the proposition
"Both A and B are true", and -|A the negation of A. Then, the consistent rules of
combination are:
P(AB | C) = P(A | BC) P(B | C), and
P(A | B) + P(->A|B) = 1.
Thus, "Cox proved that any method of inference in which we represent degrees of
plausibility by real numbers, is necessarily either equivalent to Laplaces, or
inconsistent." (Jaynes, 1983).
The second line of development starts with James Clerk Maxwell in the 1850s
who, in trying to find the probability distribution for the velocity direction of spherical
molecules after impact, realized that knowledge of the meaning of the physical
parameters of any system constituted extremely relevant prior information. The
development of the concept of entropy maximization started with Boltzmann who
investigated the distribution of molecules in a conservative force field in a closed system.
Given that there are N molecules in the closed system, the total energy E remains
constant irrespective of the distribution of the molecules inside the system. All positions
and velocities are not equally likely. The problem is to find the most probable
distribution of the molecules. Boltzmann partitioned the phase space of position and
momentum into a discrete number of cells Rk, where 1 < k < s. These cells were
assumed to be such that the k-th cell is a region which is small enough so that the energy
of a molecule as it moves inside that region does not change significantly, but which is


I cannot conclude without expressing my deepest sense of gratitude to my mother,
Dr. Seeta Garimella, who constantly encouraged me in ways too numerous to recount
and made it possible for me to pursue my studies in the land of my dreams.
IV


77
Result 3.7: The extension of result 3.1 on the characterization of optimal
compensation schemes to the problem (PA) is:
Up(q c(q,y)) + /\x(z).fe(q,y\z,e(z))P() U(c(q,y)) ffiq,y\z,e(z))p(z)dz
The interpretation of result 3.7 is similar to that of result 3.1. Analogous to result 3.2,
n(z) ^ 0, and /x(z) < 0 for some z and fx(z) > 0 for other z, which implies, as in
result 3.2, that result 3.7 characterizes solutions which are second-best.
5.3.4 Model 4: Communication under Asymmetry
This model (Christensen, 1981) attempts an analysis similar to model 3, and
includes communication structures in the agency. The special assumptions are as
follows:
(a) There is a set of messages M that the agent uses to communicate with the
principal; compensation is based on the output and the message picked by
the agent; hence, the message is public knowledge.
(b) There is a set of signals about the environment; the agent chooses his effort
level based on the signal he observes; the agent also selects his compensation
scheme at this time by selecting an appropriate message to communicate to
the principal; selection of the message is based on the effort.


124
ordered across the 5 experiments. The following is the decreasing order of explanatory
power:
Experience, risk, and physical qualities (tied),
Managerial skills,
Motivation,
Age, and general social skills (tied),
Education,
Communication skills, and other personal skills (tied).
The above results and analysis support the hypothesis that behavioral
characteristics and complex compensation plans play a significant role in determining
good compensation rules (Hypothesis 1 in Sec. 9.2 ). However Hypothesis 2, regarding
the high relative importance of Basic Pay and Share in the case of completely certain
information (Experiment 5), has not been supported (see Sec. 9.2). The results show
that even when complete and certain information is present, it is not reasonable for the
principal to try to induce the agent to exert optimum effort by presenting a contract based
solely on Basic Pay and Share of output. Further, the results provide a counterexample
to the seemingly intuitive notion that either perfect information about the behavioral
characteristics of the agent will yield the most satisfaction or that a complete lack of
information about the agent will lead to minimum satisfaction. This suggests that
Hypothesis 3 (see Sec. 9.2) is also not supported.


(b) output q = q(e); assume q(0) = 0;
(c) existence of nonseparable utility functions;
(d) decision criterion: maximization of utility;
(e) no uncertainty in the state of nature.
B. Public information:
(a) compensation scheme, c;
(b) range of possible outputs, Q;
(c) .
Information private to the principal: UP
Information private to the agent:
(a) UA;
(b) disutility of effort, d;
(c) range of effort levels, e.
C. Timing:
(1) the principal makes an offer of fixed wage
(2) the agent either rejects or accepts the offer;
(3) if he accepts it, exerts effort level e;
(4)output q(e) results;


179
TABLE 10.26: Correlation of LP with Rule Activation in the Final Iteration
(Model 5)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E[ALL]
SD[ALL]
LP
-
-
-
-
-
-
TABLE 10.27: Correlation of LP and CP with Payoffs from Agents (Model 5)
E[QUIT]
SD[QUIT]
SD[FIRED]
E[NORMAL]
SD [NORMAL]
E[ALL]
SD[ALL]
LP
+
-
+
-
+
-
CP
-
+
+
+
-
+
TABLE 10.28: Correlation of LP and CP with Principals Satisfaction, Principals
Factor and Least Squares (Model 5)
E[SATP]
SD[SATP]
LASTSATP2
FACTOR3
BEH-LS4
EST-LS5
LP
-
-
-
+
+
CP
+
+
-
1 SATP: Principals Satisfaction
2 Principals Satisfaction at Termination
3 Principals Factor
4 Least Squares Deviation from Agents True Behavior
5 Least Squares Deviation from Principals Estimate of Agents Behavior
TABLE 10.29: Correlation of Agent Factors with Agent Satisfaction (Model 5)
AGENT
FACTORS
AGENT SATISFACTION
SD[QUIT]
SD[FIRED]
SD [NORMAL]
SD[ALL]
SD[QUIT]
+
SD[FIRED]
+
SD[NORMAL]
+
SD[ALL]
+


14
2.3.2 Definitions and Paradigms
Any activity that improves performance or skills with time may be defined as
learning. This includes motor skills and general problem-solving skills. This is a highly
functional definition of learning and may be objected to on the grounds that humans learn
even in a context that does not demand action or performance. However, the functional
definition may be justified by noting that performance can be understood as improvement
in knowledge and acquisition of new knowledge or cognitive skills that are potentially
usable in some context to improve actions or enable better decisions to be taken.
Learning may be characterized by several criteria. Most paradigms fall under
more than one category. Some of these are
1. Involvement of the learner.
2. Sources of knowledge.
3. Presence and role of a teacher.
4. Access to an oracle (learning from internally generated examples).
5. Learning "richness."
6. Activation of learning:
(a) systematic;
(b) continuous;
(c) periodic or random;
(d) background;
(e) explicit or external (also known as intentional);


122
This suggests that the final knowledge base of Experiment 4 is comparatively highly
"fragmented" than that of Experiment 5.
Tables 9.9, 9.15, 9.21, 9.27, and 9.33 show the direct factor pattern. Variables
that load high on a factor indicate a greater role played in explaining that factor.
Moreover, each factor accounts for a small proportion of the total variation. A measure
of the explanatory power of a variable may be the expected factor identification, defined
as the sum of the products of each factor loading and the proportion of variation of that
factor, the sum being taken over the total number of factors that account for all the
variation in the population. Table 9.36 shows the expected factor identification of each
of the compensation variables for each experiment. Table 9.37 shows the expected factor
identification computed from the varimax rotated factor matrices.
Table 9.36 shows that except in Experiment 3, Basic Pay and Share did not have
the highest explanatory measure. Comparing across all the five experiments and ranking
the compensation variables, the following is the order of variables in decreasing
explanatory measure:
Benefits and stock participation (tied),
Terminal pay,
Bonus,
Basic pay (also called Rent or Fixed pay), and
Share.
A similar comparison from the data in Table 9.37 for the varimax rotated factors
yields the following ordering of the compensation variables:


9.14: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 2 Eigenvalues of the Correlation Matrix 132
9.15: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 2 Factor Pattern 133
9.16: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 2 -Varimax Rotated Factor Pattern 134
9.17: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 3 135
9.18: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 3 135
9.19: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 3 135
9.20: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 3 Eigenvalues of the Correlation Matrix 136
9.21: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 3 Factor Pattern 137
9.22: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 3 Varimax Rotated Factor Pattern 138
9.23: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 4 139
9.24: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 4 139
9.25: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 4 139
9.26: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 4 Eigenvalues of the Correlation Matrix 140
9.27: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 4 Factor Pattern 141
9.28: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 4 Varimax Rotated Factor Pattern 143
IX


ACKNOWLEDGMENTS
I thank Prof. Gary Koehler, chairman of the DIS department, a guru to me in the
deepest sense of the word who made it possible for me to grow intellectually and
experience the richness and fulfillment of an active mind.
I also want to thank Prof. Selcuk Erenguc for encouraging me at all times; Prof.
Harold Benson who taught me care, caution, and clarity in thinking by patiently teaching
me proof techniques in mathematics; Prof. David E.M. Sappington for giving me
invaluable lessons, by his teaching and example, on research techniques, for writing
papers and books that are replete with elegance and clarity, and for ensuring that my
research is meaningful and interesting from an economists perspective; Prof. Sanford
V. Berg, for providing valuable suggestions in agency theory; and Prof. Richard Elnicki,
Prof. Antal Majthay, and Prof. Ira Horowitz for their advice and help with the research.
I thank Prof. Malay Ghosh, Department of Statistics, and Prof. Scott
McCullough, Department of Mathematics, for their guidance in statistics and
mathematics.
I also thank the administrative staff of the DIS department for helping me in
numerous ways and making my work extremely pleasant.
I thank my wife, Raji, for her patience and understanding while I put in long and
erratic hours.
in


141
TABLE 9.27: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 4 Factor Pattern
Factor
1
2
3
4
5
X
0.39987
0.52286
-0.38231
0.31635
0.00739
D
0.65507
0.02692
0.14216
-0.45863
0.14832
A
-0.69786
-0.01735
-0.21577
-0.09847
-0.45496
RISK
-0.56345
0.48709
0.00618
0.07723
0.29746
GSS
0.12282
0.34586
0.57027
0.25255
-0.09610
OMS
-0.18220
-0.28764
0.47685
0.37232
-0.13876
M
-0.10416
0.01902
0.71620
0.06443
0.17785
PQ
0.05916
0.70795
-0.11360
0.13412
0.32138
L
-0.26565
0.09598
0.42751
-0.65510
0.17288
OPC
0.16943
0.49388
-0.14315
-0.39151
-0.43841
BP
0.66360
-0.28499
0.05754
0.13749
-0.12937
S
-0.00000
0.00000
-0.00000
0.00000
-0.00000
BO
-0.09702
-0.33988
-0.32518
-0.18613
0.66939
TP
-0.19261
-0.15261
-0.17228
0.42969
0.19808
B
0.47077
-0.02466
0.13058
0.11620
0.10372
SP
-0.05247
0.36153
0.30017
0.08792
0.06952
Factor
6
7
8
9
10
X
0.11952
-0.10795
0.17609
-0.14149
-0.19329
D
-0.15335
-0.24955
0.24565
0.01985
0.09769
A
-0.06005
0.00624
-0.11661
0.29239
0.18458
RISK
0.39016
-0.07852
-0.10355
-0.06561
-0.11007
GSS
0.13077
0.31075
0.14084
-0.09173
0.39591
OMS
0.30435
-0.27467
0.39357
-0.17861
0.10779
M
-0.27035
0.15311
-0.03593
0.09622
-0.51882
PQ
-0.25059
0.18421
-0.20210
-0.05302
0.22436
L
-0.03394
0.21155
0.01226
-0.07221
0.14553
OPC
0.03602
0.11633
0.44300
0.11891
-0.14114
BP
-0.15691
0.01890
-0.35834
-0.07636
0.12265
S
0.00000
-0.00000
0.00000
0.00000
-0.00000
BO
0.19577
-0.06597
0.22588
0.05967
0.12389
TP
-0.53566
0.27996
0.43910
0.23157
0.07421
B
0.52889
0.24791
-0.08326
0.59940
-0.00482
SP
-0.23789
-0.73091
-0.06188
0.34125
0.12271
Factor
11
12
13
14
15
X
0.32008
0.12801
-0.22099
-0.11673
0.15746
D
-0.12094
-0.17286
-0.12805
0.27294
0.16169
A
0.19543
-0.01042
0.01472
0.10009
0.25320


181
TABLE 10.33: Correlation of Principals Satisfaction with Outcomes from Agents
(Model 5)
PS1
OUTCOMES FROM AGENTS
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
4
j
E[ALL]
SD[ALL]
2
-
+
-
+
-
+
-
+
5
-
-
-
-
1 PS: This column contains the mean and standard deviation of the Principals
Satisfaction
2 Mean Principals Satisfaction
3 Standard Deviation of Principals Satisfaction
4 E[NORMAL] : Mean Outcome from Normal (non-terminated) Agents
5 SD[NORMAL]
TABLE 10.34: Correlation of Principals Factor with Agents Factors (Model 5)
E[FIRED]
SD[FIRED]
SD [NORMAL]
PRINCIPALS FACTOR
+
-
+
TABLE 10.35: Correlation of LP and CP with Simulation Statistics (Model 6)
AVEFIT
MAXFIT
VARIANCE
ENTROPY
LP
-
-
-
+
CP
-
+
+
-
TABLE 10.36: Correlation of LP and CP with Compensation Offered to Agents
(Model 6)
E1
SD1
SD2
SD3
E4
SD4
SD5
E6
SD6
E7
SD7
LP
-
-
-
-
-
-
-
-
-
-
+
CP
-
+
+
+
1 BASIC PAY; 2 SHARE OF OUTPUT; 3 BONUS PAYMENTS; 4 TERMINAL
PAY
5 BENEFITS; 6 STOCK PARTICIPATION; 7 TOTAL CONTRACT


9.29: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 5 144
9.30: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 5 144
9.31: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 5 144
9.32: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 5 Eigenvalues of the Correlation Matrix 145
9.33: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 5 Factor Pattern 145
9.34: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 5 Varimax Rotated Factor Pattern 146
9.35: Summary of Factor Analytic Results for the Five Experiments 146
9.36: Expected Factor Identification of Compensation Variables for the Five
Experiments Derived from the Direct Factor Analytic Solution 147
9.37: Expected Factor Identification of Compensation Variables for the Five
Experiments Derived from the Varimax Rotated Factor Analytic
Solution 147
9.38: Expected Factor Identification of Behavioral and Risk Variables for the
Five Experiments Derived from the Direct Factor Pattern 148
9.39: Expected Factor Identification of Behavioral and Risk Variables for the
Five Experiments Derived from Varimax Rotated Factor Analytic
Solution 148
10.1: Correlation of LP and CP with Simulation Statistics (Model 4) 174
10.2: Correlation of LP and CP with Compensation Offered to Agents (Model
4) 174
10.3: Correlation of LP and CP with Compensation in the Principals Final KB
(Model 4) 174
10.4: Correlation of LP and CP with the Movement of Agents (Model 44 174
x


79
(g) sharing of output takes place.
Note that in the timing, (d) and (e) could be interchanged in this model without affecting
anything.
The following is the principals problem:
(P) Find (c*(q,m),e*(£,m),m*(£)) such that c* G C, e* G E, and
m* G M solves:
Maxc(q,m),e),m(i) E[UP(q c(q,m))]
such that
E[UA(c(q,m)) d(e)] > , (IRC)
e(£) G argmaxe.£E E[UA(c(q,m(£))) d(e) (self-selection of action),
m(0 G argmaxm.6M E[UA(c(q,m))-d(e(£,m))|£] (self-selection of
message),
where e(£,m) is the optimal act given that £ is observed and m is reported.
The following assumptions are used for analyzing the problem in the above formulation:
(a) UP( ) and UA( ) d( ) are concave and twice continuously differentiable in
all arguments.
(b) Compensation functions are piecewise continuous and differentiable a.e.(£).
(c) The density function f is twice differentiable a.e.
(d) Regularity conditions enable differentiation under the integral sign.
(e) Existence of an optimal solution is assumed.


108
(9) Language and Communication Skills (L), and
(10) Miscellaneous Personal Characteristics (OPC).
The consequent variables that denote the elements of compensation plans are listed
in order below, with the variable names in parentheses:
(1) Basic Pay (BP),
(2) Share or Commission of Output (S),
(3) Bonus Payments (BO),
(4) Long Term Payments (TP),
(5) Benefits (B), and
(6) Stock Participation (SP).
We assume that each of the 10 variables representing the agents characteristics
(including exogenous risk) and the 6 variables that represent the elements of
compensation has 5 possible values. This is a convenient number of values for nominal
variables and represents one of the Likert scales.
In effect, every rule is represented as an ordered sequence of 16 integer numbers
of 1 through 5. The first ten numbers are understood to be the antecedents, and the next
six the consequents. The nominal scale linked to the consequent variables is as follows:
1: minimum; 2: low; 3: average; 4: high; 5: very high
For example, consider the following rule:
IF <2,3,1,4,5,2,3,1,4,3> THEN <3,2,4,3,2,2>
This rule means:
IF


163
10.5 Model 5: Discussion of Results
Model 5 has two elements of compensation, and the principal evaluates the
performance of agents in a discriminatory manner. The value of individual elements of
the contract as well as the value of the total contract offered to agents decreased with
increases in the number of learning periods. When the number of contract periods for
each learning period was increased, only the mean share offered to the agents increased,
but no significant results were available for the rest of the elements of contract. The
variance of the total contract increased both times (Table 10.18). The principals final
knowledge base is also consistent with this result (Table 10.19).
Increasing the number of learning periods left the agents worse off at termination,
while increasing the number of contract periods merely decreased the variance of the
agent factors (Table 10.21). However, the agents satisfaction showed positive
correlation with the number of learning periods, except for agents who were fired (Table
10.22). This positive correlation also extends to those agents who quit of their own
accord. This implies that while the satisfactions rose with more learning periods, they
did not rise high enough or in a timely way for some agents. Again, as in Model 4,
increasing observability (number of contract periods) by the principal correlated
negatively with agents satisfactions, while decreasing their variance.
In Model 5, payoff from individual agents is known, which enables the principal
to practice discrimination in firing agents. The mean payoff of agents who quit, of those
who stayed on (normal agents), and also of all the agents (considered as a whole),
showed positive correlation with the number of learning periods, while the number of


200
are changed). However, a correlational study of the compensation variables in the final
knowledge base is a starting point for characterizing good contracts. The acceptance or
rejection of contracts by the agents, or the effort-inducing influence of different
contracts, may be better predicted by forming correlational links between the different
compensation elements.
One potential benefit in investigating the role of behavior and motivation theory
is that compensation rules may be modified according to correlations. For example, if,
for a particular class of agents, benefits and share of output are strongly positively
correlated, then all rules that do not reflect this property may be discarded. Normal
genetic operators may then be applied. The mutation operator would ensure exploration
of new rules in the search space, while the correlation-modified rules would fix the rule
population in a desirable sector of the search space. This procedure may not be
defensible if, upon further research, it was found that the correlations are purely random.
This research indicates that this is unlikely to happen.
12,3 Machine Learning
PAC-leaming may be applied to the set of final contracts in order to determine
their closeness to optimality. Genetic algorithms do not guarantee optimality, even
though in practice they perform well. However, some measure of goodness of solutions
is necessary. PAC-leaming, described in Chapter 2, provides such a measure along with
the confidence level. PAC theory is statistical and non-parametric in nature.


37
The technique can be extended to cover prior knowledge expressed in the form
of probabilistic knowledge bases by using two key MaxEnt solutions: non-informativeness
(as covered in the last example above), and statistical independence of two random
variables given no knowledge to the contrary (in other words, given two probability
distributions f and g over two random variables X and Y respectively, and no further
information, the MaxEnt joint probability distribution h over X*Y is obtained as h =
f*g).


166
periods, while the mean values for some of the elements of compensation (share of
output and stock participation) and the total contract correlated positively with the
number of contract periods (Table 10.51).
The principal has available to her (in this Model 7) the payoffs from each agent.
The mean payoff from agents who quit and all the agents taken as a whole showed
positive correlation with the number of learning periods, while there was negative
correlation for the mean payoff from fired agents. This implies that the principal
succeeded in learning to control effort selection by the agents in such a way as to
increase the payoff. This need not imply that the agents are better off, or that their mean
satisfaction is high (see discussion in the next paragraph). The number of contract
periods correlated negatively with the mean payoff from all types of agents except for
fired agents (who had no significant correlation) (Table 10.59). This may seem counter
intuitive, since having more data should lead to better control. However, collecting data
takes time. The longer it takes time, the longer the principal defers using the learning
mechanisms. This gives the agents time to get away with a smaller contribution to
payoff, while collecting commensurately larger contracts until the principal learns.
The mean agent factor for fired agents, and the mean satisfaction of agents who
quit and of normal agents, correlates negatively with the mean satisfaction of the
principal (Tables 10.62 and 10.63). The principal is also able to observe the outcomes
from each agent individually. The mean outcome from all the types of agents (except
those who were fired, for whom there are no significant correlations at the 0.1 level)


85
3. Items which are designed to improve productivity of agent.
4. Status or Prestige.
5. Elements of agents disutility assumed by the firm.
As another example, note that some of the important factors not considered in the
traditional treatment of the principal-agent problem are connected to the characteristics
of the agent. In a real-world situation, the principal has a great deal of behavioral
knowledge which he acquires from acting in a social context. In dealing with the
problems associated with the agency contract, he takes into account factors of the agent
such as the following:
* General social skills, which are also known as social interaction skills, networking
skills, or people skills.
* Office and managerial skills.
* Past experience or reputation.
* Motivation or enthusiasm.
* General behavioral aspects (personal habits).
* Physical qualities deemed essential or useful to the task.
* Language/communication skills.
In the light of these shortcomings of the traditional methodology, it is desirable
to see how they make their decisions in reality. It may be more fruitful to think of
people making decisions based on some underlying probabilistic knowledge bases. These
knowledge bases would capture all the rules of behavior and decision-making, such as


147
TABLE 9.36: Expected Factor Identification of Compensation Variables for the Five
Experiments Derived from the Direct Factor Analytic Solution
COMPENSATION
VARIABLE
EXPECTED FACTOR IDENTIFICATION
EXP 1
EXP 2
EXP 3
EXP 4
EXP 5
BASIC PAY
0.2675
0.1652
0.3053
0.2394
0.3043
SHARE
0.2350
0.2267
0.3081
0.0000
0.3371
BONUS
0.2767
0.2190
0.2325
0.2279
0.3591
TERMINAL PAY
0.2587
0.2467
0.2480
0.2400
0.3529
BENEFITS
0.2619
0.2506
0.2784
0.2104
0.3601
STOCK
0.2757
0.2385
0.2863
0.2054
0.3497
TABLE 9.37: Expected Factor Identification of Compensation Variables for the Five
Experiments Derived from the Varimax Rotated Factor Analytic Solution
COMPENSATION
VARIABLE
EXPECTED FACTOR IDENTIFICATION
EXP 1
EXP 2
EXP3
EXP 4
EXP 5
BASIC PAY
0.1212
0.0795
0.1915
0.1677
0.1667
SHARE
0.1206
0.0915
0.1177
0.0000
0.1661
BONUS
0.1017
0.0881
0.0772
0.0997
0.2095
TERMINAL PAY
0.1122
0.1032
0.1096
0.1234
0.1904
BENEFITS
0.1426
0.0907
0.1511
0.1835
0.1741
STOCK
0.1531
0.0959
0.1109
0.1272
0.1777


42
his private information system after he accepts a particular compensation scheme from
the principal subject to its satisfying the reservation constraint. This signal is caused by
the combination of the compensation scheme, an estimate of exogenous risk by the agent
based on his prior information or experience, and the agents knowledge of his risk
attitude and disutility of action. The communication structure agreed upon by both the
principal and the agent allows the agent to send a message to the principal. It is to be
noted that the agency contract can be made contingent on the message, which is jointly
observable by both the parties. The compensation scheme considers the message(s) as
one (some) of the factors in the computation of the payment to the agent, the other of
course being the output caused by the agents action. Usually, formal communication
is not essential, as the principal can just offer the agent a menu of compensation
schemes, and allow the agent to choose one element of the menu.
5.1.4 The Timing Component of Agency
Timing deals with the sequence of actions taken by the principal and the agent,
and the time when they commit themselves to specific decisions (for example, the agent
may choose an effort level before or after observing some signal about exogenous risk).
Below is one example of timing (T denotes time):
Tl. The principal selects a particular compensation scheme from a set of possible
compensation schemes.
T2. The agent accepts or rejects the suggested compensation scheme depending on
whether it satisfies his reservation constraint or not.


159
This tuning and adjustment is made possible by noting the number of times each
antecedent was applicable in the process of searching for an appropriate compensation
scheme for each agent. If, during the learning episode, the count of any antecedent of
a rule exceeded some average of the counts in the knowledge base, that would imply that
that antecedent is too general and is applicable to too many agents. In such a case, the
antecedents length of interval is reduced in a systematic manner. Again, if an
antecedent in a rule had a very low count, that would imply that the antecedent of that
rule was not being used much. In such a case, the length of interval of that antecedent
would be expanded.
The process of reducing the length of an antecedents interval is called
specialization, and the process of increasing it is called generalization. A fixed step size
may be associated with each process. We choose the same step size of 0.25 for both the
processes. If 1¡ is the lower bound of an antecedent and u¡ is its upper bound, then (u¡ -
1) times the step size (0.25) is the size of the specialization and generalization step size
(S). For the above antecedent, the learning operators would act as follows:
Specialization: 1¡ <-1¡ + S; u¡ *- u¡ S.
Generalization: 1¡ *- 1¡ S; u¡ <*- u¡ + S.
The step size S is therefore proportional to the length of the interval. Updating of the
bounds of the antecedent takes place in each learning episode after the application of the
mating operator and before the application of the mutation operator of the genetic
algorithm.


119
yield higher average fitness (or satisfaction) as can be seen by comparing Agents #5 and
#1; a complete non-informative prior (as in the case of Agent ft A) did not lead to lowest
average fitness (the lowest was obtained by Agent #3). Furthermore, the result in this
case is counter-intuitive when the behavioral characterizations of the different agents are
considered. Agent #5 seems to be the best bet for this principal to maximize satisfaction.
This is not the case. This result takes on added significance in view of the fact that
Agent #5 faced an environment having low exogenous risk compared to that faced by
Agent ft 1 (higher values for the risk variable in Table 9.1 denote less risk).
However, the uncertainty of the agents performance in maximizing total
satisfaction is least in the case of Agent #5 (about whom the principal has completely
certain information), while it is the highest in the case of Agent ft A (about whom the
principal has no information whatsoever). Agent ff5 is followed in increasing order of
uncertainty by Agents ft3, ft 1, #2, and ft A.
From Table 9.4, the ratio of the entropy of the normalized fitnesses of the
knowledge base to the theoretical maximum gives an indication of how close the
information content of the final knowledge base is to the theoretical maximum. It shows
that the final knowledge base of the non-informative case (Agent ttA) is least informative
(while satisfying maximal non-commitalness), while the case of certain information
(Agent #5) shows a highly informative knowledge base. This is intuitively reasonable.
Tables 9.5, 9.6, 9.11, 9.12, 9.17, 9.18, 9.23, 9.24, 9.29 and 9.30 show the
compensation recommendations for each of the five agents. The mean compensation
value for each variable including the standard deviation from the mean helps in the task


169
evaluation). This implies that the principal discriminated in favor of the normal agents,
while terminating the services of undesirable agents and forcing other agents to quit by
offering very low contracts. Normal agents suffered the most in Model 4 where the
number of elements of compensation are two, and the principal does not practice
discrimination. This means that the complexity of compensation plans is insufficient to
selectively reward good agents in Models 4 and 5, while a non-discriminatory evaluation
practice (as in Models 4 and 6) adds to the unfavorable atmosphere for the good agents.
It appears that increasing either the number of elements of compensation or practicing
a discriminatory evaluation is sufficient to selectively reward good agents (as in Models
5 and 6), but the dual approach does not help the normal agents (as in Model 7), even
though their factors are almost double when compared to Model 4.
Interestingly, the greatest increase in satisfaction is observed for the agents who
were fired for all the models. At the same time, their mean satisfaction is the lowest.
This implies that their payoff contribution to the principal is also low. In the case of two
elements of compensation and non-discrimination (Models 4 and 5), the agents who were
eventually fired took advantage of the principals inability to focus on their performance,
thereby increasing their satisfaction at a rate which was higher than that of other types
of agents. Whenever the principal had complex contracts as a manipulating tool (as in
Models 6 and 7), or whenever she had sufficient information to evaluate performances
discriminatively (as in Models 5 and 7), the factors for fired agents show a significant
decline. This implies that they were fired sooner before they could increase their own
payoffs to the extent they could in the other models.


REFERENCES
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Anderson, J.R. (1980). Cognitive Psychology and its Implications. W.H. Freeman and
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Anderson, J.R., and Bower, G.H. (1973). Human Associative Memory. Winston,
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Angluin, D. (1987). "Learning k-term DNF Formulas Using Queries and
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Bamberg, G., and Spremann, K. (Eds.) (1987). Agency Theory, Information, and
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206


78
(c) Uncertainty is with respect to the signals observed by the agent; the
distribution characterizing this uncertainty is public knowledge; the joint
density is defined on output and signal conditioned on the effort:
f(q£ |e) = f(q|£,e)*f(|).
(d) Both parties are Savage(1954)-rational.
(e) The principals utility of wealth is UP, with weak risk-aversion; in particular,
Up > 0 and UP < 0.
(i) The agents utility of wealth is separable into UA defined on compensation
and disutility of effort. The agent has positive marginal utility for money,
and he is strictly risk-averse; i.e. UA > 0, UA < 0, and d' > 0.
Timing:
(a) The principal and the agent determine the set compensation schemes, based
on the output and the message sent to the principal by the agent; the
principal is committed to this set of compensation schemes;
(b) the agent accepts the compensation scheme if it satisfies his reservation
welfare;
(c) the agent observes a signal £;
(d) the agent picks an effort level based on £;
(e) the agent sends a message m to the principal; this causes a compensation
scheme from the contracted set to be chosen;
(f) output occurs;


53
(5) sharing of output according to contract.
D. Payoffs:
Case 1: Agent rejects contract, i.e. e = 0;
TTp = UP[q(e)] = UP[q(0)] = UP[0].
*A = UA[U].
Case 2: Agent accepts contract;
TTp = UP[q(e) c].
*a = UA[c d(e)].
E. The principals problem:
(Ml.PI) Maxc e c maxq e Q UP[q c]
such that
c > U. (IRC)
Suppose C* Q C is the solution set of M1.P1. The principal picks c £ C* and offers
it to the agent.
The agents problem:
(M1.A1) For a given c\
Maxe e E UA[c* d(e)].
Suppose E* Q E is the solution set of Ml.Al. The agent selects e* 6 E*.


26
There are two important models for GAs in learning. One is the Pitt approach,
and the other is the Michigan approach. The approaches differ in the way they define
individuals and the goals of the search process.
3.2 The Michigan Approach
The knowledge base of the researcher or the user constitutes the genetic
population, in which each rule is an individual. The antecedents and consequents of each
rule form the chromosome. Each rule denotes a classifier or detector of a particular
signal from the environment. Upon receipt of a signal, one or more rules fire,
depending on the signal satisfying the antecedent clauses. Depending on the success of
the action taken or the consequent value realized, those rules that contributed to the
success are rewarded, and those rules that supported a different consequent value or
action are punished. This process of assigning reward or punishment is called credit
assignment.
Eventually, rules that are correct classifiers get high reward values, and their
proposed action when fired carries more weight in the overall decision of selecting an
action. The credit assignment problem is the problem of how to allocate credit (reward
or punishment). One approach is the bucket-brigade algorithm (Holland, 1986).
The Michigan approach may be combined with the usual genetic operators to
investigate other rules that may not have been considered by the researcher.


216
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Econometrica 19, pp. 293-305.
Singh, N. (1985). "Monitoring and Hierarchies: The Marginal Value of Information in
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Spremann, K. (1987). "Agent and Principal." In Agency Theory, Information, and
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New York.


17
Quinlan, 1979; Quinlan, 1986; Quinlan, 1990); contextuality arises in learning semantics,
as in conceptual dependency (see for example, Schank, 1972; Schank and Colby, 1973),
learning by analogy (see for example, Buchanan et al., 1977; Dietterich and Michalski,
1979), and case-based reasoning (Riesbeck and Schank, 1989); integration is fundamental
to forming relationships, as in semantic nets (Quillian, 1968; Anderson and Bower, 1973;
Anderson, 1976; Norman, et al., 1975; Schank and Abelson, 1977), and frame-based
learning (see for example, Minsky, 1975); abstraction deals with formation of universal
or classes, as in classification (see for example, Holland, 1975), and induction of
concepts (see for example, Mitchell, 1977; Mitchell, 1979; Valiant, 1984; Haussler,
1988); reduction arises in the context of deductive learning (see for example, Newell
and Simon, 1956; Lenat, 1977), conflict resolution (see for example, McDermott and
Forgy, 1978), and theorem-proving (see for example, Nilsson, 1980). For an excellent
treatment of these issues from a purely epistemological viewpoint, see for example Rand
(1967) and Peikoff (1991).
In discussing real-world examples of learning, it is difficult or meaningless to look
for one single paradigm or knowledge representation scheme as far as learning is
concerned. Similarly, there could be multiple teachers: humans, oracles, and an
accumulated knowledge that acts as an internal generator of examples.
In analyzing learning paradigms, it is useful to look at least three aspects, since
they each have a role in making the others possible:
1. Knowledge representation scheme.
2. Knowledge acquisition scheme.


68
Result 1.6: The principal prefers agents with lower risk aversion. This is
immediate from the fact that the principals welfare is decreasing in the agents risk
aversion for a given a2 and .
Result 1.7: Fixed fee arrangements are non-optimal, no matter how large the
agents risk aversion. This is immediate from the fact that
5* = > 0 V a > 0.
1 + 2ao2
Result 1.8: It is the connection between unobservability of the agents effort and
his risk aversion that excludes first-best solutions.
5.3.2 Model 2
This model (Gjesdal, 1982) deals with two problems:
(a) choosing an information system, and
(b) designing a sharing rule based on the information system.
Technology:
(a) presence of uncertainty, 9;
(b) finite effort set of the agent; effort has several components, and is hence
treated as a vector;
(c) output q is a function of the agents effort and the state of nature 6; the
range of output levels is finite;


176
TABLE 10.12: Correlation of Agent Factors with Agent Satisfaction (Model 4)
AGENT
FACTORS
AGENT SATISFACTION
SD[QUIT]
SD[FIRED]
SD[NORMAL]
SD[ALL]
SD[QUIT]
+
SD[FIRED]
+
SD [NORMAL]
+
SD[ALL]
+
TABLE 10.13: Correlation of Principals Satisfaction with Agent Factors (Model 4)
PRINCIPALS
SATISFACTION
AGENTS FACTORS
SD[QUIT]
E[FIRED]
SD[FIRED]
SD [NORMAL]
SD[ALL]
E[SATISFACTION]
+
+
-
+
+
SD[SATISFACTION]
-
TABLE 10.14: Correlation of Principals Satisfaction with Agents Satisfaction
(Model 4)
PRINCIPALS
SATISFACTION
AGENTS SATISFACTION
E[QUIT]
SD[QUIT]
SD[NORMAL]
E[ALL]
SD[ALL]
E[SATISFACTION]
-
+
-
+
SD[SATISFACTION]
-
+
-
+
TABLE 10.15: Correlation of Principals Last Satisfaction with Agents Last
Satisfaction (Model 4)
AGENTS
LAST
SATISFACTION
SD[FIRED]
E[NORMAL]
SD[NORMAL]
PRINCIPALS
LAST
+
SATISFACTION


220
and has been a teaching assistant for information systems, operations research and
statistics at the University of Florida.
He secured distinction and First place in the undergraduate class (1982-1983), a
University Merit Fellowship (1984), distinction in graduate studies (1985-1986), and the
Junior Doctoral Fellowship of the University Grants Commission, India (1987). He
holds honorary membership in the Alpha Chapter of Beta Gamma Sigma (1993), and in
Alpha Iota Delta (1993).
He has three conference publications (including one book reprint) and is a
member of the Association for Computing Machinery, the Decision Sciences Institute,
and the Institute of Management Sciences.


187
TABLE 10.55: Correlation of LP and CP with Agents Satisfaction at Termination
(Model 7)
SD[QUIT]
SD [FIRED]
E[ALL]
LP
+
+
CP
+
TABLE 10.56: Correlation of LP and CP with Agency Interactions (Model 7)
E[QUIT]
SD[QUIT]
SD[FIRED]
E[NORMAL]
E[ALL]
SD[ALL]
LP
-
-
+
-
-
-
CP
+
+
+
TABLE 10.57: Correlation of LP and CP with Rule Activation (Model 7)
E[QUIT]
SD[QUIT]
E[FIRED]
SD [FIRED]
E[ALL]
SD[ALL]
LP
-
-
-
-
-
-
CP
-
TABLE 10.58: Correlation of LP with Rule Activation in the Final Iteration
(Model 7)
E[QUIT]
SD[QUIT]
SD[FIRED]
E[ALL]
SD[ALL]
LP
-
-
+
-
-


93
2. Use of learning mechanisms to capture the dynamics of agency interaction.
A number of preliminary studies were conducted in order to define and fine-tune
the two frameworks. The initial studies sought to understand the behavior of optimal
compensation schemes in a dynamic environment. These initial studies supported the
idea that learning by way of the genetic algorithm paradigm leads to quick convergence
to a relatively stable solution. Of course, genetic algorithms may find multiple stable
solutions. Further, the preliminary studies led to fixing of the genetic parameters, since
it was noticed that variations in these parameters did not contribute anything of interest.
For example, increasing mutation probability delayed convergence of the solutions, and
beyond 0.5 led to a chaotic situation. Similarly, varying the mating probability had an
effect on the speed with which the solutions were found. The nature of the solutions
were not affected. The genetic parameters were therefore fixed as follows:
* Crossover mechanism uniform one-point crossover;
* Mating probability 0.6;
* Mutation probability ranging from 0.01 to 0.001 (for different models);
* Discard worst rule and copy the best rule.
The use of generalization and specialization operators for learning in later models
will be described subsequently. Below, we give an overview of the various models
studied. The details follow in later sections.
Models 1 and 2 were preliminary studies conducted to explore the new framework
for attacking agency problems. The goal of these models, as well as Model 3, was to
demonstrate the feasibility of addressing issues in agency which the traditional theory


95
factor analysis to study the principals knowledge base at the end of the simulation in
order to characterize good compensation schemes and identify important variables.
Models 1, 2 and 3 involve only a single agent. Models 4 and beyond capture
more realism in agency relationship. They are multi-agent, multi-period, dynamic
(agents are hired and fired all the time) models. Moreover, they closely follow one
traditional agency theory the LEN model of Spremann (see Chapter 5 for details).
Models 4 and 5 study the LEN model, while including only two elements of
compensation as in the original LEN model, and retaining the behavioral characteristics
of the agents. Model 4 studies the agency under a non-discriminatory firing policy of
the principal, while Model 5 studies exactly the same agency but with the principal
employing a discriminatory firing policy for the agents. Similarly, Models 6 and 7 are
non-discriminatory and discriminatory respectively. However, Models 6 and 7 employ
compensation variables not included in the original LEN model. These models study the
following issues:
* the nature of good compensation schemes under a demanding agency environment;
* the correlation between various variables of the agency;
* the correlation between the variables of the agency and the control variables of
the experiments;
* the effect of discriminatory firing practices by the principal
* the effect of complex compensation schemes.


113
selection of effort than specific behavioral traits. This is reflected in the function f20,
where the variable AT (Abilities and Traits) plays a vital role in the Porter and Lawler
model in determining effort selection. The probability distribution of AT is derived from
the probability distributions of the behavioral variables (excluding RISK, which plays a
direct role in the model) as follows:
1 10
Pr[ AT = i] = £ Pr [£>(J) = i] i = 1, ... ,5,
where b is the j-th behavioral variable, and b(4) is RISK (which is excluded).
The compensation variables enter the model in various ways, either directly as in
effort selection or indirectly as in determination of intrinsic reward. Their major role
is to induce the agent to select effort levels that lead to desired satisfaction levels.
The information available to the principal determines the weight of the different
variables in the model and their contributory effect, or the derivation of AT from the
behavioral variables. While the functions below reflect one such information system of
the principal, others are possible.
f,() = 13*BP + 12*S + 1 l*BO + 10*B + 9*SP + 8*TP;
f20 = 7*CE + 6*WE + 5*ST + 4*AT;
Effort = g() = (f,() + f2() + 3*PPER + 2*IR + PEPR)/13;
Output s f3() = Effort + RISK;
Performance, PERF = f4() = Output / Effort;
Intrinsic Reward, IR = f5() = (3*CE + 2*WE + ST)/6;
h,() = 5*S + 4*BP + 3*BO + 2*SP + B;


9
of the expert system. This knowledge is codified in the form of several rules and
heuristics. Validation and verification runs are conducted on problems of sufficient
complexity to see that the expert system does indeed model the thinking of the expert.
In the task of building expert systems, the knowledge engineer is helped by several tools,
such as EMYCIN, EXPERT, OPS5, ROSIE, GURU, etc.
The net result of the activity of knowledge mining is a knowledge base. An
inference system or engine acts on this knowledge base to solve problems in the domain
of the expert system. An important characteristic of expert systems is the ability to
justify and explain their line of reasoning. This is to create credibility during their use.
In order to do this, they must have a reasonably sophisticated input/output system.
Some of the typical problems handled by expert systems in the areas of business,
industry, and technology are presented in Feigenbaum and McCorduck (1983) and Mitra
(1986). Important cases where expert systems are brought in to handle the problems are
1. Capturing, replicating, and distributing expertise.
2. Fusing the knowledge of many experts.
3. Managing complex problems and amplifying expertise.
4. Managing knowledge.
5. Gaining a competitive edge.
As examples of successful expert systems, one can consider MYCIN, designed
to diagnose infectious diseases (Shortliffe, 1976); DENDRAL, for interpretation of
molecular spectra (Buchanan and Feigenbaum, 1978); PROSPECTOR, for geological
studies (Duda et al., 1979; Hart, 1978); and WHY, for teaching geography (Stevens and


120
of deciding on a specific compensation plan. For example, Agent #1 must be given high
basic pay but as less of the other elements of compensation as possible, while Agent #2
should be given an above average(but not high) basic pay and a low amount of bonus
(Table 9.11). Only in the non-informative case (Agent #4) a definite recommendation
is made for the share of output to be as low as possible in the compensation plan offered
to him (Table 9.24). Furthermore, if standard deviation from the mean compensation
values is to be understood as the uncertainty regarding compensation, it is interesting to
observe that in the case of Agent #4, the recommendations for compensation plans is
more definitive than in the case of Agent #5 (as can be seen from comparing the standard
deviations in Tables 9.24 and 9.30).
A few correlations at the 0.1 significance level among the compensation variables
were observed (Tables 9.7, 9.13, 9.19, 9.25, and 9.31). For Agent #1, a mild positive
correlation of 0.1173 was observed between Basic Pay and Terminal Pay (Table 9.7).
For Agent ft2, mild negative correlations between Basic Pay and Bonus (-0.2396) and
between Basic Pay and Benefits (-0.1101) were observed. Bonus and Benefits were
mildly positively correlated (Table 9.13). In the case of Agent #3, the following
correlations were evident: Basic Pay and Share (-0.2124), Benefits and Share (0.2552),
Bonus and Benefits (0.3042), and Benefits and Stock Participation (0.2762) (Table 9.19).
No correlations were observed at all (at the 0.1 significance level) for Agent #4 (the non-
informative case) (Table 9.25), while Agent #5 had the most number of significant
correlations (7 out a possible 15). However, all of these correlations were, without
exception, very weak. Basic Pay formed weak negative correlations with Share (-0.0598)


19
LH5: Given an implication, find out if it is also an equivalence.
LH6: Find out if any two or more properties are semantically the same, the opposite,
or unrelated.
LH7: If an object possesses two or more properties simultaneously from the same class
or similar classes, check for contradictions, or rearrange classes hierarchically.
LH8: An isa-tree in a semantic net creates an isa-tree with the object as a parent; find
out in which isa-tree the parent object occurs as a child.
We can contrast these with meta-rules or meta-heuristics. A meta-rule is also a
rule which says something about another rule. It is understood that meta-rules are watch
dog rules that supervise the firing of other rules. Each learning paradigm has a set of
rules that will lead to learning under that paradigm. We can have a set of meta-rules for
learning if we have a learning system that has access to several paradigms of learning
and if we are concerned with what paradigm to select at any given time. Learning meta
rules help the learner to pick a particular paradigm because the learner has knowledge
of the applicability of particular paradigms given the nature and state of a domain or
given the underlying knowledge-base representation schema.
The following are examples of meta-rules in learning:
ML1: If several instances of a domain-event occur,
then use generalization techniques.
ML2: If an event or class of events occur a number of times with little or no change on
each occurrence,
then use induction techniques.


CHAPTER 2
EXPERT SYSTEMS AND MACHINE LEARNING
2.1 Introduction
The use of artificial intelligence in a computerized world is as revolutionary as
the use of computers is in a manual world. One can make computers intelligent in the
same sense as man is intelligent. The various techniques of doing this compose the body
of the subject of artificial intelligence. At the present state of the art, computers are at
last being designed to compete with man on his own ground on something like equal
terms. To put it in another way, computers have traditionally acted as convenient tools
in areas where man is known to be deficient or inefficient, namely, doing complicated
arithmetic very quickly, or making many copies of data (i.e., files, reports, etc.).
Learning new things, discovering facts, conjecturing, evaluating and judging
complex issues (for example, consulting), using natural languages, analyzing and
understanding complex sensory inputs such as sound and light, and planning for future
action are mental processes that are peculiar to man (and to a lesser extent, to some
animals). Artificial intelligence is the science of simulating or mimicking these mental
processes in a computer.
The benefits are immediately obvious. First, computers already fill some of the
gaps in human skills; second, artificial intelligence fills some of the gaps that computers
6


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64
(b) presence of uncertainty in the state of nature, denoted by 0, where 0 ~
(c) the set of effort levels of the agent, E = [0,A]; effort is induced by
compensation;
(d) output q = q(e,0) = e + 0;
(e) the agents disutility of effort is d s d(e) = e2;
(0 the principals utility UP is linear (the principal is risk neutral);
(g) the agent has constant risk aversion a > 0, and his utility is
UA(w) = -exp(-aw), where w is his net compensation (also called the
wealth);
(h) the certainty equivalent of wealth, denoted V, is defined as:
V(w) = U '[Ee(U(w))], where U denotes the utility function, Ee is the
expectation with respect to 0; as usual, subscripts P or A on V denote the
principal or the agent respectively;
(i) the decision criterion is maximization of expected utility.
Public information:
(a) compensation scheme c(q; r,s);
(b) output q;
(c) distribution of 0;
(d) agents reservation welfare ;
(e)agents risk aversion a.


127
TABLE 9.5: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 1
Compensation
Variables
Values of the Variable
1
2
3
4
5
Basic Pay
3.0
4.5
13.1
38.2
41.2
Share
97.5
2.0
0.5
0.0
0.0
Bonus
61.8
22.6
5.5
5.5
4.5
Terminal Pay
93.0
2.0
3.0
1.5
0.5
Benefits
82.9
9.5
1.5
3.0
3.0
Stock
Participation
74.4
18.1
6.0
1.5
0.0
TABLE 9.6: Range, Mean and Standard Deviation of Values of Compensation
Variables in the Final Knowledge Base in Experiment 1
Variable
Minimum
Maximum
Mean
S.D.
BP
1.00
5.00
4.1005025
0.9949112
S
1.00
3.00
1.0301508
0.1987219
BO
1.00
5.00
1.6834171
1.0987947
TP
1.00
5.00
1.1457286
0.5807252
B
1.00
5.00
1.3366834
0.8945464
SP
1.00
4.00
1.3467337
0.6631551


CHAPTER 9
MODEL 3
9.1 Introduction
In Model 3, utility functions are replaced by knowledge bases, machine learning
replaces estimation and inference replaces optimization. In so doing, complex contractual
structures and behavioral and motivational considerations can be directly incorporated
into the model.
In Section 2 we describe a series of experiments used to illustrate our approach.
These experiments study a realistic situation. Section 3 covers the methodology and
details of the experiments. Section 4 tabulates the results of our experiments, while
Section 5 describes and discusses the results.
Initially, the principals knowledge base reflects her current state of knowledge
about the agent (if any). The agents knowledge base reflects the way he will produce
under a contract. This knowledge base incorporates motivational and behavioral
characteristics. It includes his perception of exogenous risk, social skills, experience,
etc. The details are provided in Section 3.
The principal will refine her knowledge base through a learning mechanism.
Using the current knowledge base, the principal will use inference to determine a
97


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117
rules. The processing involves removal of those rules which have at least one antecedent
value (i.e. value of a behavioral variable) which is not within one standard deviation
range of the mean (given in Table 9.1). The processed knowledge bases of all the runs
of each experiment are pooled to form the final knowledge base.
Table 9.3 shows the fitness statistics for the various experiments, where MATE
= 0.6, MUTATION = 0.01 and ITER = 200 is fixed. Table 9.3 also shows the
redundancy ratio of the knowledge base of each experiment. This is the ratio of the total
number of rules to the number of distinct rules. This ratio may be greater than one
because the learning process may generate copies of highly stable rules.
Table 9.4 shows the attained Shannon entropy of normalized fitness of the final
knowledge base for each experiment. Table 9.4 also shows the theoretical maximum
entropy of fitness (defined as the natural logarithm of the number of rules), and the ratio
of the attained entropy to the maximum entropy. The fitness of each rule is multiplied
by 10000 for readability.
Tables 9.5 9.34 summarize the results of the five experiments in detail. Tables
9.5, 9.11, 9.17, 9.23, and 9.29 show the frequency of values of the compensation
variables in the final knowledge base. Tables 9.6, 9.12, 9.18, 9.24, and 9.30 show the
range (minimum and maximum), mean, and standard deviation of the compensation
variables. Tables 9.7, 9.13, 9.19, 9.25, and 9.31 show the results of Spearman
correlation analysis on the final knowledge base. Tables 9.8, 9.9, 9.10, 9.14, 9.15,
9.16, 9.20, 9.21, 9.22, 9.26, 9.27, 9.28, 9.32, 9.33, and 9.34 deal with factor analysis
of the final knowledge base. Tables 9.8, 9.14, 9.20, 9.26, and 9.32 list the eigenvalues


167
correlates negatively with the principals satisfaction (Table 10.65). Observability, in
this case also, is detrimental to the interests of the agents.
10.8 Comparison of the Models
Table 10.67 summarizes the key statistics of the four models. The contracts
offered to the agents by the principal are higher in value in Models 6 and 7 (than in
Models 4 and 5) where the number of elements are more (six, as compared to two in
Models 4 and 5). However, the value of the contract per element of compensation (i.e.
the normalized statistic) is the highest in Model 4 (two elements of compensation and
non-discriminatory evaluation), followed by Models 6 and 7 (Table 10.67). This
suggests that in the absence of complex contracts and individualized observability, the
principal can only offer higher contracts in an effort to second-guess the reservation
welfare of the agents and to retain the services of good agents. Again, since
observability is poor, the principal can only offer comparatively higher contracts to all
the agents. Increasing either the complexity of contracts or the observability enables the
principal to be more efficient. However, the principal must have an instrument capable
of being flexible in order to be efficient. This is not possible when the contracts are very
simple, even if the principal is able to observe each agent individually. Hence, in Model
5, the principal can only effectively punish poor performance. If she attempts to reward
good performance using only two elements of compensation (basic pay and share of
output), her own welfare is affected. Hence, the value of contracts in Model 5 is
uniformly lower than in the other models. This also leads us to expect that the


150
changing conditions (such as the number, characteristics and risk aversion of the agents,
and also the nature of exogenous risk).
The timing of the agency problem is as follows:
1. The principal offers a compensation scheme to an agent chosen at random. The
principal selects this scheme from out of a large number of possible ones based
on her current knowledge base and on her estimate of the agents characteristics.
2. The agent either accepts or rejects the contract according to his reservation
welfare. If the agent rejects the contract, nothing further is done. If all the
agents reject the contracts they are offered, the principal seeks a fixed number
(here, 5) of new agents. This process continues until an agent accepts a contract.
3. If an agent accepts the contract, he selects an effort level based on his
characteristics, the contract, and his private information.
4. Nature acts to render an exogenous environment level.
5. Output occurs as a function of the agents effort level and the exogenous risk.
6. Sharing of the output between the agent and the principal occurs.
7. The principal reviews the agents performance and using certain criteria either
fires him or continues to deal with him in subsequent periods.
The following are the main features common to these models:
1. The agency is multi-period a number of periods are simulated.
2. The models are all multi-agent models.
3. The agency is dynamic agents are hired and fired all the time.


160
10.3 Notation and Conventions
We use the following notation to describe the results for all the models:
The prefix E[] denotes the Mean (expected value), and the prefix SD[]
denotes the Standard Deviation;
BP: Basic Pay;
SH: Share;
BO: Bonus;
TP: Terminal Pay;
BE: Benefits;
SP: Stock Participation;
LP: Learning Periods;
CP: Contract Periods;
MAXFIT: Maximum Fitness of Rules;
AVEFIT: Average Fitness of Rules;
VARFIT: Variance of Fitness of Rules;
ENTROPY: Shannon Entropy of Normalized Fitnesses of Rules;
COMP: Total Compensation Package;
FIRED: Agents who were Fired;
QUIT: Agents who Resigned;
NORMAL: Agents who remained until the end;
ALL: All the agents;


105
Nothing is known about Agent #4 in Experiment 4, while everything known about
Agent #5 in Experiment 5 is known with certainty. Agent #5 is in the same age bracket
as Agent #3, while he has more experience. His office and managerial skills, motivation
and enthusiasm are of the highest. He is physically very fit, and has very good
communication skills. He perceives the principals company and work environment to
be the best in the market, and he is very certain of his superior talents. He firmly
believes that effort is always rewarded.
The nominal scales are used throughout the experiments are given below.
For the variables CE, WE, SI, AT, GSS, OMS, P, L, OPC:
1: very bad, 2: bad, 3: average, 4: good, 5: excellent.
For PPER and M (Motivation):
1: very low, 2: low, 3: average, 4: high, 5: very high.
For X (Experience):
1: none, 2: < 1 year, 3: between 1 and 5 years,
4: between 5 and 10 years, 5: more than 10 years.
For D (Education):
1: below high school, 2: high school, 3: undergraduate,
4: graduate, 5: graduate (specialization/2 or more degrees).
For A (Age):
1: < 18 years, 2: between 18 and 25 years, 3: between 25 and 35 years, 4:
between 35 and 50 years, 5: above 50 years.
For RISK:


91
FIGURE 1: THE PORTER AND LAWLER MODEL OF INSTRUMENTALITY THEORY
FIGURE 2: MODIFIED PORTER AND LAWLER MODEL


2
The underlying domains of most of the early applications were relatively well
structured, whether they were the stylized rules of checkers and chess or the digitized
images of visual sensors. Our research focus is on importing these ideas into the area
of business decisionmaking.
Genetic algorithms, a relatively new paradigm of machine learning, deals with
adaptive processes modeled on ideas from natural genetics. Genetic algorithms use the
ideas of parallelism, randomized search, fitness criteria for individuals, and the formation
of new exploratory solutions using reproduction, survival and mutation. The concept is
extremely elegant, powerful, and easy to work with from the viewpoint of the amount
of knowledge necessary to start the search for solutions.
A related issue is maximum entropy. The Maximum Entropy Principle is an
extension of Bayesian theory and is founded on two other principles: the Desideratum of
Consistency and Maximal-Noncommitment. While Bayesian analysis begins by assuming
a prior, the Maximum Entropy Principle seeks distributions that maximize the Shannon
entropy and at the same time satisfy whatever constraints may apply. The justification
for using Shannon entropy comes from the works of Bernoulli, Laplace, Jeffreys, and
Cox on the one hand, and from the works of Maxwell, Boltzmann, Gibbs, and Shannon
on the other; the principle has been extensively championed by Jaynes and is only just
now penetrating into economic analysis.
Under the maximum entropy technique, the task of updating priors based on data
is now subsumed under the general goal of maximizing entropy of distributions given any
and all applicable constraints, where the data (or sufficient statistics on the data) play the


211
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Jaynes, E.T. (1991). "Notes on Present Status and Future Prospects." In Maximum
Entropy and Bayesian Methods, Grandy, W.T. Jr. and Schick, L.H. (eds.),
Kluwer Academic Publishers, Boston, MA, pp. 1-13.
Jensen, M.C., and Meckling, W.H. (1976). "Theory of the Firm: Managerial Behavior,
Agency Costs and Ownership Structure." Journal of Financial Economics 3, pp.
305-360.
Kahn, A.E. (1978). "Applying Economics to an Imperfect World." Regulation, pp. 17-
27.
Kahneman, D., and Tversky, A. (1982a). "Subjective Probability: A Judgment of
Representativeness." In Judgment Under Uncertainty: Heuristics and Biases;
Kahneman, D., Slovic, P., and Tversky, A., (eds.), Cambridge University Press,
New York, pp. 32-47.
Kahneman, D., and Tversky, A. (1982b). "On the Psychology of Prediction." In
Judgment Under Uncertainty: Heuristics and Biases; Kahneman, D., Slovic, P.,
and Tversky, A., (eds.), Cambridge University Press, New York, pp. 48-68.
Kahneman, D., and Tversky, A. (1982c). "On the Study of Statistical Intuitions." In
Judgment Under Uncertainty: Heuristics and Biases; Kahneman, D., Slovic, P.,
and Tversky, A., (eds.), Cambridge University Press, New York, pp. 493-508.


39
"reservation constraint", and that he is free to act in a rational manner. The assumption
of rationality also applies to the principal. After agreeing to a contract, the agent
proceeds to act on behalf of the principal, which in due course yields a certain outcome.
The outcome is not only dependent on the agents actions but also on exogenous factors.
Finally the outcome, when expressed in monetary terms, is shared between the principal
and the agent in the manner decided upon by the selected compensation plan.
The specific ways in which the agency relationship differs from the usual
employer-employee relationship are (Simon, 1951):
(1) The agent does not recognize the authority of the principal over specific tasks the
agent must do to realize the output.
(2) The agent does not inform the principal about his "area of acceptance" of
desirable work behavior.
(3) The work behavior of the agent is not directly (or costlessly) observable by the
principal.
Some of the first contributions to the analysis of principal-agent problems can be
found in Simon (1951), Alchian & Demsetz (1972), Ross (1973), Sitglitz (1974), Jensen
& Meckling (1976), Shavell (1979a, 1979b), Holmstrom (1979, 1982), Grossman & Hart
(1983), Rees (1985), Pratt & Zeckhauser (1985), and Arrow (1986).
There are three critical components in the principal-agent model: the technology,
the informational assumptions, and the timing. Each of these three components is
described below.


75
Result 3.5: An extension of result 3.1 on the characterization of optimal
compensation schemes is as follows:
X + \i.
Aq,y,e)
Up(q c(q,y))
U'Mqj))
where X and n are as in result 3.1.
Result 3.6: Any informative signal, no matter how noisy it is, has a positive value
if costlessly obtained and administered into the contract.
Note: This result is based on rigorous definitions of value and informativeness of signals
(Holmstrom, 1979).
In the second part of this model, an assumption is made about additional
knowledge of the state of nature revealed to the agent alone, denoted z. This introduces
asymmetry into the model. The timing is as follows:
(a) the principal offers a contract c based on the output and an observed signal
y;
(b) the agent accepts the contract;
(c) the agent observes a signal z about 9;
(d) the agent chooses an effort level;
(e) a state of nature occurs;
(f) agents effort and state of nature yield an output;
(g) sharing of output takes place.


CHAPTER 8
RESEARCH FRAMEWORK
The object of the research is to develop and demonstrate an alternative
methodology for studying agency problems. To this end, we study several agency
models from a common framework described below. There are two types of issues
associated with the studies. One deals with the issues of modeling the agency problem
itself. The other deals with the issues of the method, in this case, knowledge bases,
genetic learning operators, and the operators of specialization and generalization.
The common framework for the agency problems has these elements:
1. The use of rule bases to model the information and expertise possessed by the
principal and the agent.
2. The use of probability distributions to model the uncertain nature of some of the
information.
3. Consideration of a number of elements of compensation.
4. Offering compensation to an agent based on the agents characteristics.
The common framework for the methodology for studying agency issues has these
elements:
1. Simulation of the agency interactions over a period of time.
92


156
resignation. For the agents who have been fired, this is the satisfaction they
derived in the agency period they were fired. For normal agents, this is the
satisfaction they obtained at the termination of the simulation.
8. The eighth group of statistics covers the mean and variance of the number
of agency interactions, reporting separately for resigned, fired and normal
agents.
9. The ninth group of statistics details the mean and variance of the number of
rules that were activated for each of the three types of agents in the
principals knowledge base.
10. The tenth group of statistics describes the mean and variance of the number
of rules that were activated during the final iteration of the simulation.
11. The eleventh group of statistics deals with the principal, and report on the
mean and variance of the principals satisfaction, the principals factor
(which helps answer the question, "Is the principal better off in this agency
model?"), and the satisfaction derived by the principal at termination.
12. The twelfth group of statistics details the mean and variance of payoff
received by the principal from each of the three kinds of agents. This group
of statistics are relevant only in Models 5 and 7, since this information is
used by the principal to engage in discriminatory evaluation of the agents
performance.
13. The final group of statistics computes the fit of the principals knowledge
base with the dynamic agency environment. This fit is characterized by a


CHAPTER 10
REALISTIC AGENCY MODELS
In this chapter we describe Models 4 through 7. These models incorporate
realism to a greater extent than previous models. The simulation design of these four
models is the same. Each model has 200 simulations conducted with a common set of
simulation parameters. The two control variables for the simulations are the number of
learning periods and the number of contract renegotiation periods. The learning periods
run from 5 to 200, while the contract renegotiation periods run from 5 to 25.
In each learning period, there are a number of contract renegotiation periods.
The principal utilizes these periods to collect data about the performance of the agents
and the usefulness of her knowledge. In each contract renegotiation period, all the agents
are offered new compensation by the principal, which they are at liberty to accept or
reject. At the end of a prespecified number of contract renegotiation periods (this
number being a control variable), the principal uses the data to initiate the learning
process. The learning paradigms are two: the genetic algorithm used in the previous
studies, and the specialization-generalization learning operator (described in Sec. 10.2
below). This learning process actually uses the data collected in the contract
renegotiation periods to change the principals knowledge base and bring it in line with
149


130
TABLE 9.10: Experiment 1 Varimax Rotation
Factor 1
Factor 2
Factor 3
Factor 4
Factor 5
Factor 6
X
0.00592
-0.00592
-0.06160
-0.00152
0.03289
-0.03681
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
0.00697
0.01680
0.02680
-0.04246
0.99219
0.03829
GSS
-0.00519
-0.02315
0.99595
-0.00698
0.02638
-0.02607
OMS
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
M
0.00646
-0.06592
0.03811
0.04031
-0.08515
0.02529
PQ
-0.10498
0.00895
-0.01482
-0.00856
-0.01218
0.03838
L
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
BP
0.02878
-0.05624
-0.02624
0.01905
0.03809
0.99414
S
-0.04050
-0.01274
-0.00694
0.99688
-0.04193
0.01893
BO
-0.02424
-0.05007
0.01906
-0.01453
-0.04793
0.00752
TP
0.01929
0.00864
0.02160
-0.02133
-0.02683
0.04298
B
-0.00484
0.99454
-0.02324
-0.01282
0.01670
-0.05616
SP
0.99305
-0.00485
-0.00525
-0.04099
0.00693
0.02892
Factor 7
Factor 8
Factor 9
Factor 10
Factor 11
X
-0.07567
0.99216
-0.05006
-0.03047
0.01219
D
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
-0.02644
0.03284
-0.04665
-0.08451
-0.01179
GSS
0.02122
-0.06089
0.01826
0.03736
-0.01414
OMS
0.00000
0.00000
O.OOOO0
0.00000
0.00000
M
0.06591
-0.03072
-0.01159
0.98940
0.01758
PQ
0.02316
0.01277
0.15553
0.01808
0.98070
L
0.00000
0.00000
0.00000
0.00000
0.00000
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
BP
0.04274
-0.03658
0.00741
0.02495
0.03682
S
-0.02106
-0.00149
-0.01395
0.03942
-0.00818
BO
-0.03591
-0.05154
0.98287
-0.01188
0.15448
TP
0.99215
-0.07568
-0.03483
0.06528
0.02213
B
0.00860
-0.00589
-0.04828
-0.06490
0.00843
SP
0.01928
0.00591
-0.02373
0.00641
-0.10112
Notes: Final Communality Estimates total 11.1
3 and are as
follows: 0.0 for D,
A, OMS, L, and OPC; 1.0 for the rest of the variables.


10.62: Correlation of Principals Satisfaction with Agent Factors (Model 7) ... 188
10.63: Correlation of Principals Satisfaction with Agents Satisfaction (Model
7) 189
10.64: Correlation of Principals Last Satisfaction with Agents Last Satisfaction
(Model 7) 189
10.65: Correlation of Principals Satisfaction with Outcomes from Agents (Model
7) 189
10.66: Correlation of Principals Factor with Agents Factor (Model 7) 189
10.67: Comparison of Models 190
10.68: Probability Distributions for Models 4, 5, 6, and 7 193
xiv


8
applications of expert systems, concepts of decision analysis find expression (Phillips,
1986). Manual application of these techniques is not cost effective, whereas their use
in certain expert systems, which go by the generic name of Decision Analysis Expert
Systems, leads to quick solutions of what were previously thought to be intractable
problems (Conway, 1986). Several systems have been proposed that range from
scheduling to strategy planning. See for example, Williams (1986).
2,2 Expert Systems
The most fascinating and economically justifiable area of artificial intelligence is
the development of expert systems. These are computer systems that are designed to
provide expert advice in any area. The kind of information that distinguishes an expert
from a nonexpert forms the central idea in any expert system. This is perhaps the only
area that provides concrete and conclusive proof of the power of artificial intelligence
techniques. Many expert systems are commercially viable and motivate diverse sources
of funding for research into artificial intelligence. An expert system incorporates many
of the techniques of artificial intelligence, and a positive response to artificial intelligence
depends on the reception of expert systems by informed laymen.
To construct an expert system, the knowledge engineer works with an expert in
the domain and extracts knowledge of relevant facts, rules, rules-of-thumb, exceptions
to standard theory, and so on. This is a difficult task and is known variously as
knowledge acquisition or mining. Because of the complex nature of the knowledge and
the ways humans store knowledge, this is bound to be a bottleneck to the development


102
The agents knowledge base is varied from experiment to experiment to reflect
different behavioral characteristics, abilities, and perceptions. The experiments differ
with respect to each other in the probability distributions of the variables representing the
agents characteristics and the agents personal information about the principal.
An experiment consists of 10 runs of a sequence of 200 learning cycles including
the following steps:
1. Using her current knowledge base, the principal infers a compensation plan.
2. The agent performs under this compensation plan and an output is realized.
3. A satisfaction level is computed which reflects the total welfare of the principal
and the agent.
4. The principal notes the results of the compensation plan and revises her
knowledge base using a genetic algorithm learning method.
The following hypotheses are considered:
Hypothesis 1: Behavioral characteristics and complex compensation plans play a
significant role in determining good compensation rules.
Hypothesis 2: In the presence of complete certainty regarding behavioral
characteristics, the most important variables that explain variation in good compensation
rules are the same as those considered in the traditional principal-agent models.
Hypothesis 3: Extra information about behavioral characteristics yields better
compensation rules. Specifically, any information is better than having non-informative
pnors.


59
C. Timing:
(a) the principal determines the set of all compensation schemes that maximize
her expected utility;
(b) the principal presents this set to the agent as the set of offered contracts;
(c) the agent picks from this set of compensation schemes a compensation
scheme that maximizes his net compensation, and a corresponding effort
level;
(d) a state of nature occurs;
(e) an output results;
(f) sharing of the output takes place as contracted.
D. Payoffs:
Case 1: Agent rejects contract, i.e. e = 0;
xP = UP[q(e,0)] = UP[q(O,0)].
tta = UA[U],
Case 2: Agent accepts contract;
xP = UP[q(e,0) c(q)].
tTa = UA[c(q) d(e)].


94
ignored (see, for example, Chapter 6 for a methodological analysis). Models 1 and 2 led
to the choice of genetic parameters (as described above), and finalizing the agency
interaction mechanism (namely, timing and information), including the Porter-Lawler
model of human behavior and motivation. While both Models 1 and 2 are more realistic
than the traditional models, they still do not capture the entire realism of an agency. The
later models capture increasing amounts of realism.
Model 3 is the first formal study. The goal of this study is to develop a model
which provides a counter-example to the traditional theory which considers fixed pay,
share of output, and exogenous risk to be important agency variables, and ignores the
role of the agents behavioral and motivational characteristics in selecting his
compensation scheme. This study tries to answer the following questions: Is there a
non-trivial and formal agency scenario where the lack of dependence of the compensation
scheme on the agents characteristics leads to a sub-optimal solution (as compared to the
standard theory)? Is there a scenario wherein consideration of other elements of
compensation lead to better results for both the principal and the agent? Is there a
scenario where, from a principals perspective, exogenous risk (which can only be
observed ex-post) plays a lesser role than other agency variables? How does certainty
of information affect the nature of the solutions? What measures may be used to
characterize good solutions, or identify important variables? The last question is
non-trivial, because all the variables used in these studies are discrete nominal valued,
and hence are not amenable to any formal measure theory. This study involves five
experiments (which differ in the information available to the principal), and the use of


170
The mean satisfaction of agents showed significant increase (about 70%) in
Models 6 and 7 over Models 4 and 5. Comparing with the drop in agent factors in
Models 6 and 7 over Models 4 and 5, this implies that using more elements of
compensation raises the level of satisfaction by about 70%, but does not cause a
comparatively higher rise in satisfaction as the agency progresses. When the number of
elements of compensation are two (Models 4 and 5), the mean satisfaction of agents is
higher in the discriminatory case compared to the non-discriminatory case, except (of
course) for agents who were eventually fired. However, when the number of elements
of compensation were increased to six (Models 6 and 7), all agents experienced decreased
mean satisfaction in the discrimination case (Model 7). This seems to suggest that
complexity of contracts and the practice of discrimination work at cross purposes in
satisfying all agents.
On the one hand, if the goal of the agency is to rapidly improve satisfaction levels
(or increase the rate of their improvement), then discrimination is the best policy (since
Model 5 has the highest agent factors if the factors for fired agents is ignored). Such a
goal might be reasonable for an existing agency currently suffering from low satisfaction
levels or low profit levels. A discrimination policy would get rid of shirking agents,
convey a motivational message to good agents, and increase profits by paring down the
value of contracts temporarily.
On the other hand, if the goal of the agency is to achieve a high mean satisfaction
level, attract better agents by matching the general reservation welfare, and decrease
agent turnover, then a non-discriminatory evaluation policy coupled with complex


47
5.1.7 Efficiency of Cooperation and Incentive Compatibility
In the absence of asymmetry of information, both principal and agent would
cooperatively determine both the payoff and the effort or work behavior of the agent.
Subsequently, the "game" would be played cooperatively between the principal and the
agent. This would lead to an efficient agreement termed the first-best design of
cooperation. First-best solutions are often absent not merely because of the presence of
externalities but mainly because of adverse selection and moral hazard (Spremann, 1987).
Let F = { (c,e) }, where compensation c and effort e satisfy the principals and
the agents decision criteria respectively. In other words, F is the set of first-best
designs of cooperation, also called efficient designs with respect to the principal-agent
decision criteria. Now, suppose that the agents action e is induced as above by a
function I: 1(c) = e. Let S = { (c,I(c)) } i.e. S denotes the set of designs feasible
under information asymmetry. If it were not the case that F D S = 0, then efficient
designs of cooperation would be easily induced by the principal. Situations where this
occurs are said to be incentive compatible. In all other cases, the principal has available
to her only second-best designs of cooperation, which are defined as those schemes that
arise in the presence of information asymmetry.
5.1.8 Agency Costs
There are three types of agency costs (Schneider, 1987):
(1) the cost of monitoring the hidden effort of the agent,
(2) the bonding costs of the agent, and


CHAPTER 7
MOTIVATION THEORY
There are many models of motivation. One is drive theory (W.B. Cannon, 1939;
C.L. Hull, 1943). The main assumption in drive theory is that decisions concerning
present behavior are based in large part on the consequences, or rewards, of past
behavior. Where past actions led to positive consequences, individuals would tend to
repeat such actions; where past actions led to negative consequences or punishment,
individuals would tend to avoid repeating them. C.L. Hull (1943) defines "drive" as an
energizing influence which determined the intensity of behavior, and which theoretically
increased along with the level of deprivation. "Habit" is defined as the strength of
relationship between past stimulus and response (S-R). The strength of this relationship
depends not only upon the closeness of the S-R event to reinforcement but also upon the
magnitude and number of such reinforcements. Hence effort, or motivational force, is
a multiplicative function of magnitude and number of reinforcements.
In the context of the principal-agent model, drive theory would explain the agents
effort as arising from some past experience of deprivation (need of money) and from the
strength of feeling that effort leads to reward. So, the drive model of motivation defines
effort as follows:
87


189
TABLE 10.63: Correlation of Principals Satisfaction with Agents Satisfaction
(Model 7)
PRINCIPALS
SATISFACTION
AGENTS SATISFACTION
E[QUIT]
SD[FIRED]
E[ALL]
E[SATISFACTION]
-
-
-
SD[SATISFACTION]
+
+
+
TABLE 10.64: Correlation of Principals Last Satisfaction with Agents Last
Satisfaction (Model 7)
AGENTS LAST SATISFACTION
E[QUIT]
E[NORMAL]
SD[NORMAL]
E[ALL]
SD[ALL]
PRINCIPALS
LAST
SATISFACTION
-
-
+
-
+
TABLE 10.65: Correlation of Principals Satisfaction with Outcomes from Agents
(Model 7)
PS1
OUTCOMES FROM AGENTS
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
3
5
E[ALL]
SD[ALL]
" 7
-
+
+
-
+
-
+
3
+
-
+
-
+
-
+
-
1 PS: This column contains the mean and standard deviation of the Principals
Satisfaction
2 Mean Principals Satisfaction
3 Standard Deviation of Principals Satisfaction
4 E[NORMAL] : Mean Outcome from Normal (non-terminated) Agents
5 SD[NORMAL]
TABLE 10.66: Correlation of Principals Factor with Agents Factor (Model 7)
E[FIRED]
PRINCIPALS FACTOR
+


41
(d) it enables the computation of the cost of maintaining or establishing
communication structures, or the cost of obtaining additional information.
For example, one usual assumption in the principal-agent literature is that the
agents reservation level is known to both parties. As another example of the way in
which additional information affects the decisions of the principal, note that the principal,
in choosing a set of compensation schemes for presenting to the agent, wishes to
maximize her welfare. It is in her interest, therefore, to make the agent accept a payment
scheme which induces him to choose an effort level that will yield a desired level of
output (taking into consideration exogenous risk). The principal would be greatly
assisted in her decision making if she had knowledge of the "function" which induces the
agent to choose an effort level based on the compensation scheme, and also knowledge
of the hidden characteristics of the agent such as his utility of income, disutility of effort,
risk attitude, reservation constraint, etc. Similarly, the agent would be able to take better
decisions if he were more aware of his risk attitude, disutility of effort and exogenous
factors. Any information, even if imperfect, would reduce either the magnitude or the
variance of risk or both. However, better information for the agent does not always
imply that the agent will choose an act or effort level that is also optimal for the
principal. In some cases, the total welfare of the agency may be reduced as a result
(Christensen, 1981).
The gap in information may be reduced by employing a system of messages from
the agent to the principal. This system of messages may be termed a "communication
structure" (Christensen, 1981). The agent chooses his action by observing a signal from


16
is from "raw data" to simple functions, complicated functions, simple rules, complex
knowledge bases, semantic nets, scripts, and so on.
One fundamental distinction can be made from observation of human learning.
The most widespread form of human learning is incidental learning. The learning
process is incidental to some other cognitive process. Perception of the world, for
example, leads to formation of concepts, classification of objects in classes or primitives,
the discovery of the abstract concepts of number, similarity, and so on (see for example,
Rand 1967). These activities are not indulged in deliberately. As opposed to incidental
learning, we have intentional learning, where there is a deliberate and explicit effort to
learn. The study of human learning processes from the standpoint of implicit or explicit
cognition is the main subject of research in psychological learning. (See for example,
Anderson, 1980; Craik and Tulving, 1975; Glass and Holyoak, 1986; Hasher and Zacks,
1979; Hebb, 1961; Mandler, 1967; Reber, 1967; Reber, 1976; Reber and Allen, 1978;
Reber et al., 1980).
A useful paradigm for the area of expert systems might be learning through
failure. The explanation facility ensures that the expert system knows why it is correct
when it is correct, but it needs to know why it is wrong when it is wrong, if it must
improve performance with time. Failure analysis helps in focussing on deficient areas
of knowledge.
Research in machine learning raises several wider epistemological issues such as
hierarchy of knowledge, contextuality, integration, conditionality, abstraction, and
reduction. The issue of hierarchy arises in induction of decision trees (see for example,


109
Experience is less than one year, AND
Education is undergraduate, AND
Age is below 18 years, AND
Exogenous RISK is low (favorable business climate), AND
General Social Skills are excellent, AND
Office and Managerial Skills are bad (no skills at all), AND
Motivation is average, AND
Physical Qualities are very bad (frail health), AND
Communication Skills are good, AND
Other Characteristics are good
THEN
Basic Pay is average, AND
Commission is low, AND
Bonus payments are high, AND
Long term payments are average, AND
Benefits are low, AND
Stock Participation is low.
The total number of possible rules for the principal is 516 = 152,587,890,625.
The goal of each trial is to pick a small number, say 500 (= 3.2768 10"7 %) of rules
from among these 516 rules so that the final rules have very high satisfaction associated
with them.


98
contract. This contract is used by the agent. The resulting output and welfare are used
by the principal to construct a "better" knowledge base through a learning procedure.
In the following we incorporate specific models and components to achieve an
implementation of our new principal-agent model. We link behavioral factors by the
model of Porter & Lawler (1968), which also incorporates the calculation of satisfaction
and subsequent effort levels by the agent. The Porter & Lawler model derives from the
instrumentality theory of motivation, which emphasizes the anticipation of future events,
unlike most models of motivation based on drive theory. The key ideas of the Porter &
Lawler model are the recognition of the appropriateness of rationality and cognition as
descriptive of the behavior of managers, and the incorporation of motives such as status,
achievement, and power as factors that play a role in attitudes and performance.
Effort is determined by the utility or value of compensation and the perceived
probability of effort leading to reward. Performance, determined by the effort level,
abilities of the agent, and role perceptions, leads to intrinsic and extrinsic rewards, which
in turn influence the satisfaction derived by the agent. A comparison of performance and
the satisfaction derived from it influences the perception of equity of reward, and
reinforces or weakens satisfaction. Performance also plays a role in the revision of the
probability of effort leading to adequate reward.
The principal and agent knowledge-bases in our model consist of rules. Each rule
has a set of antecedent variables and a set of consequent variables. The antecedent
variables are the agents behavioral characteristics and the exogenous risk, while the
consequent variables are the variables denoting the elements of compensation. The


193
TABLE 10.68: Probability Distributions for Models 4, 5, 6, and 7
VARIABLE
NOMINAL VALUES (Code Mappings)
1
2
3
4
5
AGE, A
< 20
(20,25]
(25,35]
(35,55]
> 55
Prob(A)
0.10
0.15
0.30
0.35
0.10
EDUCATION, D
none
high school
vocational
undergrad
graduate
Prob(DjA)
1
2
3
4
5
A
1
0.10
0.30
0.40
0.20
0.00
2
0.10
0.20
0.40
0.20
0.10
3
0.05
0.10
0.30
0.50
0.05
4
0.05
0.05
0.30
0.30
0.30
5
0.00
0.10
0.10
0.30
0.50
EXPERIENCE, X
none
< 2 years
< 5 years
< 20 years
> 20
years
Prob(X ¡ A)
1
2
3
4
5
A
1
0.70
0.20
0.10
0.00
0.00
2
0.60
0.30
0.10
0.00
0.00
3
0.20
0.40
0.30
0.10
0.00
4
0.00
0.10
0.30
0.60
0.00
5
0.00
0.00
0.00
0.20
0.80
GENERAL SOCIAL
SKILLS, GSS
Prob(GSSjA)
1
2
3
4
5
A
1
0.20
0.30
0.30
0.15
0.05
2
0.10
0.40
0.30
0.10
0.10
3
0.10
0.20
0.40
0.20
0.10
4
0.05
0.10
0.20
0.40
0.25
5
0.05
0.10
0.20
0.30
0.35
OFFICE AND
MANAGERIAL
SKILLS, OMS
Prob(OMS ¡ D)
1
2
3
4
5
D
1
0.60
0.25
0.05
0.05
0.05
2
0.50
0.20
0.15
0.10
0.05
3
0.30
0.30
0.20
0.10
0.10
4
0.10
0.10
0.20
0.40
0.20
5
0.05
0.05
0.30
0.40
0.20


36
we get
n n
£ <9j |i) x = 0
= 1
which is a polynomial in x, whose roots can be determined numerically.
For example, let n = 3, 9 take values {1,2,3}, /e = 1.25. Solving as above and
taking the appropriate roots, we obtain
X, 2.2752509, X2 -1.5132312, giving
p, 0.7882, p2 = 0.1671, and p3 0.0382.
Partial knowledge of probabilities. Suppose we know p¡, i = l,...,k. Since we
have n-1 degrees of freedom in choosing p¡, assume k < n-2 to make the example non
trivial. Then, the problem may be formulated as:
n
n
max g( {pA )
{Pi}
- Pi In P + A.
i C+1
E Pi + Q 1 '
= k*l
k
where g = ^2 Pi-
i = 1
Solving, we obtain
Pi
1 q
n k'
V i
k+1,
n.
This is again fairly intuitive: the remaining probability 1-q is distributed non-
informatively over the rest of the probability space. For example, if n = 4, p, = 0.5,
and p2 = 0.3, then k = 2, q = 0.8, and p3 = p4 = (1 0.8)/(4 2) = 0.2/2 = 0.1.
Note that the first case is a special case of the last one, with q = k = 0.


144
TABLE 9.29: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 5
COMPENSATION
VARIABLE
VALUES OF THE VARIABLE
1
2
3
4
5
BASIC PAY
5.9
15.6
18.0
9.7
50.7
SHARE
96.5
1.5
0.9
0.8
0.4
BONUS
43.1
oo
d
27.0
11.9
7.1
TERMINAL PAY
89.8
1.9
OO
cn
2.4
2.0
BENEFITS
70.7
18.1
3.6
3.0
4.6
STOCK
80.6
9.9
4.7
2.5
2.3
TABLE 9.30: Range, Mean and Standard Deviation of Values of Compensation
Variables in the Final Knowledge Base in Experiment 5
Variable
Minimum
Maximum
Mean
S.D.
BP
1.0000
5.0000
3.8376590
1.3484571
S
L000
5.0000
1.0692112
0.4127470
BO
1.0000
5.0000
2.2910941
1.3171851
TP
1.0000
5.0000
1.2498728
0.8092869
B
1.0000
5.0000
1.5251908
1.0241491
SP
1.0000
5.0000
1.3603053
0.8659971
TABLE 9.31: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 5
(Spearman Correlation Coefficients in the first row for each variable,
Prob> ¡R¡ under Ho: Rho=0 in the second)
BP
S
BO
TP
B
SP
BP
1.00000
-0.05978
0.15907
-0.05684
-0.00131
0.03886
0.00000
0.0080
0.0001
0.0117
0.9538
0.0850
S
-0.05978
1.00000
-0.00454
0.01208
0.05571
-0.02912
0.0080
0.00000
0.8408
0.5925
0.0135
0.1970
BO
0.15907
-0.00454
1.00000
0.02932
-0.02295
0.05081
0.0001
0.8408
0.00000
0.1930
0.3093
0.0243
TP
-0.05684
0.01208
0.02932
1.00000
-0.00354
0.00990
0.0117
0.5925
0.1939
0.00000
0.8755
0.6611
B
-0.00131
0.05571
-0.02295
-0.00354
1.00000
0.06052
0.9538
0.0135
0.3093
0.8755
0.00000
0.0073
SP
0.03886
-0.02912
0.05081
0.00990
0.06052
1.00000
0.0850
0.1970
0.0243
0.6611
0.0073
0.00000


where
C E range(g), and
V is the agents private information.
101
The two constraints of the original problem (Individual Rationality and Incentive
Compatibility) are subsumed in the calculation of F. The agent, for example, selects his
effort level so as to increase his satisfaction or welfare based on his behavioral
characteristics and the compensation plan offered by the principal. It is not necessary
to check for IRC explicitly. Our model ensures that the agent, when presented with a
compensation plan that does not satisfy his IRC, picks an effort level that yields
extremely low total satisfaction. The dynamic learning process (described below)
discards all such compensation plans. In order to formalize the constraints in our new
model, it is necessary to introduce details of the functions, knowledge bases,
representation scheme for the knowledge bases, and the inference strategy. This is done
in Section 9.3.
9.2 An Implementation and Study
To both illustrate our method and to study the results of our approach, a series
of experiments were conducted. All the simulation experiments start with the same
initial set of rules for the principal, with the variables denoting agent characteristics
acting as the antecedents and the variables denoting elements of compensation acting as
consequents. This initial knowledge base of 500 rules is generated randomly, which
ensures that no initial bias is introduced into the model.


100
Sp = SP(V,Effort,C), and
S = S(SA,SP),
where V is the agents private information about the principal and her company.
Thus, S(b¡,Ci) denotes the total satisfaction derived when the agent has the
behavioral profile b¡ and the principal offers compensation plan c¡. Define fitness to be
the total satisfaction S(b;,Ci) normalized with respect to the whole knowledge base K. Let
F(g) denote the average fitness of a mapping g G G which specifies a knowledge base
1C£B*C.
1 n
Fig) = Y,s{bi'ci)' biEB' Cjtc.
n 1=1
The objective function of the principal-agent problem in our formulation is:
Max E EF-(sr) ] =E [A SibilCi)]
n 2 1
gzG
= e [- s(b, c,e, v) ]
nU.
= E S(E, C, 0, V) ] .
Our formulation of the principal-agent problem may be stated formally as:
Max E [F(gr) ] = E [S(E,C,Q)]
geG
such that
E e aigmax SA(B,C,,V),


132
TABLE 9.14: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 2 Eigenvalues of the Correlation Matrix
Factors
1
2
3
4
5
6
Eigenvalue
1.562150
1.349480
1.288563
1.186437
1.075113
1.008861
Difference
0.212669
0.060917
0.102126
0.111324
0.066252
0.039300
Proportion
0.1202
0.1038
0.0991
0.0913
0.0827
0.0776
Cumulative
0.1202
0.2240
0.3231
0.4144
0.4971
0.5747
7
8
9
10
11
12
Eigenvalue
0.969560
0.913091
0.869975
0.797047
0.744512
0.637679
Difference
0.056469
0.043117
0.072927
0.052535
0.106833
0.040147
Proportion
0.0746
0.0702
0.0669
0.0613
0.0573
0.0491
Cumulative
0.6492
0.7195
0.7864
0.8477
0.9050
0.9540
13
14
15
16
Eigenvalue
0.597532
0.000000
0.000000
0.000000
Difference
0.597532
0.000000
0.000000
Proportion
0.0460
0.0000
0.0000
0.0000
Cumulative
1.0000
1.0000
1.0000
1.0000


72
5.3.3 Model 3
Holmstroms model (Holmstrom, 1979) examines the role of imperfect
information under two conditions: (i) when the compensation scheme is based on output
alone, and (ii) when additional information is used. The assumptions about technology,
information and timing are more or less standard, as in the earlier models. The model
specifically uses the following:
(a) In the first part of the model, almost all information is public; in the second
part, asymmetry is brought in by assuming extra knowledge on the part of
the agent.
(b) output is a function of the agents effort and state of nature: q == q(e,0), and
3q/3e > 0.
(c) The agents utility function is separable in compensation and effort, where
UA(c) is defined on compensation, and d(e) is the disutility defined on effort.
(d) Disutility of effort d(e) is increasing in effort.
(e) The agent is risk averse, so that UA < 0.
(f) The principal is weakly risk neutral, so that Up < 0.
(g) Compensation is based on output alone.
(h) Knowledge of the probability distribution on the state of nature 0 is public.
(i) Timing: The agent chooses effort before the state of nature is observed.
The problem:
(P) Maxc6C eeE E[UP(q c(q))]


21
4. The learning algorithm(s) of the chosen learning paradigm(s) execute(s).
2.3.3 Probably Approximately Close Learning
Early research on inductive inference dealt with supervised learning from
examples (see for example, Michalski, 1983; Michalski, Carbonell, and Mitchell, 1983).
The goal was to learn the correct concept by looking at both positive and negative
examples of the concept in question. These examples were provided in one of two ways:
either the learner obtained them by observation, or they were provided to the learner by
some external instructor. In both cases, the class to which each example belonged was
conveyed to the learner by the instructor (supervisor, or oracle). The examples provided
to the learner were drawn from a population of examples or instances. This is the
framework underlying early research in inductive inference (see for example, Quinlan,
1979; Quinlan, 1986: Angluin and Smith 1983).
Probably Approximately Close Identification (or PAC-ID for short) is a powerful
machine-learning methodology that seeks inductive solutions in a supervised
nonincremental learning environment. It may be viewed as a multiple-criteria learning
problem in which there are at least three major objectives:
(1) to derive (or induce) the correct solution, concept or rule, which is as close as we
please to the optimal (which is unknown);
(2) to achieve as high a degree of confidence as we please that the solution so derived
above is in fact as close to the optimal as we intended;
(3) to ensure that the "cost" of achieving the above two objectives is "reasonable."


13
The above inadequacies on the part of humans pertain to higher cognitive
thinking. It goes without saying that humans are poor at manipulating numbers quickly,
and are subject to physical fatigue and lack of concentration when involved in mental
activity for a long time. Computers are, of course, subject to no such limitations.
It is important to note that these inadequacies usually do not lead to disastrous
consequences in most everyday circumstances. However, the complexity of the modem
world gives rise to intricate and substantial problems, solutions to which forbid
inadequacies of the above type.
Machine learning must be viewed as an integrated research area that seeks to
understand the learning strategies employed by humans, incorporate them into learning
algorithms, remove any cognitive inadequacies faced by humans, investigate the
possibility of better learning strategies, and characterize the solutions yielded by such
research in terms of proof of correctness, convergence to optimality (where meaningful),
robustness, graceful degradation, intelligibility, credibility, and plausibility.
Such an integrated view does not see the different goals of machine learning
research as separate and clashing; insights in one area have implications for another.
For example, insights into how humans learn help spot their strengths and weaknesses,
which motivates research into how to incorporate the strengths into algorithms and how
to cover up the weaknesses; similarly, discovering solutions from machine learning
algorithms that are at first nonintuitive to humans motivates deeper analysis of the
domain theory and of the human cognitive processes in order to come up with at least
plausible explanations.


205
where rc is the critical correlation value, n is the number of variables, and r is the
position number of the factor being considered.
The Burt-Banks formula ensures that the acceptable level of factor loadings
increases for later factors, so that the criteria for significance become more stringent as
one progresses from the first factor to higher factors. This is essential, because specific
variance plays an increasing role in later factors at the expense of common variance.
The Burt-Banks formula, in addition to adjusting the significance, also accounts for the
sample size and the number of variables.


116
therefore ln(501) 6.2166061. Addition of constraints or information (such as the
value of the mean or variance) may result in a smaller entropy. The object of
calculating the entropy of the knowledge base is to measure its informativeness. When
the fitnesses, expressed as a distribution, achieve the maximum entropy while satisfying
all the constraints of the system, the knowledge base is most informative yet maximally
non-committal (see, for example, Jaynes 1982, 1986a, 1986b, 1991). An entropy value
which is smaller than the maximum indicates some loss of information, while a larger
entropy indicates unwarranted assumption of information. The entropy values will be
compared across experiments to give an indication of the nature of the learned rules.
9.4 Results
The distribution of first iteration to achieve the maximum fitness bound is shown
in Table 9.2 (expressed as a percentage) for the experiments. The table shows that there
is more than a 38% chance of the maximum occurring within the first 30 iterations, a
50% chance of the maximum occurring within the first 60 iterations, and more than a
78% chance that it will do so within the first 120 iterations.
Learning appeared to converge quickly to the best knowledge base formed over
the 200 learning episodes. Table 9.2 only indicates the way the learning process
converges. Based on a number of pre-tests, this trend was found to be consistent.
However, it should not be taken as an exact guide in any replication of the experiments.
Since random mutations in the learning process might result in rules which are
not representative of the agent, the final knowledge base is processed to remove such


examples to traditional agency theory and that emphasize the need for going beyond the
traditional framework. The new framework is more robust, easily extensible in a
modular manner, and yields contracts tailored to the behavioral characteristics of
individual agents.
Factor analysis of final knowledge bases after extensive learning shows that
elements of compensation besides basic pay and share of output play a greater role in
characterizing good contracts. The learning algorithms tailor contracts to the behavioral
and motivational characteristics of individual agents. Further, neither did perfect
information yield the highest satisfaction nor did the complete absence of information
yield the least satisfaction. This calls into question the traditional agency wisdom that
more information is always desirable.
Studies of other models study the effect of two different policies of evaluating
agents performance by the principal-individualized (discriminatory) evaluation versus the
relative (nondiscriminatory) evaluation. The results suggest guidelines for employing
different types of models to simulate different agency environments.
xvi


110
9.3.2 Inference Method
The key heuristics that motivate the inference process are:
(1) compensation plans are conditional on the characteristics of the agent and the
assessment of exogenous risk;
(2) compensation plans which are close to optimal, rather than optimal, are sought.
We assume that the agent and the principal both have the same information on the
exogenous risk. At each learning episode in an experiment, the values in the rules are
changed by means of applying genetic operators (see Chapter 3 for details). The learning
algorithm ensures that rules having "robust" combinations of compensation plans survive
and refine over learning episodes. Such compensation plans are then identified as most
effective for that particular agent.
The "functional" relationship of the different variables in the inference scheme
is as follows (the subscript t denotes the learning episode or time):
Effort, = g(f1(Ct),f2(Vt),PPERt,IRt.1,PEPRO,
where C, is the compensation offered by the principal in time or learning episode
t,
where PPER denotes perceived probability of effort leading to reward,
PEPR denotes perceived equity of past reward,
PERR is perceived equity of current reward,
V, = (CE,, WE,, ST AT,), the agents private information in time t,
g is a fixed real-valued effort selection mapping,
f, is a fixed real-valued mapping of compensation, and


55
(b) the agent accepts the contract;
(c) the agent picks an effort level e* which is a solution to M1.A2 and reports
the corresponding c* (or its index if appropriate) to the principal.
2. The agent may decide to solve an additional problem: from among two or more
competing optimal effort levels, he may wish to select a minimum effort level.
Then, his problem would be:
(Ml.A3) Min e* d(e*)
such that
e* G argmaxe 6 E UA[c* d(e)].
Example:
Let E = (e,, 63},
C* = {cc2,c3}.
Suppose,
Ci(q(e,)) = 5, d(e,) = 2;
C2(q(e2)) = 6, dfe) = 3;
c3(q(e3)) = 6, d(e,) = 4;
The net compensation to the agent in choosing the three effort levels is 3, 3, and
2 respectively. Assuming d(e) is monotone increasing in e, the agent chooses e!
to e2, and so prefers compensation c, to C2.


LIST OF TABLES
Table page
9.1: Characterization of Agents 125
9.2: Iteration of First Occurrence of Maximum Fitness 126
9.3: Learning Statistics for Fitness of Final Knowledge Bases 126
9.4: Entropy of Final Knowledge Bases and Closeness to the Maximum 126
9.5: Frequency (as Percentage) of Values of Compensation Variables in the Final
Knowledge Base in Experiment 1 127
9.6: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 1 127
9.7: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 1 128
9.8: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 1 128
9.9: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 1 Factor Pattern 129
9.10: Experiment 1 Varimax Rotation 130
9.11: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 2 131
9.12: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 2 131
9.13: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 2 131
viii


46
and the firm, or the unobservability or ignorance of "hidden characteristics" (in the latter
sense, moral hazard is caused by "hidden effort or actions").
In the theory of agency, the hidden characteristic problem is addressed by
designing various sorting and screening mechanisms, or communication systems that pass
signals or messages about the hidden characteristics (of course, the latter can also be used
to solve the moral hazard problem).
On the one hand, the screening mechanisms can be so arranged as to induce the
target party to select by itself one of the several alternative contracts (or "packages").
The selection would then reveal some particular hidden characteristic of the party. In
such cases, these mechanisms are called "self-selection" devices. See, for example,
Spremann (1987) for a discussion of self-selection contracts designed to reveal the agents
risk attitude. On the other hand, the screening mechanisms may be used as indirect
estimators of the hidden characteristics, as when aptitude tests and interviews are used
to select agents.
The significance of the problem caused by the asymmetry of information is related
to the degree of lack of trust between the parties to the agency contract which, however,
may be compensated for by observation of effort. However, most real life situations
involving an agency relationship of any complexity are characterized not only by a lack
of trust but also by a lack of observability of the agents effort. The full context to the
concept of information asymmetry is the fact that each party in the agency relationship
is either unaware or has only imperfect knowledge of certain factors which are better
known to the other party.


185
TABLE 10.47: Correlation of Principals Satisfaction with Agents Factors and
Agents Satisfaction (Model 6)
PRINCIPALS
SATISFACTION
AGENTS FACTORS
AGENTS SATISFACTION
E[QUIT]
SD[NORMAL]
E[QUIT]
E[ALL]
E[SATISFACTION]
+
-
-
SD[SATISFACTION]
+
4-
+
TABLE 10.48: Correlation of Principals Factor with Agents Factor (Model 6)
E[FIRED]
SD[FIRED]
SD[NORMAL]
PRINCIPALS
FACTOR
-
-
+
TABLE 10.49: Correlation of LP and CP with Simulation Statistics (Model 7)
AVEFIT
MAXFIT
VARIANCE
ENTROPY
LP
-
+
CP
-
+
+
-
TABLE 10.50: Correlation of LP and CP with Compensation Offered to Agents
(Model 7)
E1
SD1
E2
SD2
E3
SD3
SD4
SD5
E6
SD6
E7
SD7
LP
-
-
-
-
-
-
-
-
-
-
+
CP
-
+
+
+
+
1 BASIC PAY; 2 SHARE OF OUTPUT; 3 BONUS PAYMENTS; 4 TERMINAL
PAY;
5 BENEFITS; 6 STOCK PARTICIPATION; 7 TOTAL CONTRACT


112
(2) an act of nature is generated randomly according to the specified distribution of
exogenous risk;
(3) output is a function of effort and the act of nature;
(4) performance is a function of output and effort;
(5) the agents intrinsic reward is calculated;
(6) the agents perceived equity of reward is calculated;
(7) the agents disutility of effort is calculated;
(8) the agents satisfaction is a function of effort, performance, act of nature, intrinsic
reward, perceived equity of reward, compensation, and disutility of effort;
(9) the principals satisfaction is a function of output and compensation; and
(10) the total satisfaction is the sum of the satisfactions of the agent and the principal.
The functions used in inference, selection of effort by the agent, and calculation
of satisfaction are given below. The variables are multiplied by coefficients which
denote an arbitrary priority of these variables for decision-making. Any such priority
scheme may be used, or the functions replaced by knowledge-bases which help decide
in selecting or calculating values for the decision variables. These functions are kept
fixed for all the agents in the experiments. In function f,0 for example, basic pay
received the greatest weight, and terminal pay the least. Consideration of basic pay and
share of output as the most important variables in determination of effort is consistent
with the assumptions in the traditional principal-agent theory. Further, based on her
experience of most agents, the principal expects the company environment and corporate
ranking to play a more important role in the agents acceptance of contracts and in


20
ML3: If a problem description similar to the problem on hand exists in a different
domain or situation and that problem has a known solution,
then use leaming-by-analogy techniques.
ML4: If several facts are known about a domain including axioms and production rules,
then use deductive learning techniques.
ML5: If undefined variables or unknown variables are present and no other learning rule
was successful,
then use the leaming-from-instruction paradigm.
In all cases of learning, meta-rules dictate learning strategies, whether explicitly as in a
multi-strategy system, or implicitly as when the researcher or user selects a paradigm.
Just as in expert systems, the learning strategy may be either goal directed or
knowledge directed. Goal-directed learning proceeds as follows:
1. Meta-rules select learning paradigm(s).
2. Learner imposes the learning paradigm on the knowledge base.
3. The structure of the knowledge base and the characteristics of the paradigm
determine the representation scheme.
4. The learning algorithm(s) of the paradigm(s) execute(s).
Knowledge directed learning, on the other hand, proceeds as follows:
1. The learner examines the available knowledge base.
2. The structure of the knowledge base limits the extent and type of learning, which
is determined by the meta-rules.
The learner chooses an appropriate representation scheme.
3.


Ill
f2 is a fixed real-valued mapping of the agents private information;
similarly, functions f3 through f10, and h, through h3 are fixed real-valued mapping
defined on the appropriate domains;
Output, = f3(Effort RISKJ;
PERF, = f4(Outputt, Effort,);
IR, = f5(CE,, WE,, ST,);
PERR, = f6(PERF h,(C,));
Disutility, = f7(EffortJ;
PEPR, = PERR,.,;
SA, = fg(PERF IR,, h2(Q, PERR,, Effort,, RISK,, Disutility,);
Sp, = f9(0utput h3(C Output^); and
St = floC^AD SpJ.
The functions g, f, through fio and h, through h3 used in the inference scheme
to select effort levels, infer intrinsic reward, disutility, satisfactions, etc., are given in
Section 5.3 below.
9.3.3 Calculation of Satisfaction
At each learning episode, the following steps are carried out to compute the
satisfaction of the principal and the agent:
(0) the principal infers a compensation plan;
(1) the agent selects an effort level based on the compensation plan, his perception
of the principal, and other variables from the Porter & Lawler model;


210
Harris, M. and Raviv, A. (1979). "Optimal Incentive Contracts with Imperfect
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Hart, P.E., Duda, R.O., and Einaudi, M.T. (1978). "A Computer-based Consultation
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Hasher, L., and Zacks, R.T. (1979). "Automatic and Effortful Processes in Memory."
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Haussler, D. (1988). "Quantifying Inductive Bias: AI Learning Algorithms and Valiants
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Haussler, D. (1989). "Learning Conjunctive Concepts in Structural Domains." Machine
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Kodratoff, Y. and Michalski, R. (eds.), Morgan Kaufmann, San Mateo, CA., pp.
641-669.
Haussler, D. (1990b). "Decision Theoretic Generalizations of the PAC Learning Model
for Neural Net and Other Learning Applications." Technical Report UCSC-CRL-
91-02, University of CA, Santa Cruz.
Hayes-Roth, F., and Lesser, V.R. (1977). "Focus of Attention in the Hearsay-II
System." Proc. IJCAI 5.
Hayes-Roth, F., and McDermott, J. (1978). "An Interference Matching Technique for
Inducing Abstractions." CACM 21(5), pp. 401-410.
Hebb, D.O. (1961). "Distinctive Features of Learning in the Higher Animal." In Brain
Mechanisms and Learning; Delafresnaye, J.F. (ed.), Blackwell, London.
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Holland, J.H. (1986). "Escaping Brittleness: The Possibilities of General-Purpose
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623.
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10, pp. 74-91.


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
A KNOWLEDGE-INTENSIVE MACHINE-LEARNING APPROACH
TO THE PRINCIPAL-AGENT PROBLEM
By
Kiran K. Garimella
August 1993
Chairperson: Gary J. Koehler
Major Department: Decision and Information Sciences
The objective of the research is to explore an alternative approach to the solution
of the principal-agent problem, which is extremely important since it is applicable in
almost all business environments. It has been traditionally addressed by the optimization-
analytical framework. However, there is a clearly recognized need for techniques that
allow the incorporation of behavioral and motivational characteristics of the agent and
the principal that influence their selection of effort and payment levels.
The alternative proposed is a knowledge-intensive, machine-learning approach,
where all the relevant knowledge and the constraints of the problem are taken into
account in the form of knowledge-bases.
Genetic algorithms are employed for learning, supplemented in later models by
specialization and generalization operators. A number of models are studied in order of
increasing complexity and realism. Initial studies are presented that provide counter-
xv


164
contract periods correlated negatively with all but normal agents. For agents who were
fired, there were no significant correlations. This implies that on the whole,
observability by the principal affects the agents payoffs adversely (Table 10.30).
The principals satisfaction also correlated negatively with the mean outcomes
from the agents (Table 10.33). Mean payoff from an agent may increase with an
increase in the number of learning periods while the outcome from that agent decreases
because the principal is offering smaller contracts.
The mean satisfaction of the two parties showed positive correlation only in the
case of agents who were fired and normal agents. There is an inverse relationship
between the mean satisfaction of the principal and the mean satisfaction of agents who
quit. This is also true in the case of all the agents (taken as a whole) (Table 10.31).
This implies that while the principals satisfaction was high, most of the contribution
came from agents who ultimately resigned from the agency, while those who were fired
used less effort and had commensurately higher contracts. This may suggest the reason
for why some agents quit and why some agents were fired. On the whole, this Model
is extremely dynamic since the total number of agents who quit (996) and the total
number of agents who were fired (16) is the highest for all the four models (Table
10.67).
10.6 Model 6: Discussion of Results
Model 6 has six elements of compensation, and the principal does not practice any
discrimination in evaluating the performance of the agents. As with the previous Models


182
TABLE 10.37: Correlation of LP and CP with Compensation in the Principals
Final Knowledge Base (Model 6)
E1
SD1
SD2
SD3
SD4
SD5
SD6
SD7
LP
-
-
-
-
-
-
-
CP
-
-
-
-
-
-
1 BASIC PAY; 2 SHARE OF OUTPUT; 3 BONUS PAYMENTS; 4 TERMINAL
PAY
5 BENEFITS; 6 STOCK PARTICIPATION; 7 TOTAL CONTRACT
TABLE 10.38: Correlation of LP and CP with the Movement of Agents (Model 6)
QUIT
E[QUIT]
SD[QUIT]
FIRED
E[FIRED]
SD[FIRED]
LP
+
+
+
+
CP
+
+
-
-
TABLE 10.39: Correlation of LP and CP with Agent Factors (Model 6)
SD[QUIT]
E[NORMAL]
SD[ALL]
LP
-
-
CP
+
TABLE 10.40: Correlation of LP and CP with Agents Satisfaction (Model 6)
SD[QUIT]
SD [FIRED]
LP
+
CP
+


217
Stefk, M., Aikins, J., Balzer, R., Benoit, J., Birnbaum, L., Hayes-Roth, F., and
Sacerdoti, E.D. (1982). "The Organization of Expert Systems." Artificial
Intelligence 18, pp. 135-173.
Stevens, A.L., and Collins, A. (1977). "The Goal Structure of a Socratic Tutor." BBN
Rep. No. 3518, Bolt Beranek and Newman, Inc., Cambridge, MA.
Stiglitz, J.E. (1974). "Risk Sharing and Incentives in Sharecropping." Review of
Economic Studies 41, pp. 219-256.
Tversky, A., and Kahneman, D. (1982a). "Judgment Under Uncertainty: Heuristics and
Biases." In Judgment Under Uncertainty: Heuristics and Biases; Kahneman, D.,
Slovic, P., and Tversky, A., (eds.), Cambridge University Press, New York, pp.
3-20.
Tversky, A., and Kahneman, D. (1982b). "Belief in the Law of Small Numbers." In
Judgment Under Uncertainty: Heuristics and Biases; Kahneman, D., Slovic, P.,
and Tversky, A., (eds.), Cambridge University Press, New York, pp. 23-31.
Tversky, A., and Kahneman, D. (1982c). "Availability: A Heuristic for Judging
Frequency and Probability." In Judgment Under Uncertainty: Heuristics and
Biases; Kahneman, D., Slovic, P., and Tversky, A., (eds.), Cambridge
University Press, New York, pp. 163-178.
Tversky, A., and Kahneman, D. (1982d). "The Simulation Heuristic." In Judgment
Under Uncertainty: Heuristics and Biases; Kahneman, D., Slovic, P., and
Tversky, A., (eds.), Cambridge University Press, New York, pp. 201-210.
Valiant, L.G. (1984). "A Theory of the Learnable." CACM 27 (11), pp. 1134-1142.
Valiant, L.G. (1985). "Learning Disjunctions of Conjunctions." Proc. 9th UCAI 1, pp.
560-566.
Vapnik, V.N. (1982). Estimation of Dependences Based on Empirical Data. Springer-
Verlag, New York.
Vapnik, V.N., and Chervonenkis, A.Ya. (1971). "On the Uniform Convergence of
Relative Frequencies of Events to Their Probabilities." Theory of Probability and
its Applications 16(2), pp. 264-280.
Vere, S.A. (1975). "Induction of Concepts in the Predicate Calculus." Proc. 4th IJCAI,
pp. 281-287.


To my mother, Dr. Seeta Garimella


137
TABLE 9.21: Factor Analysis (Principal Components Method) of the Final
FACTOR
1
2
3
4
5
X
-0.59074
-0.06170
-0.06894
0.46822
-0.20218
D
0.00000
0.00000
0.00000
0.00000
0.00000
A
-0.00000
0.00000
0.00000
-0.00000
-0.00000
RISK
0.10996
0.76295
0.33072
-0.11407
-0.01594
GSS
0.85184
0.10329
0.21497
-0.12037
-0.04482
OMS
0.80467
0.01491
0.07961
0.16731
-0.18963
M
-0.00000
0.00000
-0.00000
0.00000
0.00000
PQ
-0.00000
0.00000
-0.00000
0.00000
0.00000
L
-0.00000
0.00000
-0.00000
0.00000
0.00000
OPC
-0.00000
0.00000
-0.00000
0.00000
0.00000
BP
-0.39157
0.65888
0.22137
0.06324
0.23306
S
0.17892
-0.38179
0.38789
0.52832
0.35570
BO
0.13728
0.13920
-0.35713
-0.07526
0.82400
TP
-0.12358
-0.02483
0.78267
0.33425
0.10374
B
0.29624
0.09962
-0.43582
0.64893
0.08771
SP
0.10276
0.52831
-0.31264
0.45432
-0.24887
FACTOR
6
7
8
9
10
X
0.50944
0.05741
-0.05787
0.29569
0.16957
D
0.00000
0.00000
0.00000
0.00000
0.00000
A
-0.00000
0.00000
-0.00000
0.00000
-0.00000
RISK
0.19694
-0.09151
-0.48027
-0.04820
-0.05509
GSS
0.03364
-0.02060
0.09967
0.10779
0.42176
OMS
0.29181
0.03604
0.17912
0.22710
-0.33448
M
-0.00000
0.00000
-0.00000
-0.00000
0.00000
PQ
-0.00000
0.00000
0.00000
-0.00000
0.00000
L
-0.00000
0.00000
-0.00000
-0.00000
0.00000
OPC
-0.00000
0.00000
0.00000
0.00000
0.00000
BP
-0.19754
-0.26443
0.35986
0.25771
-0.01930
S
-0.35026
-0.00881
-0.28183
0.25181
-0.02289
BO
0.27700
0.26878
0.01950
0.01442
0.00576
TP
0.18578
0.19317
0.20941
-0.36516
0.00462
B
0.06503
-0.44763
0.00951
-0.27895
0.03276
SP
-0.32300
0.48794
0.01272
-0.03113
0.02641
M, PQ, L, and OPC; 1.0 for the rest of the variables.


50
The word "scheme" is used here instead of "function" since complicated
compensation packages will be considered as an extension later on. In the literature, the
word "scheme" may be seen, but it is used in the sense of "function", and several nice
properties are assumed for the function (such as continuity, differentiability, and so on).
Depending on the contract, the compensation may be negative a penalty for the agent.
Typical components of the compensation functions considered in the literature are rent
(fixed and possibly negative), and share of the output.
The principals residuum. The economic incentive to the principal to engage in
the agency is the principals residuum. The residuum is the output (expressed in
monetary terms) less the compensation to the agent. Hence, the principal is sometimes
called the residual claimant.
Payoff. Both the agents compensation and the principals residuum are called
the payoffs.
Reservation welfare (of the agent). The monetary equivalent of the best of the
alternative opportunities (with other competing principals, if any) available to the agent
is known as the reservation welfare of the agent. Accordingly, it is the minimum
compensation that induces an agent to accept the contract, but not necessarily induce him
to his best effort level. Also known as reservation utility or individual utility, it is
variously denoted in the literature as m or .
Disutility of effort. The cost of inputs which the agent must supply himself when
he expends effort contributes to disutility, and hence is called the disutility of effort.


152
1. The agent knows his own characteristics and has access to his private information,
both of which affect effort selection. This information is personal to the agent
and not shared with the other agents or with the principal.
2. The principal possesses a personal knowledge base which consists of if-then rules.
These rules help the principal select compensation schemes based on her estimate
of the agents characteristics. The principal also has available to her an estimate
of the agents characteristics. Some of these estimates are exact (eg. age), while
others are close (such estimates are based on some deviation around the true
characteristics).
3. The principal can only observe the exogenous risk parameter ex-post. The
principal evaluates the performance of each agent in the light of the observed ex
post risk and may decide to fire or retain him.
4. All the agents share a common probability distribution from which their
reservation welfare is derived. This distribution (called the rw-pdf) is for a
random variable which is a sum of the values of the elements of compensation.
In Models 4 and 5, this sum ranges from 2 to 10 (since they have two elements
of compensation, and each element has 5 possible values from 1 to 5). The rw-
pdf has a peak value at 4 with probability mass 0.6. In Models 6 and 7, this sum
ranges from 6 to 30 (since they have six elements of compensation), and the rw-
pdf has a probability mass of 0.6 at its peak value of 12. For all the models, the
rw-pdf is monotonically increasing for values below the peak value, and is
monotonically decreasing for values after the peak value.


148
TABLE 9.38: Expected Factor Identification of Behavioral and Risk Variables for the
Five Experiments Derived from the Direct Factor Pattern
VARIABLE
EXPECTED FACTOR IDENTIFICATION
Exp 1
Exp 2
Exp 3
Exp 4
Exp 5
Risk
0.2594
0.2238
0.2490
0.2430
0.0000
Experience
0.2808
0.2518
0.2875
0.2688
0.0000
Education
0.0000
0.0000
0.0000
0.2454
0.0000
Age
0.0000
0.0000
0.0000
0.2275
0.0000
General Social Skills
0.2670
0.2117
0.2685
0.2441
0.0000
Managerial Skills
0.0000
0.2244
0.2757
0.2656
0.0000
Motivation
0.2622
0.2160
0.0000
0.1970
0.0000
Physical Qualities
0.2509
0.2667
0.0000
0.2262
0.0000
Communication
Ability
0.0000
0.2489
0.0000
0.2294
0.0000
Other Qualities
0.0000
0.0000
0.0000
0.2396
0.0000
TABLE 9.39: Expected Factor Identification of Behavioral and Risk Variables for the
Five Experiments Derived from Varimax Rotated Factor Analytic Solution
VARIABLE
EXPECTED FACTOR IDENTIFICATION
Exp 1
Exp 2
Exp 3
Exp 4
Exp 5
Risk
0.1226
0.1153
0.1919
0.0472
0.0000
Experience
0.1015
0.1300
0.2416
0.0337
0.0000
Education
0.0000
0.0000
0.0000
0.0502
0.0000
Age
0.0000
0.0000
0.0000
0.0549
0.0000
General Social Skills
0.1251
0.1016
0.1648
0.0204
0.0000
Managerial Skills
0.0000
0.1030
0.2086
0.0507
0.0000
Motivation
0.1014
0.1453
0.0000
0.0272
0.0000
Physical Qualities
0.0895
0.1260
0.0000
0.1764
0.0000
Communication
Ability
0.0000
0.0900
0.0000
0.0374
0.0000
Other Qualities
0.0000
0.0000
0.0000
0.0413
0.0000


83
Secondly, a certain amount of bias is introduced into the model by requiring that
the functions involved in the constraints satisfy some properties, such as differentiability,
monotone likelihood ratio, and so on. It must be noted that many of these properties are
reasonable and meaningful from the standpoint of accepted economic theory. However,
standard economic theory itself relies heavily on concepts such as utility and risk
aversion in order to explain the behavior of economic agents. Such assumptions have
been criticized on the grounds that individuals violate them; for example, it is known that
individuals sometimes violate properties of the Neumann-Morgenstem utility functions.
Decision theory addressing economic problems also uses concepts such as utility, risk,
loss, and regret, and relies on classical statistical inference procedures. However, real
life individuals are rarely consistent in their inference, lacking in statistical sophistication,
and unreliable on probability calculations. Several references to support this view are
cited in Chapter 2. If the term "rational man" as used in economic theory means that
individuals act as if they were sophisticated and infallible (in terms of method and not
merely content), then economic analysis might very well yield erroneous solutions.
Consider, as an example, the treatment of compensation schemes in the literature.
They are assumed to be quite simple, either being linear in the output, or involving a
fixed element called the rent. (See chapter 5 for details). In practice, compensation
schemes are fairly comprehensive and involved. They cover as many contingencies as
possible, provide for a variety of payment and reward criteria, specify grievance
procedures, termination, promotion, varieties of fringe benefits, support services, access
to company resources, and so on.


103
The experiments are designed to study the compensation rules which achieve
close-to-optimal satisfaction for the principal and the agent under different informational
assumptions. Each experiment pertains to a different agent having specific behavioral
characteristics and perception of the principal or the company.
Nine characteristics of the agent. They are: experience, education, age, general
social skills, office and managerial skills, motivation, physical qualities deemed essential
to the task, language and communication skills, and miscellaneous personal
characteristics.
The elements of compensation that are taken into account are: basic pay, share
of output or commission, bonus payments, long term payments, benefits, and stock
participation.
In the calculation of satisfaction (total welfare of the principal and the agent), we
also take into account variables that denote the agents perception or assessment of the
principal or her company. These variables may be called the agents "personal"
variables, since the principal has no information about them. The agents personal
variables we consider are: company environment, work environment, status, his own
traits and abilities, and his perceived probability of effort leading to reward.
Characterization of the agent in each of the five experiments is given below:
Agent #1 (involved in Experiment 1) is moderately experienced, has completed high
school, is above 55 years of age. His general social skills are average, but his office and
managerial skills are quite good. He has slightly above average motivation and
enthusiasm for the job, and he is more or less physically fit, but the principal is not very


168
reservation welfare of many agents may not be met. Table 10.67 confirms this. The
number of agents who quit of their own accord is the highest of all models. Similarly,
the principal is unable to induce proper effort selection using only two elements of
compensation. However, this does not stop her from punishing (effectively and
individually) poor performers. This leads us to expect that the number of agents fired
in Model 5 would be highest of all the models. Table 10.67 again confirms this
expectation.
Agent factors indicate whether the agents were better off or worse off on the
whole in the particular agency model (with positive factors indicating better off and
negative factors indicating worse off). This is a measure of the difference in satisfaction
enjoyed by the agents normalized for number of learning periods and contract periods.
Agents were better off to a greater extent when the number of compensation elements
were two rather than six, and when the principal practiced non-discriminatory evaluation
of agents performance. This is because the principal has less scope for controlling
agents effort selection through complex contracts, and no individualized evaluation of
agents performances and hence no possibility of penalizing agents with poor
performance. Therefore, in all cases except Model 7, agents as a whole were better off.
Looking at specific types of agents, the agents who quit were better off in the
non-discriminatory cases (Models 4 and 6), and in the case of two elements of
compensation (Models 4 and 5). The same holds true for agents who were fired.
However, for normal agents, the greatest increase in satisfaction (compared across the
models) occurred in Model 5 (two elements of compensation with discriminatory


81
and ICC. Let Y denote a non-informative signal. Then, the two results yield a ranking
of informativeness: W(Y) > W(Y). When Q is an information system denoting perfect
observability of the output q, and the timing of the agency relationship is as in model 1
(i.e. payment is made to the agent after observing the output), then W(Q) > W(Y) as
well.


5.1.5 Limited Observability, Moral Hazard, and Monitoring 44
5.1.6 Informational Asymmetry, Adverse Selection, and Screening 45
5.1.7 Efficiency of Cooperation and Incentive Compatibility 47
5.1.8 Agency Costs 47
5.2 Formulation of the Principal-Agent Problem 48
5.3 Main Results in the Literature 62
5.3.1 Model 1: The Linear-Exponential-Normal Model 63
5.3.2 Model 2 68
5.3.3 Model 3 72
5.3.4 Model 4: Communication under Asymmetry 77
5.3.5 Model G: Some General Results 80
6 METHODOLOGICAL ANALYSIS 82
7 MOTIVATION THEORY 87
8 RESEARCH FRAMEWORK 92
9 MODEL 3 97
9.1 Introduction 97
9.2 An Implementation and Study 101
9.3 Details of Experiments 106
9.3.1 Rule Representation 106
9.3.2 Inference Method 110
9.3.3 Calculation of Satisfaction Ill
9.3.4 Genetic Learning Details 114
9.3.5 Statistics Captured for Analysis 115
9.4 Results 116
9.5 Analysis of Results 118
10 REALISTIC AGENCY MODELS 149
10.1 Characteristics of Agents 157
10.2 Learning with Specialization and Generalization 158
10.3 Notation and Conventions 160
10.4 Model 4: Discussion of Results 161
10.5 Model 5: Discussion of Results 163
10.6 Model 6: Discussion of Results 164
10.7 Model 7: Discussion of Results 165
10.8 Comparison of the Models 167
10.9 Examination of Learning 172
11 CONCLUSION 194
vi


3
role of constraints. Maximum entropy is related to machine learning by the fact that the
initial distributions (or assumptions) used in a learning framework, such as genetic
algorithms, may be maximum entropy distributions. A topic of research interest is the
development of machine learning algorithms or frameworks that are robust with respect
to maximum entropy. In other words, deviation of initial distributions from maximum
entropy distributions should not have any significant effect on the learning algorithms (in
the sense of departure from good solutions).
The overall goal of the research is to present an integrated methodology involving
machine learning with genetic algorithms in knowledge bases and to illustrate its use by
application to an important problem in business. The principal-agent problem was
chosen for the following reasons: it is widespread, important, nontrivial, and fairly
general so that different models of the problem can be investigated, and information-
theoretic considerations play a crucial role in the problem. Moreover, a fair amount of
interest over the problem has been generated among researchers in economics, finance,
accounting, and game theory, whose predominant approach to the problem is that of
constrained optimization. Several analytical insights have been generated, which should
serve as points of comparison to results that are expected from our new methodology.
The most important component of the new proposed methodology is information
in the form of knowledge bases, coupled with strength of performance of the individual
pieces of knowledge. These knowledge bases, the associated strengths, their relation to
one another, and their role in the scheme of things are derived from the individuals prior
knowledge and from the theory of human behavior and motivation. These knowledge


154
terminal pay, benefits, and stock participation), as in the previous studies. In Model 6,
the principal follows a non-discriminatory evaluation and firing policy, while in Model
7, she follows a discriminatory policy.
The two basic control variables for the simulation are the number of learning
periods and the number of contract renegotiation (or data gathering) periods. A number
of statistics are collected in these studies, and they are grouped by their ability to address
some fundamental questions:
1. The first group of statistics pertains to the simulation methodology. They
report the state of the principals knowledge base. These statistics cover the
average and maximum fitness of the rules, their variance around the mean,
and the entropy of the normalized fitnesses.
2. The second group of statistics describes the type of compensation schemes
offered to the agents by the principal throughout the life of the agency.
They report the mean and variance of each element of compensation.
3. The third group of statistics describes the composition of compensation
schemes in the final knowledge base of the principal (i.e., at the termination
of the simulation). They report the mean and variance of each element of
compensation. These statistics differ from those in group two in that they
characterize the state of the principals knowledge base, while those in the
second group also capture the compensations activated as a result of the
characteristics of the agents who participate in the agency.


196
a consequence, the firing policy is individualized to the agents. This is described as a
"discriminatory" policy. In Models 4 and 6, the evaluation of the performance of an
agent is relative to the performance of the other agents. Hence, there is one common
firing policy for all agents. This policy is described as a "non-discriminatory" policy.
This design of the experiments enables one to study the effect of the two policies on
agency performance.
Models 4 through 7 reveal several interesting results. The practice of
discriminatory evaluation of performance is beneficial to some agents (those who work
hard and are well motivated), while it is detrimental to others (shirkers). Discrimination
is not a desirable policy for the principal, since the mean satisfaction obtained by the
principal in the discriminatory models is comparatively less. However, a discriminatory
evaluation may serve to bootstrap an organization having low morale (by firing the
shirkers), and ensuring the highest rate of increase of satisfaction for the principal.
Increasing the complexity of contracts ensures low agent turnover (because of
increased flexibility) and increased overall satisfaction. This finding takes on added
significance when the cost of human resource management (such as hiring, terminating,
and training) is taken into account. This is suggested as future research in Chapter 12.
Complexity of contracts and the selective practice of relative evaluation of agent
performance are powerful tools which can be used by the principal to achieve the goals
of the agency. Their interaction and the trade-offs involved are, however, far from
straight-forward. Section 10.4 through 10.8 provide the details. Further research is


12
Recent research has shown that it is also undeniable that humans perform very poorly in
the following respects:
* they do not solve problems in probability theory correctly ;
* while they are good at deciding cogency of information, they are poor at judging
relevance (see Raiffa, accident witnesses, etc.);
* they lack statistical sophistication;
* they find it difficult to detect contradictions in long chains of reasoning;
* they find it difficult to avoid bias in inference and in fact may not be able to
identify it.
(See for example, Einhorn, 1982; Kahneman and Tversky, 1982a, 1982b, 1982c, 1982d;
Lichtenstein et al., 1982; Nisbett et al., 1982; Tversky and Kahneman, 1982a, 1982b,
1982c, 1982d.)
Tversky and Kahneman (1982a) classify, for example, several misconceptions in
probability theory as follows:
* insensitivity to prior probability of outcomes;
* insensitivity to sample size;
* misconceptions of chance;
* insensitivity to predictability;
* the illusion of validity;
* misconceptions of regression.


67
Result 1.4: Suppose 2ao2 > 1. Then, an increase in share s requires an increase
in rent r (in order to satisfy IRC).
To see this, suppose we increase the share s by 5,
s0 = s + 8, 0 < 5 < 1-s. From Result 1.2, for IRC to hold we need,
T. Vu 2ot2)
ro 2 u 4
jj (s + 6)2(1 2oeg2)
4
-Q (1 2ao2)[52 + 2s5 + 62]
4
jj (1 2o2)2 (2sb + d2)(l 2a o2)
4 4
(2sb + 62)(1 2ao2)
4
^ r ( v 1 < 2a a2).
Result 1.5: The welfare attained by the agent is U, while the principals welfare
is given by:
v.
4 s *


121
and Terminal Pay (-0.0568), and weak positive correlations with Bonus (0.1591) and
Stock Participation (0.0389). Benefits and Share were weakly positively correlated
(0.0557). Stock Participation formed weak positive correlations with Basic Pay (0.0389),
Bonus (0.0508) and Benefits (0.0605) (Table 9.31).
Without further research, the causes of these correlations cannot be known
definitely. While the compensation schemes are definitely tailored to the behavioral
characteristics of the agents, motivation theory does not enable (at the present state of
the art) to make definitive causal connections between specific behavioral patterns and
effort-inducing compensation. Directions for future research are described in Chapter
12.
Factor analysis of the final knowledge base of each experiment was carried out
to see if the knowledge base had any significant factors. A factor with eigenvalue greater
than one may be deemed to be significant since it accounts for more variation in the rules
than any one variable alone. Table 9.9 provides a summary of pertinent data from
Tables 9.8, 9.14, 9.20, 9.26, and 9.32.
The percentage of total variation accounted for by the significant factors is rather
low, the maximum being for experiment 3. Experiment 4 required the maximum number
of factors (almost as many as the number of variables, which is 16). Experiment 4 also
had the highest average eigenvalue, and Experiment 5 the lowest. The number of
significant factors was least in the case of Experiment 5, and each factor accounted for
a greater proportion of the variation than the non-informative situation of Experiment 4.


22
PAC-ID therefore replaces the original research direction in inductive machine
learning (seeking the true solution) by the more practical goal of seeking solutions close
to the true one in polynomial time. The technique has been applied to certain classes of
concepts, such as conjunctive normal forms (CNF). Estimates of necessary distribution
independent sample sizes are derived based on the error and confidence criteria; the
sample sizes are found to be polynomial in some factor such as the number of attributes.
Applications to science and engineering have been demonstrated.
The pioneering work on PAC-ID was by Valiant (1984, 1985) who proposed the
idea of finding approximate solutions in polynomial time. The ideas of characterizing
the notion of approximation by using the concept of functional complexity of the
underlying hypothesis spaces, introducing confidence in the closeness to optimality, and
obtaining results that are independent of the underlying probability distribution with
which the supervisory examples are generated (by nature or by the supervisor), compose
the direction of the latest research. (See for example, Haussler, 1988; Haussler, 1990a;
Haussler, 1990b; Angluin, 1987; Angluin, 1988; Angluin and Laird, 1988; Blumer,
Ehrenfeucht, Haussler, and Warmuth, 1989; Pitt and Valiant, 1988; and Rivest, 1987).
The theoretical foundations for the mathematical ideas of learning convergence
with high confidence are mainly derived from ideas in statistics, probability, statistical
decision theory, and fractal theory. (See for example, Vapnik, 1982; Vapnik and
Chervonenkis, 1971; Dudley, 1978; Dudley, 1984; Dudley, 1987; Kolmogorov and
Tihomirov, 1961; Kullback, 1959; Mandelbrot, 1982; Pollard, 1984; Weiss and
Kulikowski, 1991).


175
TABLE 10.6: Correlation of LP and CP with Agents Satisfaction (Model 4)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E[NORMAL]
E[ALL]
SD[ALL]
LP
+
-
+
+
+
CP
-
+
-
+
TABLE 10.7: Correlation of LP and CP with Agents Satisfaction at Termination
(Model 4)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E[ALL]
SD[ALL]
LP
-
+
+
CP
-
+
-
+
TABLE 10.8: Correlation of LP and CP with Agency Interactions (Model 4)
E[QUIT]
SD[QUIT]
SD[FIRED]
E[NORMAL]
E[ALL]
SD[ALL]
LP
-
-
+
-
-
-
CP
+
+
+
+
+
TABLE 10.9: Correlation of LP with Rule Activation (Model 4)
E[QUIT]
SD[QUIT]
E[FIRED]
E[ALL]
SD[ALL]
LP
-
-
-
-
-
TABLE 10.10: Correlation of LP with Rule Activation in the Final Iteration
(Model 4)
E[QUIT]
SD[QUIT]
E[ALL]
SD[ALL]
LP
-
-
-
-
TABLE 10.11: Correlation of LP and CP with Principals Satisfaction and Least
Squares (Model 4)
E[SATP]
SD[SATP]
LASTSATP
FACTOR
BEH-LS
EST-LS
LP
-
+
-
-
+
+
CP
+
-
+
+


90
1954) and are administered by the individual to himself rather than by some external
agent. Extrinsic rewards are rewards administered by an external party such as the
principal.
Perceived equitable rewards describes the level of reward that an individual feels
is appropriate. The appropriateness of the reward is linked to role perceptions and
perception of performance.
Satisfaction is referred to as a "derivative variable". It is derived by the individual
(here, the agent) by comparing actual reward to perceived equitable reward. Satisfaction
may therefore be defined as the correspondence or correlation between actual reward and
perceived equitable reward.
Research in instrumentality theory is detailed in (Campbell and Pritchard, 1976;
Mitchell, 1974). Most of the tests of both their initial model and later versions have
yielded similar results: effort is predicted more accurately than performance. This makes
sense logically. Individuals have effort under their control but not always performance.
The environment (exogenous or random risk) plays a major role in determining if and
how effort yields levels of performance (Steers and Porter, 1983).


29
(2) when the available evidence does not favor any one alternative among others,
then the state of knowledge is described correctly by assigning equal
probabilities to all the alternatives;
(3) suppose A is an event or occurrence for which some favorable cases out of
some set of possible cases exist. Suppose also that all the cases are equally
likely. Then, the probability that A will occur is the ratio of the number of
cases favorable to A to the total number of equally possible cases. This idea
is formally expressed as
Pr [a] Number of cases favorable to A
N Number of equally possible cases '
In cases where Pr[] is difficult to estimate (such as when the number of cases is
infinite or impossible to find out), Bernoullis weak law of large numbers may be
applied, where
Pi [A]
M Number of cases favorable to A
N Total number of equally likely cases
Number of times A occurs
Number of trials
m
n '
Limit theorems in statistics show that given (M,N) as the true state of nature, the
observed frequency f(m,n) = m/n approaches Pr[A] = P(M,N) = M/N as the number
of trials increase.


12 FUTURE RESEARCH 198
12.1 Nature of the Agency 198
12.2 Behavior and Motivation Theory 199
12.3 Machine Learning 200
12.4 Maximum Entropy 203
APPENDIX FACTOR ANALYSIS 204
REFERENCES 206
BIOGRAPHICAL SKETCH 219
Vll


A. Technology:
(a) presence of uncertainty in the state of nature;
(b) compensation scheme c = c(q);
(c) output q = q(e,0);
(d) existence of known utility functions for the agent and the principal;
(e) disutility of effort for the agent is monotone increasing in effort e;
B. Public information:
(a) presence of uncertainty, and range of 0;
(b) output function q;
(c) payment functions c;
(d) range of effort levels of the agent.
Information private to the principal:
(a) the principals utility function;
(b) the principals estimate of the state of nature.
Information private to the agent:
(a) the agents utility function;
(b) the agents estimate of the state of nature;
(c) disutility of effort;
(d)reservation welfare;


CHAPTER 6
METHODOLOGICAL ANALYSIS
The solution to the principal-agent problem is influenced by the way the model
itself is setup in the literature. Highly specialized assumptions, which are necessary in
order to use the optimization technique, contribute a certain amount of bias. As an
analogy, one may note that a linear regression model assumes implicit bias by seeking
solutions only among linear relationships between the variables; a correlation coefficient
of zero therefore implies only that the variables are not linearly correlated, not that they
are not correlated. Examples of such specialized assumptions abound in the literature,
a small but typical sample of which are detailed in the models presented in Chapter 5.
The consequences of using the optimization methodology are primarily of two.
Firstly, much of the pertinent information that is available to the principal, the agent and
the researcher must be ignored, since this information deals with variables which are not
easily quantifiable, or which can only be ranked nominally, such as those that deal with
behavioral and motivational characteristics of the agent and the prior beliefs of the agent
and principal (regarding the task at hand, the environment, and other exogenous
variables). Most of this knowledge takes the form of rules linking antecedents and
consequents, and which have associated certainty factors.
82


57
such that
c* ^ UA(U), (IRC)
c argmax M1.P3.
In other words, the principal solves her problem the best way she can, and hopes
the solution is acceptable to the agent.
5. Negotiation. Negotiation of a contract can occur in two contexts:
(a) when there is no solution to the initial problem, the agent may communicate
to the principal his reservation welfare, and the principal may design new
compensation schemes or revise her old schemes so that a solution may be
found. This type of negotiation also occurs in the case of problems M1.P3
and M1.A5.
(b) The principal may offer c* E argmaxc 6 c Ml .PI. The agent either accepts
it or does not; if he does not, then the principal may offer another optimal
contract, if any. This interaction may continue until either the agent accepts
some compensation scheme or the principal runs out of optimal
compensations.
Development of the problem: Model 2. This model differs from the first by
incorporating uncertainty in the state of nature, and conditioning the compensation
functions on the output.


71
Result 2.2: Information systems having no marginal insurance value but having
marginal incentive informativeness may be used to improve risk sharing, as for example,
when the signals which are perfectly correlated with output on the agents effort are
completely observable.
Result 2.3: Under the assumptions of result 2.2, when the output alone is
observed, it must be used for both incentives and insurance. If the effort is observed as
well, then a contract may consist of two parts: one part is based on the effort, and takes
care of incentives; the other part is based on output, and so takes care of risk-sharing.
For example, consider auto insurance. The principal (the insurer) cannot observe
the actions taken by the driver (such as care, caution and good driving habits) to avoid
collisions. However, any positive signals of effort can be the basis of discounts on
insurance premiums, as for example when the driver has proof of regular maintenance
and safety check up for the vehicle or undergoes safe driving courses. Also factors such
as age, marital status and expected usage are taken into account. The "output" in this
case is the driving history, which can be used for risk- sharing; another indicator of risk
which may be used is the locale of usage (country lanes or heavy city traffic). This
example motivates result 2.4, a corollary to results 2.2 and 2.3.
Result 2,4: Information systems having no marginal incentive informativeness
but having marginal insurance value may be used to offer improved incentives.
Result 2.5: If the uncertainty in the informative signal system is influenced by
the choices of the principal and the agent, then such information systems may be used
for control in decentralized decision-making.


73
such that
E[UA(c(q),e)] > U, (IRC)
e e argmaxe.6E E[UA(c(q), e)]. (ICC)
To obtain a workable formulation, two further assumptions are made:
(a) There exists a distribution induced on output and effort by the state of
nature, denoted F(q,e), where q = q(e,0). Since 3q/de > 0 by assumption,
it implies 3F(q,e)/3e < 0. For a given e, assume 3F(q,e)/de < 0 for some
range of values q.
(b) F has density function f(q,e), where (denoting fc s= df/de) fe and f^. are well
defined for all (q,e).
The ICC constraint in (P) is replaced by its first order condition using f, and the
following formulation is obtained:
(P) Maxc{EC>eeE f UP(q c(q)) f(q,e) dq
such that
[UA(c(q)) d(e)] f(q,e) dq > U, (IRC)
UA(c(q)) fe(q,e) dq = d(e). (ICC)
Results:
Result 3.1: Let X and / be the Lagrange multipliers for IRC and ICC in (P)
respectively. Then, the optimal compensation schemes are characterized as follows:


66
Results:
Result 1.1: The optimal effort level of the agent given a compensation scheme
(r,s) is denoted e\ and is obtained by straightforward maximization to yield:
e* ss e*(r,s) = s/2.
This shows that the rent r and the reservation welfare have no impact on the selection
of the agents effort.
Result 1.2: A necessary and sufficient condition for IRC to be satisfied for a
given compensation scheme (r,s) is:
r V s2{1 ~ 2a2)
4
Result 1.3: The optimal compensation scheme for the principal is c* = (r*,s*),
where
1 + 2ao*
and
r* = u -
1 2ao:
4s
*2
Corollary 1.3: The agents optimal effort given a compensation scheme (r*,s*)
is (using result 1.1):
2 (1 + 2ao2)


146
TABLE 9.34: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 5 Varimax Rotated Factor Pattern
FACTOR
1
2
3
4
5
6
X
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
GSS
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
OMS
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
M
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
PQ
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
L
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
BP
0.07084
-0.03061
0.02061
-0.01879
-0.01860
0.99645
S
-0.0025
7
0.01489
-0.00424
0.03512
0.99909
-0.01845
BO
0.99737
0.01480
0.00534
0.00245
-0.00259
0.07065
TP
0.01471
0.99928
-0.00697
0.00628
0.01488
-0.03035
B
0.00243
0.00629
0.01183
0.99912
0.03512
-0.01864
SP
0.00531
-0.00697
0.99967
0.01181
-0.00423
0.02042
Notes: Final Communality Estimates total 6.0 and are as follows: 1.0 for BP, S,
BO, TP, B, and SP; 0.0 for the rest of the variables.
TABLE 9.35: Summary of Factor Analytic Results for the Five Experiments
Experiment
Number of Significant
Factors (Eigenvalue >
1)
Percentage of
Total Variation
Total Factors
Average
Eigenvalue
1
6
65.35
11
0.6875
2
6
57.47
13
0.8125
3
5
72.54
10
0.6250
4
7
70.78
15
0.9375
5
3
54.50
6
0.3750


133
TABLE 9.15: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 2 Factor Pattern
Factor
1
2
3
4
5
6
7
X
0.23470
0.40822
0.41989
0.10143
-0.06455
-0.47522
-0.13029
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
-0.00000
-0.00000
0.00000
-0.00000
0.00000
0.00000
-0.00000
RISK
0.40696
0.10345
-0.15114
-0.43374
0.06063
0.00857
0.09780
GSS
0.71945
0.12878
0.06651
0.25299
-0.09613
-0.02708
0.21848
OMS
0.15988
0.26111
-0.23533
0.55088
0.53138
0.02406
-0.24275
M
0.52994
-0.06812
0.35756
0.04245
0.12138
-0.00603
0.43643
PQ
-0.49072
0.18271
0.19086
0.25694
0.29339
-0.29651
0.18784
L
-0.43182
0.11417
0.46917
-0.00994
-0.26917
-0.20723
0.25407
OPC
-0.00000
-0.00000
-0.00000
0.00000
0.00000
-0.00000
-0.00000
BP
0.00206
0.73317
0.02383
-0.14116
0.09366
0.15727
-0.00144
S
0.15005
0.08440
0.48987
0.00873
-0.35507
0.37735
-0.43373
BO
0.16081
-0.64356
0.15230
0.08186
0.15639
-0.23750
0.04318
TP
-0.11221
0.09559
0.22871
-0.50489
0.50146
0.27257
0.26726
B
-0.07398
-0.24228
0.54532
0.23797
0.32011
0.41360
-0.14065
SP
-0.15402
0.09822
-0.17831
0.46301
-0.29859
0.42643
0.51464
Factor
8
9
10
11
12
13
X
-0.34093
0.12914
0.28987
-0.21169
-0.06036
-0.28162
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
-0.00000
0.00000
nmoum
-0.00000
RISK
0.64290
0.27270
0.17846
-0.21469
-0.03416
-0.18056
GSS
0.03558
-0.12787
0.18071
0.00686
-0.21839
0.49158
OMS
0.14111
0.00621
0.04899
-0.09147
0.41684
0.03269
M
-0.03356
-0.10222
-0.53502
0.03731
0.16803
-0.22844
PQ
0.21954
0.40686
-0.28804
-0.04598
-0.29716
0.16419
L
0.35726
-0.28314
0.19616
0.00520
0.37074
0.12874
OPC
-0.00000
0.00000
0.00000
0.00000
0.00000
-0.00000
BP
0.05725
-0.04855
0.03755
0.62106
-0.07920
-0.09706
S
0.05131
0.43120
-0.18876
-0.00933
0.15673
0.15771
BO
0.00810
0.35568
0.28456
0.47545
0.11527
-0.02132
TP
-0.35860
0.14954
0.18191
-0.15212
0.14461
0.21390
B
0.20155
-0.28888
0.19343
-0.05661
-0.30269
-0.17940
SP
-0.10104
0.29287
0.22341
-0.05877
0.02784
-0.18570
Notes: Final Communality Estimates total 13.0 and are as follows: 0.0 for D, A,
and OPC; 1.0 for the rest of the variables.


44
5.1.5 Limited Observability. Moral Hazard, and Monitoring
An important characteristic of principal-agent problems limited observability of
the agents actions gives rise to moral hazard. Moral hazard is a situation in which one
party (say, the agent) may take actions detrimental to the principal and which cannot be
perfectly and/or costlessly observed by the principal (see for example, [Holmstrom,
1979]). Formally, perfect observation might very well impose "infinite" costs on the
principal. The problem of unobservability is usually addressed by designing monitoring
systems or signals which act as estimators of the agents effort. The selection of
monitoring signals and their value is discussed for the case of costless signals in Harris
and Raviv (1979), Holmstrom (1979), Shavell (1979), Gjesdal (1982), Singh (1985), and
Blickle (1987). Costly signals are discussed for three cases in Blickle (1987).
On determining the appropriate monitoring signals, the principal invites the agent
to select a compensation scheme from a class of compensation schemes which she, the
principal, compiles. Suppose the principal determines monitoring signals s,, ..., sn, and
has a compensation scheme c(q, s,, ..., sj, where q is the output, which the agent
accepts. There is no agreement between the principal and the agent as to the level of the
effort e. Since the signals s¡, i = 1, ..., n determine the payoff and the effort level e of
the agent (assuming the signals have been chosen carefully), the agent is thereby induced
to an effort level which maximizes the expected utility of his payoff (or some other
decision criterion). The only decision still in the agents control is the choice of how
much payoff he wants; the assumption is that the agent is rational in an economic sense.
The principals residuum is the output q less the compensation c(*)- The principal


62
5.3 Main Results in the Literature
Several results from basic agency models will be presented using the framework
established in the development of the problem. The following will be presented for each
model:
Technology,
Information,
Timing,
Payoffs, and
Results.
It must be noted that the literature rarely presents such an explicit format; rather,
several assumptions are often buried within the results, or implied or just not stated.
Only by trying an algorithmic formulation is it possible to unearth unspecified
assumptions. In many cases, some of the factors are assumed for the sake of formal
completeness, even though the original paper neither mentions nor uses those factors in
its results. This type of modeling is essential when the algorithms are implemented
subsequently using a knowledge-intensive methodology.
One recurrent example of incomplete specification is the treatment of the agents
individual rationality constraint (IRC). The principal has to pick a compensation which
satisfies IRC. However, some consistency in using IRC is necessary. The agents
reservation welfare U is also a compensation (albeit a default one). The agent must


96
Chapter 9 describes Model 3 in detail. Chapter 10 introduces Models 4 through
7, and describes each in detail. The conclusions are given in Chapter 11, and directions
for future research are covered in Chapter 12.


135
TABLE 9.17: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 3
COMPENSATION VARIABLE
VALUES OF THE VARIABLE
1
2
3
4
5
BASIC PAY
11.1
15.9
14.3
17.5
41.3
SHARE
92.1
6.3
0.0
1.6
0.0
BONUS
30.2
33.3
25.4
7.9
3.2
TERMINAL PAY
85.7
6.3
3.2
1.6
3.2
BENEFITS
76.2
12.7
3.2
3.2
4.8
STOCK
66.7
14.3
6.3
9.5
3.2
TABLE 9.18: Range, Mean and Standard Deviation of Values of Compensation
Variables in the Final Knowledge Base in Experiment 3
Variable
Minimum
Maximum
Mean
S.D.
BP
1.00
5.00
3.6190476
1.4416452
S
1.00
4.00
1.1111111
0.4439962
BO
1.00
5.00
2.2063492
1.0649660
TP
1.00
5.00
1.3015873
0.8731648
B
1.00
5.00
1.4761905
1.0450674
SP
1.00
5.00
1.6825397
1.1475837
TABLE 9.19: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 3
BP
S
BO
TP
B
SP
BP
1.00000
-0.21239
0.04193
0.09919
-0.06653
0.16112
0.0
0.0947
0.7442
0.4392
0.6044
0.2071
S
-0.21239
1.00000
0.13992
0.06965
0.25522
-0.06207
0.0947
0.0
0.2741
0.5875
0.0435
0.6289
BO
0.04193
0.13992
1.00000
-0.02696
0.30417
0.02454
0.7442
0.2741
0.0
0.8339
0.0154
0.8486
TP
0.09919
0.06965
-0.02696
1.00000
-0.05317
-0.09539
0.4392
0.5875
0.8339
0.0
0.6790
0.4571
B
-0.06653
0.25522
0.30417
-0.05317
0.27619
0.6044
0.0435
0.0154
0.6790
0.0
0.0284
SP
0.16112
-0.06207
0.02454
-0.09539
0.27619
1.00000
0.2071
0.6289
0.8486
0.4571
0.0284
0.0


25
such as his beliefs about which combinations play an important role. In such
cases, the simulation may start with the researchers population and not a
random population; if it turns out that the whole or some part of this
knowledge is incorrect or irrelevant, then the corresponding individuals get
low fitness values and hence have a high probability of eventually
disappearing from the population.
3. The remarks in point 2 above apply in the case of mutation also. If mutation
gives rise to a useless feature, that individual gets a low fitness value and
hence has a low probability of remaining in the population for a long time.
4. Since GAs use many individuals, the probability of getting stuck at local
optima is minimized.
According to Holland (1975), there are essentially four ways in which genetic
algorithms differ from optimization techniques:
1. GAs manipulate codings of attributes directly.
2. They conduct search from a population and not from a single point.
3. It is not necessary to know or assume extra simplifications in order to
conduct the search; GAs conduct the search "blindly." It must be noted
however, that randomized search does not imply directionless search.
4. The search is conducted using stochastic operators (random selection
according to fitness) and not by using deterministic rules.


177
TABLE 10.16: Correlation of Principals Factor with Agent Factors (Model 4)
TABLE 10.17: Correlation of LP and CP with Simulation Statistics (Model 5)
AVEFIT
MAXFIT
VARIANCE
ENTROPY
LP
-
-
+
CP
-
+
+
-
TABLE 10.18: Correlation of LP and CP with Compensation Offered to Agents
(Model 5)
E[BP]
SD[BP]
E[SH]
SD[SH]
E[COMP]
SD[COMP]
LP
-
-
-
-
+
CP
+
+
+
TABLE 10.19: Correlation of LP and CP with Compensation in the Principals Final
Knowledge Base (Model 5)
E[BP]
SD[BP]
E[SH]
SD[SH]
E[COMP]
SD[COMP]
LP
-
-
-
CP
+
+
+
TABLE 10.20: Correlation of LP and CP with the Movement of Agents (Model 5)
QUIT
E[QUIT]
SD[QUIT]
FIRED
E[FIRED]
SD [FIRED]
LP
+
+
+
+
-
-
CP
+
-
+
-
-


76
We can think of the signal y as information about the state of nature which both
parties share and agree upon, and the signal z as special post-contract information about
the state of nature received by the agent alone.
For example, a salesmans compensation may be some combination of percentage
of orders and a fixed fee. If both the salesman and his manager agree that the economy
is in a recession, the manager may offer a year-long contract which does not penalize the
salesman for poor sales, but offers above subsistence level fixed fee to motivate loyalty
to the firm on the part of the salesman, and a clause thrown in which transfers a larger
share of output than normal to the agent (i.e. incentives for extra effort in a time of
recession).
Now suppose the salesman, as he sets out on his rounds, discovers that the
economy is in an upswing, and that his orders are being filled with little effort on his
part. Then the agent may continue to exert little effort, realize high output, get a higher
share of output in addition to a higher initial fixed fee as his compensation.
In the case of asymmetric information, the problem is formulated as follows:
(PA) Maxc(qy)ec>e(z)eE \ UP(q c(q,y))f(q,y|z,e(z))p(z)dqdydz
such that
UA(c(q,y))f(q,y|z,e(z))p(z)dqdydz- ) d(e(z))pzdz > , (IRC)
e(z) £ argmaxc.eE j UA(c(q,y))f(q,y |z,e)dqdy d(e) V z (ICC)
where p(z) is the marginal density of z, d(e(z)) is the disutility of effort e(z).
Let X and i(z)p(z) be the Lagrange multipliers for (IRC) and (ICC) in (PA) respectively.


CHAPTER 1
OVERVIEW
The basic research addressed by this dissertation is the theory and application of
machine learning to assist in the solution of decision problems in business. Much of the
earlier research in machine learning was devoted to addressing specific and ad-hoc
problems or to fill a gap or make up for some deficiency in an existing framework,
usually motivated by developments in expert systems and statistical pattern recognition.
The first applications were to technical problems such as knowledge acquisition, coping
with a changing environment and filtering of noise (where filtering and optimal control
were considered inadequate because of poorly understood domains), data or knowledge
reduction (where the usual statistical theory is inadequate to express the symbolic
richness of the underlying domain), and scene and pattern analysis (where the classical
statistical techniques fail to take into account pertinent prior information; see for
example, Jaynes, 1986a).
The initial research was concerned with gaining an understanding of learning in
extremely simple toy world models, such as checkers (Samuel, 1963), SHRDLU blocks
world (Winograd, 1972), and various discovery systems. The insights gained by such
research soon influenced serious applications.
1


Benefits and stock participation (tied),
Basic pay and terminal pay (tied),
Share, and
123
Bonus.
Using the direct factor matrices, the expected factor identifications of behavioral
variables were computed (Table 9.38). These variables were ranked and ordered across
the 5 experiments. The exogenous risk variable, though not a behavioral variable, was
included to study its relative importance also. The following is the decreasing order of
explanatory power:
Experience,
Managerial skills,
General social skills,
Risk,
Physical qualities,
Communication skills,
Education,
Motivation,
Other personal skills, and
Age.
Using the varimax factor matrices, the expected factor identifications of
behavioral variables were computed (Table 9.38). These variables were ranked and


88
Effort = Drive Habit
= fd(past deprivation) fh( E( | S-R | ))
where fd is some "function" denoting drive as dependent on past deprivation,
fh is some "function" denoting habit as dependent on the sum of the strengths of
a number of instances of S-R reinforcements, and
| S-R | is the magnitude of an S-R reinforcement.
Drive theory, in its simplest form, states that individuals have basic biological
drives (eg., hunger and thirst) that must be satisfied. As these drives increase in strength,
there is an accompanying increase in tension. Tension is aversive to the organism, and
anything reducing that tension is viewed positively. The process of performing action that
achieves this is termed learning. All higher human motives are deemed to be derivatives
of this learning.
Another view is given in Instrumentality Theory which rejects the drive model
(L.W. Porter & E.E. Lawler, 1968), and emphasizes the anticipation of future events.
This emphasis provides a cognitive element ignored in most of the drive models. The
reasons for preferring instrumentality theory over other theories may be summarized as
follows:
(1) The terminology and concepts of instrumentality theory are more applicable
to the problems of human motivation; the emphasis on rationality and
cognition is appropriate for describing the behavior of managers.
(2) Instrumentality theory greatly facilitates the incorporation of motives such
as status, achievement, and power into a theory of attitudes and performance.


172
is marginally positive in Model 7 (complex contracts and discrimination), while it is
marginally negative in Model 6 (complex contracts and no discrimination). Hence,
depending on the goals of the agency vis-a-vis satisfaction of the principal, Model 5
(which ensures greatest rate of increase of satisfaction) or Model 6 (which ensures
highest mean satisfaction) may be chosen.
Predictably, the greatest number of agents were fired in the case of discriminatory
evaluation (Models 5 and 7), while the greatest number of agents quit in Model 5,
followed by Model 4. This implies that in Model 4, some of the agents were not
satisfied with the simple contracts offered to them (which did not meet their reservation
levels), while in Model 5, the principal forced some of the poorly performing agents to
resign by assigning them comparatively low contracts. The use of complex contracts
significantly reduces the number of agents who quit and also the number of agents who
were fired. This is because complex contracts enable the principal tailor contracts
efficiently to as many agents as possible. This ensures a more stable agency
environment.
10.9 Examination of Learning
There is no significant advantage in conducting a longer simulation in order to
increase maximum fitness of rules. Only uniformity of rule fitnesses (denoted by
entropy) is better achieved through longer simulations. Increasing the length of the
contract period increases the maximum fitness while also increasing the variance (Tables
10.1, 10.17, 10.35, and 10.49). Only in the case of Model 5 the average fitness showed


27
3.3 The Pitt Approach
The Pitt Approach, by De Jong (see for example, De Jong, 1988), considers the
whole knowledge base as one individual. The simulation starts with a collection of
knowledge bases. The operation of crossover works by randomly dichotomizing two
parent knowledge bases (selected at random) and mixing the dichotomized portions across
the parents to obtain two new knowledge bases. The Pitt approach may be used when
the researcher has available to him a panel of experts or professionals, each of whom
provides one knowledge base for some decision problem at hand. The crossover operator
therefore enables one to consider combinations of the knowledge of the individuals, a
process that resembles a brainstorming session. This is similar to a group decision
making approach. The final knowledge base or bases that perform well empirically
would then constitute a collection of rules obtained from the best rules of the original
expertise, along with some additional rules that the expert panel did not consider before.
The Michigan approach will be used in this research to simulate learning on one
knowledge base.


188
TABLE 10.59: Correlation of LP and CP with Payoffs from Agents (Model 7)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E1
SD1
E[ALL]
SD[ALL]
LP
+
-
-
+
-
+
-
CP
-
+
-
-
+
1 NORMAL (Active) Agents
TABLE 10.60: Correlation of LP and CP with Principals Satisfaction (Model 7)
E[SATP']
SD[SATP]
LASTS ATP2
LP
-
+
-
1 SATP: Principals Satisfaction
2 Principals Satisfction at Termination
TABLE 10.61: Correlation of Agent Factors with Agent Satisfaction (Model 7)
AGENTS
FACTOR
AGENTS SATISFACTION
SD[QUIT]
E[FIRED]
SD[FIRED]
SD[NORMAL]
SD[ALL]
SD[QUIT]
+
E[FIRED]
-
SD[FIRED]
+
SD[NORMAL]
+
SD[ALL]
+
TABLE 10.62: Correlation of Principals Satisfaction with Agent Factors (Model 7)
PRINCIPALS
SATISFACTION
AGENTS FACTORS
E[FIRED]
SD[FIRED]
SD[NORMAL]
SD[ALL]
E[SATISFACTION]
-
-
+
+
SD[SATISFACTION]
-


CHAPTER 5
THE PRINCIPAL-AGENT PROBLEM
5.1 Introduction
5.1.1 The Agency Relationship
The principal-agent problem arises in the context of the agency relationship in
social interaction. The agency relationship occurs when one party, the agent, contracts
to act as a representative of another party, the principal, in a particular domain of
decision problems.
The principal-agent problem is a special case of a dynamic two-person game. The
principal has available to her a set of possible compensation schemes, out of which she
must select one that both motivates the agent and maximizes her welfare. The agent also
must choose a compensation scheme which maximizes his welfare, and he does so by
accepting or rejecting the compensation schemes presented to him by the principal. Each
compensation package he considers implicitly influences him to choose a particular
(possibly complex) action or level of effort. Every action has associated with it certain
disutilities to the agent, in that he must expend a certain amount of effort and/or expense.
It is reasonable to assume that the agent will reject outright any compensation package
which yields less than that which can be obtained elsewhere in the market. This
assumption is in turn based on the assumptions that the agent is knowledgeable about his
38


CHAPTER 12
FUTURE RESEARCH
A number of directions for future research are possible. These directions are
related to the nature of the agency, behavior and motivation theory, additional learning
capabilities, and the role of maximum entropy.
12.1 Nature of the Agency
The following enhancements to the agency attempt to include greater realism.
This would enable the study of existing agencies, and would ensure applicability of
research results.
1. The principal warns an agent whenever his performance triggers a firing decision.
The number of warnings could be a control variable to study agency models.
2. The role of the private information of the agent could be control variable -
number of elements of private information, and changing their values in different
periods of the agency.
3. Agents modify their behavior with time. This is an extremely realistic situation.
This would imply that the agents also employ learning mechanisms. The effort
selection mechanism of the agents and their acceptance/rejection criteria would
198


48
(3) the residual loss, defined as the monetary equivalent of the loss in welfare of the
principal caused by the actions taken by the agent which are non-optimal with
respect to the principal.
Agency costs may be interpreted in the following two ways:
(1) they may be used to measure the "distance" between the first-best and the second-
best designs;
(2) they may be looked upon as the value of information necessary to achieve second-
best designs which are arbitrarily close to the first-best designs.
Obviously, the value of perfect information should be considered as an upper
bound on the agency costs (see for example, [Jensen and Meckling, 1976]).
5.2 Formulation of the Principal-Agent Problem
The following notation and definitions will be used throughout:
D: the set of decision criteria, such as (maximin, minimax, maximax, minimin,
minimax regret, expected value, expected loss,...}. We use A G D.
AP: the decision criterion of the principal.
Aa: the decision criterion of the agent.
UP: the principals utility function.
UA: the agents utility function.
C: the set of all compensation schemes. We use c G C.
E: the set of actions or effort levels of the agent. We use e G E.
0: a random variable denoting the true state of nature.


203
12,4 Maximum Entropy
Maximum entropy (MaxEnt) distributions seek to capture all the information about
a random variable without introducing unwarranted bias in the distribution. This is
called "maximal non-commitalness". The information of the agents and of the principal
is specified by using probability distributions. The role of MaxEnt distributions was not
attempted in this thesis. It is worthwhile to pursue the question of whether using a
maximum entropy distribution having the same mean and variance as the original
distribution makes any difference. In other words, an interesting future study might be
examination of the "MaxEnt robustness" of agency models. The results might have
interesting implications. If the results show that agency models coupled with learning
(as in this thesis) are MaxEnt robust, then it is not necessary to insist on using MaxEnt
distributions (which are computationally difficult to find). Similarly, if the models are
not MaxEnt robust, then deviation from MaxEnt behavior might yield a clue about the
tradeoffs involved in seeking a MaxEnt distribution.


126
TABLE 9.2: Iteration of First Occurrence of Maximum Fitness
RANGE
PERCENTAGE
RANGE
PERCENTAGE
[1,10]
14
(100,110]
4
(10,20]
14
(110,120]
4
(20,30]
10
(120,130]
0
(30,40]
6
(130,140]
6
(40,50]
2
(140,150]
2
(50,60]
4
(150,160]
2
(60,70]
6
(160,170]
2
(70,80]
4
(170,180]
4
(80,90]
4
(180,190]
0
(90,100]
6
(190,200]
6
TABLE 9.3: Learning Statistics for Fitness of Final Knowledge Bases
Experiment
Number of
Rules
Redundancy
Ratio
Minimum
Maximum
Mean
S.D.
1
199
1.3724
13.96
27.19
20.29
2.87
2
397
1.3690
7.77
27.16
19.92
3.18
3
63
1.1455
11.09
24.66
19.71
2.42
4
74
1.1563
11.92
26.68
19.82
3.69
5
1965
5.7794
3.09
24.72
19.94
2.35
TABLE 9.4: Entropy of Final Knowledge Bases and Closeness to the Maximum
Experiment
Number of
Rules
Entropy
Maximum
Entropy
Ratio1
1
199
5.2834
5.2933
0.9981
2
397
5.9709
5.9839
0.9978
3
63
4.1355
4.1431
0.9982
4
74
4.2869
4.3041
0.9960
5
1965
7.5760
7.5833
0.9990
Ratio of Entropy to Maximum Entropy


54
F. The solution:
(a) the principal offers c* E C* to the agent;
(b) the agent accepts the contract;
(c) the agent exerts effort e*(c*) E E;
(d) output q(e*(c*)) occurs;
(e) payoffs:
Tp = UP[q(e*(0) c*];
xA = UA[c* d(e*(c*))].
Notes:
1. The agent accepts the contract in F.b since IRC is present in Ml.PI, and C*
is nonempty since U E C.
2. Effort of the agent is a function of the offered compensation.
3. Since one of the informational assumptions was that the principal does not
know the agents utility function, is a compensation rather than the agents
utility of compensation, so UA() is meaningful.
G. Variations:
1. The principal offers C* to the agent instead of a c* E C*. The agents problem
then becomes:
(M1.A2) Maxc* 6 c* maxe e E UA[c* d(e)].
The first three steps in the solution then become:
(a) the principal offers C* to the agent;


a.e.[c,c\,
1A
U'M ~ cm + fe(q,e)
V'Mq)) q>e)
where c is the agents wealth, and "c is the principals wealth plus the output (these form
the lower and upper bounds). If the equality in the above characterization does not hold,
then c(q) = c or "c depending on the direction of inequality.
Result 3.2: Under the given assumptions and the characterization in result 3.1,
/i > 0; this is equivalent to saying that the principal prefers the agent increase his effort
given a second-best compensation scheme as in the above result 3.1. The second-best
solution is strictly inferior to a first-best solution.
Result 3.3: |fe|/f is interpreted as a benefit-cost ratio for deviation from optimal
risk sharing. Result 3.1 states that such deviation must be proportional to this ratio
taking individual risk aversion into account. From Result 3.2, incentives for increased
effort are preferable to the principal. The following compensation scheme accomplishes
this (where cF(q) denotes the first-best solution for a given X):
c(q) > cF(q), if the marginal return on effort is positive to the agent;
c(q) < cF(q), otherwise.
Result 3.4: Intuitively, the agent carries excess responsibility for the output. This
is implied by result 3.3 and the assumptions on the induced distribution f.
A previous assumption is now modified as follows: Compensation c is a function
of output and some other signal y which is public knowledge. Associated with this is a
joint distribution F(q,y,e) (as above), with f(q,y,e) the corresponding density function.


CHAPTER 4
THE MAXIMUM ENTROPY PRINCIPLE
4.1 Historical Introduction
The principle of maximum entropy was championed by E.T. Jaynes in the 1950s
and has gained many adherents since. There are a number of excellent papers by E.T.
Jaynes explaining the rationale and philosophy of the maximum entropy principle. The
discussion of the principle essentially follows Jaynes (1982, 1983, 1986a, 1986b, and
1991).
The maximum entropy principle may be viewed as "a natural extension and
unification of two separate lines of development. . The first line is identified with the
names Bernoulli, Laplace, Jeffreys, Cox; the second with Maxwell, Boltzmann, Gibbs,
Shannon." (Jaynes, 1983).
The question of approaching any decision problem with some form of prior
information is historically known as the Principle of Insufficient Reason (so named by
James Bernoulli in 1713). Jaynes (1983) suggests the name Desideratum of Consistency,
which may be formally stated as follows:
(1) a probability assignment is a way of describing a certain state of knowledge;
i.e., probability is an epistemological concept, not a metaphysical one;
28


15
(f) implicit (also known as incidental);
(g) call on success; and
(h) call on failure.
When classified by the criterion of the learners involvement, the standard is the
degree of activity or passivity of the learner. The following paradigms of learning are
classified by this criterion, in increasing order of learner control:
1. Learning by being told (learner only needs to memorize by rote);
2. Learning by instruction (learner needs to abstract, induce, or integrate to some
extent, and then store it);
3. Learning by examples (learner needs to induce to a great extent the correct
concept, examples of which are supplied by the instructor);
4. Learning by analogy (learner needs to abstract and induce to a greater degree in
order to learn or solve a problem by drawing the analogy. This implies that the
learner already has a store of cases against which he can compare the analogy and
that he knows how to abstract and induce knowledge);
5. Learning by observation and discovery (here the role of the learner is greatest;
the learner needs to focus on only the relevant observations, use principles of
logic and evidence, apply some value judgments, and discover new knowledge
either by using induction or deduction).
The above learning paradigms may also be classified on the basis of richness of
knowledge. Under this criterion, the focus is on the richness of the resulting knowledge,
which may be independent of the involvement of the learner. The spectrum of learning


107
for a rule to be activated in our experiments, all the specified antecedent conditions must
be fulfilled, and the result of the activation of the rule is to yield a compensation plan
having all the specified elements. Hence, a compensation plan is dependent on the
specific characteristics of the agent and also on the exact realization of exogenous risk.
The effectiveness of each compensation plan is therefore dependent on how well it takes
into account the characteristics of the agent. It is not necessary for each rule in the
knowledge base to have all the m antecedents and all the n consequents specified.
However, we adopt a uniform representation for the knowledge base where all the rules
have full specification of all the antecedent and consequent variables.
All the variables are positionally fixed, which facilitates pattern-matching during
inference (described in Sec. 5.2 below). The antecedent variables dealing with the
agents characteristics (including exogenous risk) are listed in order below, with the
variable names in parentheses (b4 is not a behavioral variable: it represents 9, the
exogenous risk):
(1) Experience (X),
(2) Education (D),
(3) Age (A),
(4) Exogenous Risk (RISK),
(5) General Social Skills (GSS),
(6) Office and Managerial Skills (OMS),
(7) Motivation (M),
(8) Physical Qualities deemed essential to the task (PQ),


CHAPTER 3
GENETIC ALGORITHMS
3.1 Introduction
Genetic classification algorithms are learning algorithms that are modeled on the
lines of natural genetics (Holland, 1975). Specifically, they use operators such as
reproduction, crossover, mutation, and fitness functions. Genetic algorithms make use
of inherent parallelism of chromosome populations and search for better solutions through
randomized exchange of chromosome material and mutation. The goal is to improve the
gene pool with respect to the fitness criterion from generation to generation.
In order to use the idea of genetic algorithms, problems must be appropriately
modeled. The parameters or attributes that constitute an individual of the population
must be specified. These parameters are then coded. The simulation begins with a
random generation of an initial population of chromosomes, and the fitness of each is
calculated. Depending on the problem and the type of convergence desired, it may be
decided to keep the population size constant or varying across iterations of the
simulation.
Using the population of an iteration, individuals are selected randomly according
to their fitness level to survive intact or to mate with other similarly selected individuals.
For mating members, a crossover point is randomly determined (an individual with n
23


114
PERR = f6() = (6*PERF + h,0)/21;
Disutility of Effort, Dis = f7() = -Effort / 10;
h2() = 10*BP + 9*S + 8*BO + 7*SP + 6*B + 5*TP;
Satisfaction of the agent, SAt:
SAl = fgQ = (12*PERF+ll*IR+h20+4*PERR+3*Effort-2*RISK+Dis)/66;
h30 = BP + (S/10 Output) + BO + TP + B + SP;
Principals Satisfaction, Sp, = f9 = Output h3();
Total Satisfaction, St = f10() = SAt + Sp,.
9.3.4 Genetic Learning Details
Genetic learning by the principal requires a "fitness measure" for each rule.
Here, the fitness of a rule is the (weighted) sum of the satisfactions of the principal and
the agent, and normalized with respect to the full knowledge base. As already noted, the
satisfaction of the principal is the utility of the principals residuum, while the satisfaction
of the agent is derived from the Porter-Lawler model of motivation. The average fitness
of the knowledge base is derived, and the fitnesses of the individual rules are normalized
to the interval [0,1]. One-point crossover and mutation are then applied to the
knowledge base to yield the next generation of rules. A copy of the rule with the
maximum fitness is passed unchanged to the next knowledge base. Pilot studies for this
model showed that in no case did the maximum fitness across iterations peak after 200
iterations. Hence, 200 iterations were employed for all the experiments.


180
TABLE 10.30: Correlation of Principals Satisfaction with Agent Factors (Model 5)
PRINCIPALS
SATISFACTION
AGENTS FACTORS
SD[QUIT]
E[FIRED]
SD[FIRED]
SD [NORMAL]
SD[ALL]
E[SATISFACTION]
+
+
-
+
+
SD[SATISFACTION]
+
-
+
+
TABLE 10.31: Correlation of Principals Satisfaction with Agents Satisfaction
(Model 5)
PS1
AGENTS SATISFACTION
E[QUIT]
SD[QUIT]
E[FIRED]
SD [FIRED]
SD[NORMAL]
E[ALL]
SD[ALL]
T~
-
+
+
-
+
-
+
'i
-
+
-
+
1 PS: This column contains the mean and standard deviation of the Principals
Satisfaction
2 Mean Principals Satisfaction
3 Standard Deviation of Principals Satisfaction
TABLE 10.32: Correlation of Principals Last Satisfaction with Agents Last
Satisfaction (Model 5)
AGENTS LAST SATISFACTION
E[QUIT]
E[FIRED]
E[NORMAL]
SD [NORMAL]
E[ALL]
SD[ALL]
PRINCIPALS
LAST
SATISFACTION
-
+
-
+
-
+


155
4. The fourth group of statistics deals with the movement of agents. They
describe the mean and variance of the agents who resigned from the agency
on their own (because of the failure of the principal to meet their reservation
welfares), those who were fired by the principal (because of their inadequate
performance), and those who remained active in the agency when the
simulation terminated.
5. The fifth group of statistics deals with agent factors, which measure the
change in satisfaction of the agents as they participate in the agency. They
help answer the question, "Is the agent better off by participating in this
particular model of agency?". These statistics cover the three types of agents
- those who resigned, those who were fired, and the remaining agents who
are employed (called the "normal" agents).
6. The sixth group of statistics deals with the mean and variance of the
satisfaction of the agents, again distinguishing between resigned, fired and
normal agents. An agents satisfaction is calculated from the utility of net
income of the agent. However, the term "satisfaction" is used instead of
"utility" since the former may take into consideration some intrinsic
satisfaction levels which are measured subjectively; see, for example,
Chapter 7 on Motivation Theory.
7. The seventh group of statistics reports the mean and variance of the
satisfaction level of the agents at termination. For the agents who have
resigned, this is the satisfaction derived from an agency period just prior to


35
dg
dp i
- 1 In pi + X = 0
In pi = X 1
p. = e1'1 V i = 1, .... n,
dg =
ax
E Pi = 1
i = i
E eX_1 = 1
i = 1
n ex_1 = 1
n Pi = 1
- p¡ = 2 v
i = 1.
. ,n.
n
n
n
~ E Piln Pi + K
i = 1
E ^i-1
i = 1
+ ^2
E <0iPi"^e
i = i
(Pil
This can be solved in the usual way by taking partial derivatives of g() w.r.t. p¡, )
X2, and equating them to zero. We obtain:
Pi = e
and
E 0ieA20i = ne E
i = 1 i = 1
Writing
= e 2,
i y and
x


142
TABLE 9.27 continued
Factor
11
12
13
14
15
RISK
-0.03696
0.15517
-0.05328
0.36381
-0.06798
GSS
0.31576
-0.24533
0.01240
0.05951
-0.06948
OMS
-0.22520
0.21461
0.10693
-0.04652
0.14814
M
0.15822
-0.05462
0.14185
0.02518
0.12264
PQ
-0.29957
0.03046
0.21993
-0.09147
0.15164
L
0.06466
0.35400
-0.22578
-0.15875
0.01682
OPC
-0.00639
0.15802
0.28350
0.03033
-0.09980
BP
0.18946
0.41750
0.14451
0.18472
-0.00217
S
0.00000
-0.00000
0.00000
-0.00000
0.00000
BO
0.31328
-0.00269
0.27097
-0.03495
0.03473
TP
-0.05316
0.16795
-0.14856
0.10896
-0.06195
B
-0.12859
0.06230
-0.07108
-0.04760
0.03615
SP
0.10652
0.05874
0.01048
-0.09678
-0.11597
for the rest of the variables.


165
4 and 5, compensation offered to agents correlated negatively with the number of
learning periods (Table 10.36). The value of compensation in the final knowledge base
of the principal also correlated negatively with both the number of learning periods and
the number of contract periods (Table 10.37).
The mean principals satisfaction correlated negatively with the mean satisfaction
of agents who quit and all the agents (considered as a whole). There were no
corresponding significant correlations between the principals satisfaction and the agents
factors (Table 10.47). The principals factor (which indicates if she is better off by
participating in this agency model) and factors of agents who were fired correlate
negatively. This of course explains why these agents were fired. The agency
environment is more stable than the previous two models. Only 234 agents quit, while
only 4 agents were fired (Table 10.67).
10.7 Model 7: Discussion of Results
Model 7 has six elements of compensation, and the principal practices
discrimination in her evaluation of the agents. As in the previous models, a higher
number of learning periods is associated with lower value of compensation packages
offered to the agents (Table 10.50). A higher number of contract periods correlates
negatively with mean basic pay, but positively with mean value of stock participation (no
significant correlations were observed at the 0.1 level for the other elements of
compensation) (Table 10.50). In the final knowledge base of the principal, the variances
of the elements of compensation showed negative correlation with the number of learning


40
5.1.2 The Technology Component of Agency
The technology component deals with the type and number of variables involved
(for example, production variables, technology parameters, factor prices, etc.), the type
and the nature of functions defined on these variables (for example, the type of utility
functions, the presence of uncertainty and hence the existence of probability distribution
functions, continuity, differentiability, boundedness, etc.), the objective function and the
type of optimization (maximization or minimization), the decision criteria on which
optimization is carried out (expected utility, weighted welfare measures, etc.), the nature
of the constraints, and so on.
5.1.3 The Information Component of Agency
The information component deals with the private information sources of the
principal and the agent, and information which is public (i.e. known to both the parties
and costlessly verifiable by a third party, such as a court). This component of the model
addresses the question, "who knows what?". The role of the informational assumption
in agency is as follows:
(a) it determines how the parties act and make decisions (such as offer payment
schemes or choose effort levels),
(b) it makes it possible to identify or design communication structures,
(c) it determines what additional information is necessary or desirable for
improved decision making, and


45
structures the compensation scheme c(*) in such a way as to maximize the expected
utility of her residuum (or some other decision criterion). In this manner, the principal
induces desirable work behavior in the agent.
It has been observed that "the source of moral hazard is not unobservability but
the fact that the contract cannot be conditioned on effort. Effort is noncontractible."
(Rasmusen, 1989). This is true when the principal observes shirking on the part of the
agent but is unable to prove it in a court of law. However, this only implies that a
contract on effort is imperfectly enforceable. Moral hazard may be alleviated in cases
where effort is contracted, and where both limited observability and a positive probability
of proving non-compliance exist.
5.1.6 Informational Asymmetry. Adverse Selection, and Screening
Adverse selection arises in the presence of informational asymmetry which causes
the two parties to act on different sets of information. When perfect sharing of
information is present and certain other conditions are satisfied, first-best solutions are
feasible (Sappington and Stiglitz, 1987). Typically however, adverse-selection exists.
While the effect of moral hazard makes itself felt when the agent is taking actions
(say, production or sales), adverse selection affects the formation of the relationship, and
may give rise to inefficient (in the second-best sense) contracts. In the information-
theoretic approach, we can think of both being caused by lack of information. This is
variously referred to as the dissimilarity between private information systems of the agent


202
and ordinal valued spaces. It remains to be seen how to adapt the theory of genetic
algorithms as dynamical systems to such models. It is encouraging to note that the
deterioration in average fitness with increasing learning periods (as in Models 4 through
7) is minor, suggesting that the model might be GA-deceptive instead of GA-hard (GA-
hard problems are those that seriously mislead the genetic algorithm). Further
encouragement derives from Whitleys theorem which states that the only challenging
problems are GA-deceptive (Whitley, L.D., 1991). Hence, one is at least assured, while
studying the more realistic models of agency, that these models are in fact sufficiently
challenging.
It is fairly straight-forward to include learning mechanisms wherever knowledge
bases are employed. In addition to having knowledge bases for selection of appropriate
compensation schemes and firing of agents, one may also have knowledge bases for the
agent(s) for effort selection, acceptance or rejection of contracts, and resigning from the
agency. The rules for calculation of satisfaction or welfare in the agency may be made
as extensive and detailed as one pleases. This highlights the flexibility of the new
framework it is possible to extend the model by adding knowledge bases in a modular
manner without increasing the complexity of the simulation beyond that caused by the
size and number of knowledge bases. In contrast, models in mathematical optimization
quickly become intractable by the addition of additional variables.


151
4.Agents not only have the option of leaving during contract negotiation time, but
they may also be fired by the principal for poor performance. The performance
of the agents is evaluated only at the end of the first contract renegotiation period
after every learning episode.
Furthermore, all the models follow the basic LEN model of Spremann. The
features of the LEN model are:
1. The principal is risk neutral. So, her utility function is linear (L).
2. The agents are all risk averse. In particular, their utility functions are exponential
(E).
3. The exogenous risk is distributed normally around a mean of zero (N).
4. The agents effort is in [0,0.5].
5. The agents disutility of effort is the square root of effort.
6. The output is the sum of the agents effort and the exogenous risk.
7. The agents payoff is the compensation less the disutility of effort.
8. The principals payoff is the output less the compensation.
9. The total output of the agency is separable and is the sum of the outputs derived
from the actions of the individual agents.
10. Each agents output is determined by a random value of the exogenous risk,
which may or may not be the same as those faced by the other agents.
Features 1 to 8 are explicit in the original LEN model, while features 9 and 10 are
implicit.
The informational characteristics of the models are the same, and are as follows:


18
3. Learning scheme.
At the present time, we do not yet have a comprehensive classification of learning
paradigms and their systematic integration into a theory. One of the first attempts in this
direction was taken by Michalski, Carbonell, and Mitchell (1983).
An extremely interesting area of research in machine learning that will have far-
reaching consequences for such a theory of learning is multistrategy systems, which try
to combine one or more paradigms or types of learning based on domain problem
characteristics or to try a different paradigm when one fails. See for example Kodratoff
and Michalski (1990). One may call this type of research meta-learning research,
because the focus is not simply on rules and heuristics for learning, but on rules and
heuristics for learning paradigms. Here are some simple learning heuristics, for
example:
LH1: Given several "isa" relationships, find out about relations between the properties.
(For example, the observation that "Socrates is a man" motivates us to find out
why Socrates should indeed be classified as a man, i.e., to discover that the
common properties are "rational animal" and several physical properties.)
LH2: When an instance causes an existing heuristic with certainty to be revised
downwards, ask for causes.
LH3: When an instance that was thought to belong to a concept or class but later turns
out not to belong to it, find out what it does belong to.
LH4: If X isa Y1 and X isa Y2, then find the relationship between Y1 and Y2, and
check for consistency. (This arises in learning by using semantic nets).


186
TABLE 10.51: Correlation of LP and CP with Compensation in the Principals
Final Knowledge Base (Model 7)
SD1
E2
SD2
SD3
SD4
SD5
E6
SD6
E7
SD7
LP
-
-
-
-
-
-
-
CP
+
+
+
1 BASIC PAY; 2 SHARE OF OUTPUT; 3 BONUS PAYMENTS; 4 TERMINAL
PAY;
5 BENEFITS; 6 STOCK PARTICIPATION; 7 TOTAL CONTRACT
TABLE 10.52: Correlation of LP and CP with the Movement of Agents (Model 7)
QUIT
E[QUIT]
SD[QUIT]
FIRED
E[FIRED]
SD[FIRED]
LP
+
+
+
+
CP
+
-
+
-
-
TABLE 10.53: Correlation of LP with Agent Factors (Model 7)
SD[QUIT]
SD[NORMAL]
SD[ALL]
LP
-
-
-
TABLE 10.54: Correlation of LP and CP with Agents Satisfaction (Model 7)
E[QUIT]
SD[QUIT]
SD[FIRED]
SD[ALL]
LP
+
+
CP
+
+


86
the choice of effort levels by the agent. This would also enable one to bypass the use
of utility and risk aversion as artificial explanatory variables.
In order to see how behavioral and motivational factors may be integrated into the
new approach, it is necessary to review briefly some models of motivation and behavioral
theory. This is done in Chapter 7.


118
of the correlation matrix. Tables 9.9, 9.15, 9.21, 9.27, and 9.33 show the factor pattern
of the direct solution (i.e. without rotation). Tables 9.10, 9.16, 9.22, 9.28, and 9.34
show the factor pattern of the varimax rotation.
The following rules having highest fitness in each experiment are displayed below
for illustration (the rule representation format of Section 5.1 will be used; fitnesses,
denoted FIT, are multiplied by 10,000 for convenience):
EXP 1: IF <3,2,5,2,3,4,4,4,4,3> THEN <4,1,1,1,1,1 >;
EXP 2: IF <2,1,1,2,1,1,2,2,2,1 > THEN <3,1,2,1,1,1 >;
EXP 3: IF < 1,4,3,4,3,3,5,5,4,4> THEN <5,1,3,1,1,1 >;
EXP 4: IF <2,3,3,3,3,4,3,4,3,2> THEN <5,1,1,1,1,3>;
EXP 5: IF <3,4,3,4,4,5,5,5,4,4> THEN <5,1,2,1,1,3>.
9.5 Analysis of Results
In each of the experiments, letting the process run to completion usually improved
the average fitness of the population, decreased its variance and increased its entropy.
Several exceptions to this suggest that it may be a better strategy to store those
knowledge bases generated during the learning process which possess desirable
characteristics. Low variance indicates higher certainty, while higher entropy indicates
a stable state close to a global optimum and uniformity in fitness for the rules of the
population.
Agent ft 1 provides the maximum total satisfaction, followed in decreasing order
by Agents #2, #5, #4, and #3 (Table 9.3). Interestingly, certain information did not


162
However, this adverse affect is not carried through to the agents satisfactions. All the
agents seem more satisfied the longer the agency process. But the agents satisfactions
decreased on average by increasing the number of data collection periods (Table 10.6).
In other words, observability by the principal affects their satisfaction adversely. This
may be due to the fact that the principal has more data with which she can measure the
usefulness of her knowledge base (by measuring the relative importance of each of the
antecedent clauses in the rules), thus allowing her to tailor compensation schemes (which
form the consequent clauses in the rules of her knowledge base) to reward agents
accurately. Because of the fundamentally adversarial relationship between the agents and
the principal, this would decrease the mean satisfaction of the agents.
The mean agent factor for fired agents is positively correlated with the mean
satisfaction of the principal (Table 10.13). However, the agents satisfaction and the
principals satisfaction held inverse relationships, except in the case of normal agents
(Table 10.14). This is consistent with the fact that the agents who quit and those who
were fired obtained, on average, less satisfaction than the normal agents. However,
because of the extremely dynamic environment (a mean of 444 agents across all the
simulations), the overall mean satisfaction of the agents is negatively correlated with the
principals satisfaction (Table 10.67).
With increase in the length of the simulation, more agents quit and were fired.
However, the expected number of agents fired decreased. In all, a mean of 5 agents
were fired (Table 10.67).


201
The learning mechanisms may also be expanded. For example, as pointed out in
Section 12.2 above, learning could be modified by correlational findings if a significant
causal relationship could be found between motivation theory and the identification of
good contracts.
The genetic operators may be varied in future research. For example, only one-
point uniform crossover was used. The number of crossover points could be increased.
Similarly, the mutation operator may be made dependent on time (or the number of
learning periods). The knowledge base may also be coded as a binary string, instead of
being a string of multi-valued nominal and ordinal attributes. Instead of randomly trying
all combinations of genetic operators and codings, the structure of the knowledge base
should be studied in order to see if there are any clues that point to the superiority of one
scheme over the other.
Another interesting, and quite important, research is the study of deceptiveness
of the knowledge base. A particular coding of the strings (which are the rules) might
yield a population that deceives the genetic algorithm. This implies that the population
of strings wanders away from the global optimum. An examination of the learning
statistics of Chapter 10 suggest that such deception might be happening in Models 4
through 7. Deceptiveness is characterized as the tendency of hyperplanes in the space
of building blocks to direct search in non-optimal directions. The domain of the theory
of genetic algorithms is the n-dimensional euclidean space, or its subspaces (such as the
n-dimensional binary space). The main problem in the study of deceptiveness in the
models used in this research is that the relevant search spaces are n-dimensional nominal


10.5: Correlation of LP with Agent Factors (Model 4) 174
10.6: Correlation of LP and CP with Agents Satisfaction (Model 4) 175
10.7: Correlation of LP and CP with Agents Satisfaction at Termination (Model
4) 175
10.8: Correlation of LP and CP with Agency Interactions (Model 4) 175
10.9: Correlation of LP with Rule Activation (Model 4) 175
10.10: Correlation of LP with Rule Activation in the Final Iteration (Model 4) . 175
10.11: Correlation of LP and CP with Principals Satisfaction and Least Squares
(Model 4) 175
10.12: Correlation of Agent Factors with Agent Satisfaction (Model 4) 176
10.13: Correlation of Principals Satisfaction with Agent Factors (Model 4) ... 176
10.14: Correlation of Principals Satisfaction with Agents Satisfaction (Model
4) 176
10.15: Correlation of Principals Last Satisfaction with Agents Last Satisfaction
(Model 4) 176
10.16: Correlation of Principals Factor with Agent Factors (Model 4) 177
10.17: Correlation of LP and CP with Simulation Statistics (Model 5) 177
10.18: Correlation of LP and CP with Compensation Offered to Agents (Model
5) 177
10.19: Correlation of LP and CP with Compensation in the Principals Final
Knowledge Base (Model 5) 177
10.20: Correlation of LP and CP with the Movement of Agents (Model 5) .... 177
10.21: Correlation of LP with Agent Factors (Model 5) 178
10.22: Correlation of LP and CP with Agents Satisfaction (Model 5) 178
10.23: Correlation of LP and CP with Agents Satisfaction at Termination (Model
5) 178
xi


51
Individual rationality constraint (IRC). The agents (expected) utility of net
compensation (compensation from the principal less his disutility of effort) must be at
least as high as his reservation welfare. This constraint is also called the participation
constraint.
When a contract violates the individual rationality constraint, the agent rejects it
and prefers unemployment instead. Such a contract is not necessarily "bad", since
different individuals have different levels of reservation welfare. For example,
financially independent individuals may have higher than usual reservation welfare levels,
and might very well prefer leisure to work even when contracts are attractive to most
other people.
Incentive compatibility constraint (ICQ. A contract will be acceptable to the
agent if it satisfies his decision criterion on compensation, such as maximization of
expected utility of net compensation. This constraint is called the incentive compatibility
constraint.
Development of the problem: Model 1. We develop the problem from simple
cases involving the least possible assumptions on the technology and informational
constraints, to those having sophisticated assumptions. Corresponding models from the
literature are reviewed briefly in section 1.3.
A. Technology:
(a) fixed compensation, C s set of fixed compensations, U C;


208
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Probability 15(4), pp. 1306-1326.


5
Chapter 8 describes the basic research model. Elements of behavior and
motivation theory and knowledge bases are incorporated. A research strategy to study
agency problems is proposed. The use of genetic algorithms periodically to enrich the
knowledge bases and to carry out learning is suggested. An overview of the research
models, all of which incorporate many features of the basic model, is presented.
Chapter 9 describes Model 3 in detail. Chapter 10 introduces Models 4 through
7 and describes each in detail. Chapter 11 provides a summary of the results of Chapters
9 and 10. Directions for future research are covered in Chapter 12.


10.24: Correlation of LP and CP with Agency Interactions (Model 5) 178
10.25: Correlation of LP with Rule Activation (Model 5) 178
10.26: Correlation of LP with Rule Activation in the Final Iteration (Model 5 . 179
10.27: Correlation of LP and CP with Payoffs from Agents (Model 5) 179
10.28: Correlation of LP and CP with Principals Satisfaction, Principals Factor
and Least Squares (Model 5) 179
10.29: Correlation of Agent Factors with Agent Satisfaction (Model 5) 179
10.30: Correlation of Principals Satisfaction with Agent Factors (Model 5) ... 180
10.31: Correlation of Principals Satisfaction with Agents Satisfaction (Model
5) 180
10.32: Correlation of Principals Last Satisfaction with Agents Last Satisfaction
(Model 5) 180
10.33: Correlation of Principals Satisfaction with Outcomes from Agents (Model
5) 181
10.34: Correlation of Principals Factor with Agents Factors (Model 5) 181
10.35: Correlation of LP and CP with Simulation Statistics (Model 6) 181
10.36: Correlation of LP and CP with Compensation Offered to Agents (Model
6) 181
10.37: Correlation of LP and CP with Compensation in the Principals Final
Knowledge Base (Model 6) 182
10.38: Correlation of LP and CP with the Movement of Agents (Model 6) .... 182
10.39: Correlation of LP and CP with Agent Factors (Model 6) 182
10.40: Correlation of LP and CP with Agents Satisfaction (Model 6) 182
10.41: Correlation of LP and CP with Agents Satisfaction at Termination (Model
6) 183
10.42: Correlation of LP and CP with Agency Interactions (Model 6) 183
xii


104
sure about the agents health. He has good communication skills, while his other
miscellaneous personal characteristics leave something to be desired. He has a rather
pessimistic outlook about exogenous factors (economy and business conditions), but he
is not too sure of his pessimistic estimate.
His assessment of company and work environment is moderately favorable, while
he considers the companys corporate image to be rather high. His perception of his own
abilities and traits is that they are just better than average, but he feels that he is not
consistent (sometimes he does far better, sometimes far worse). He is pessimistic about
effort leading to reward, perhaps because his uninspiring characteristics and lack of good
education led to slow reward and promotion in the past.
Agent ft2 in Experiment 2 has the same assessment of personal variables as Agent
#1. However, his characteristics are more modest. He has very little experience, no
high school education, and is much below average in all other respects. He is as
pessimistic and as unsure about the exogenous variables as Agent ft 1.
Agent #3 in Experiment 3 is a college graduate in his late 20s to early 30s. He
has little experience but is very highly motivated, possesses good communication skills,
and is good in all the other characteristics. His assessment of the exogenous environment
is optimistic. Moreover, he believes the principals work and company environment is
very good, and is generally sure of his superior abilities. He believes effort will almost
always be rewarded appropriately.


197
necessary to explore these agency mechanisms more fully. Suggestions are given in
Chapter 12.
On the one hand, each of the Models 4 through 7 seem to act as templates for
organizations with different goals. On the other, a model which accurately reflects an
existing organization may be chosen for simulation of the agency environment.


49
0P: a random variable denoting the principals estimate of the state of nature.
0A: a random variable denoting the agents estimate of the state of nature.
q: output realized from the agents actions (and possibly the state of nature).
qP: monetary equivalent of the principals residuum. Note that qp = q c(*)>
where c may depend on the output and possibly other variables.
Output/outcome. The goal or purpose of the agency relationship, such as sales,
services or production, is called the output or the outcome.
Public knowledge/information. Knowledge or information known to both the
principal and the agent, and also a third enforcement party, is termed public knowledge
or information. A contract in agency can be based only on public knowledge (i.e.
observable output or signals).
Private knowledge/information. Knowledge or information known to either the
principal or the agent but not both is termed private knowledge or information.
State of nature. Any events, happenings, occurrences or information which are
not in the control of the principal or the agent and which affect the output of the agency
directly through the technology constitute the state of nature.
Compensation. The economic incentive to the agent to induce him to participate
in the agency is called the compensation. This is also called wage, payment or reward.
Compensation scheme. The package of benefits and output sharing rules or
functions that provide compensation to the agent is called the compensation scheme.
Also called contract, payment function or compensation function.


153
The experimental design is 2 X 2. The first design variable is the number of
elements of compensation, and it takes two values 2 and 6. The second design variable
is the policy of evaluation of the agents by the principal. This policy plays a role in
firing an agent for lack of adequate performance. One policy evaluates the performance
of an agent relative to the other agents. By the use of this policy, an agent is not
penalized if his performance is inadequate while the performance of the rest of the agents
is also inadequate. In this sense, it is a non-discriminatory policy. The other policy
evaluates the performance of an agent without taking into consideration the performance
of the other agents. By the use of this policy, an agent is fired if his performance is
inadequate with respect to an absolute standard set by the principal, without regard to
how the other agents have performed. In this sense, it is a discriminatory policy.
By a discriminatory policy is meant an individualized performance appraisal and
firing policy, while a non-discriminatory policy means a relative performance appraisal
and firing policy. The words "discriminatory" and "non-discriminatory" will be used in
the following discussion only in the sense defined above.
Models 4 and 5 follow the basic LEN model which has only two elements of
compensation (basic pay and share of output). In Model 4, the principal evaluates the
performance of each agent relative to the performance of the other agents, and hence
follows a non-discriminatory firing policy. In Model 5 the principal keeps track of the
output she receives from each agent and evaluates each agent on an absolute standard.
Hence, she follows a discriminatory policy. Models 6 and 7 follow the basic LEN
model, but incorporate four additional elements of compensation (bonus payments,


209
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30
The reverse problem consists of estimating P(M,N) by f(m,n). For example, the
probability of seeing m successes in n trials when each trial is independent with
probability of success p, is given by the binomial distribution:
P(m \ n, = P(m | n,p) = (n]pm(l-p)n'm.
N \ml
The inverse problem would then consist of finding Pr[M] given (m,N,n). This problem
was given a solution by Bayes in 1763 as follows: Given (m,n), then
Pi[p < ^ < p + dp] = P(dp | m,n)
(n + 1)!
ml (n m) !
pm (l p)n m dp.
which is the Beta distribution.
These ideas were generalized and put into the form they are today, known as the
Bayes theorem, by Laplace as follows: When there is an event E with possible causes
C¡, and given prior information I and the observation E, the probability that a particular
cause C¡ caused the event E is given by
, v P(E\Ci) P(Ci\l)
PiCAE.I) = ^ E-
5^- P(E\Cj) P[Cj\l)
which result has been called "learning by experience" (Jaynes, 1978).
The contributions of Laplace were rediscovered by Jeffreys around 1939 and in
1946 by Cox who, for the first time, set out to study the "possibility of constructing a
consistent set of mathematical rules for carrying out plausible, rather than deductive,
reasoning." (Jaynes, 1983).


32
also so large that a large number Nk of molecules can be accommodated in it. The
problem of Boltzmann then reduces to the problem of finding the best prediction of Nk
for any given k in 1, ,s.
The numbers Nk are called the occupation numbers. The number of ways a given
set of occupation numbers will be realized is given by the multinomial coefficient
W(Nk)
AT!
N2l ... Ngl
The constraints are given by
(1)
S
E = E Nk Ek> and
k = 1
" E "*
k = 1
Since each set {Nk} of occupation numbers represents a possible distribution, the
problem is equivalently expressed as finding the most probable set of occupation numbers
from the many possible sets. Using Stirlings approximation of factorials
n\
sj2nn
n
in equation (1) yields
log W
The right hand
- E .
k 1 V
N,
(2)
side of (2) is the familiar Shannon entropy formula for the
distribution specified by probabilities which are approximated by the frequencies Nk/N,
k = 1, ..., s. In fact, in the limit as N goes to infinity,


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Porter, L.W., and Lawler, E.E. (1968). Managerial Attitudes and Performance. Irwin-
Dorsey, Homewood, IL.
Pratt, J.W. and Zeckhauser, R.J. (1985). Principals and Agents: The Structure of
Business. Harvard University Press, Boston, MA.
Quillian, M.R. (1968). "Semantic Memory." In Semantic Information Processing;
Minsky, M. (ed.), MIT Press, Cambridge, MA, pp. 216-270.
Quinlan, J.R. (1979). "Discovering Rules from Large Collections of Examples: A Case
Study." In Expert Systems in Microelectronic Age; Michie, D. (ed.), Edinburgh
University Press, Edinburgh.
Quinlan, J.R. (1986). "Induction of Decision Trees." Machine Learning 1(1), pp. 81-
106.


CHAPTER 11
CONCLUSION
The basic model for the study of agency theory includes knowledge bases,
behavior and motivation theory, contracts contingent on the behavioral characteristics of
the agent, and learning with genetic algorithms.
The initial experiments were aimed at an exploration of the new methodology.
The goal was to deal with any technical issues in learning, such as length of simulation,
convergence behavior of solutions, choice of values for the genetic operators. The initial
studies were motivated by questions of the following nature:
* Can this new framework be used to tailor contracts to the behavioral
characteristics of the agents?
* Is it worthwhile to include in the contract elements of compensation other than
fixed pay and share of output?
* How can good contracts be characterized and understood?
Model 3 of agency described in detail in Chapter 9, includes and incorporates
theories of behavior and motivation, dynamic learning, and complex compensation plans
was examined from the viewpoint of different informational assumptions. The results
from Model 3 show that the traditional agency models are inadequate for identifying
194


171
contracts is the best policy (as in Model 6). Such a model would be very useful if the
cost of human resource management is a significant expense item for the principal.
Further, while a high satisfaction level is achieved in Model 6, further increase in
satisfaction is only gradual. The emphasis is not on agent factors. In many real-world
situations, if the initial satisfaction level of agents is high, further attempts to increase
that level might yield diminishing returns.
In Table 10.67, negative values for the mean satisfaction of agents occur because
the satisfaction of the agents is dependent on their risk-aversion of net income, which is
modeled as a negative exponential function which always takes negative values. Hence,
the absolute values in any model taken by themselves do not convey much information.
They must be compared with the values from the other models.
The mean satisfaction of the principal is greatest in Model 6 (six elements of
compensation with non-discriminatory evaluation), and least in Model 5 (two elements
of compensation with discriminatory evaluation). Her mean satisfaction is higher the
more complex the contracts (since this allows her to tailor compensation to a wide variety
of agents), and it is also higher if she does not practice discrimination. So, while
discrimination is good for some agents in some circumstances, it is never a desirable
policy for the principal. When complex contracts are involved, the practice of
discrimination erodes the mean satisfaction of all parties only marginally, while
decreasing agents factors significantly.
The greatest improvement in satisfaction for the principal, however, takes place
in Model 5 (two elements of compensation and discriminatory policy). The improvement


99
knowledge-base therefore consists of rules that specify selection of compensation plans
based on the agents characteristics and the exogenous risk. A formal description
follows.
Let N denote a nominal scale. Nk denotes the k-fold nominal product. Let C Q
Nk denote the set of all compensation plans, {c,,...,cn}. Let B Nk denote the set of
all the behavioral profiles of the agent, {b1( ..., bm}. Each compensation plan c¡ is a
finite-dimensional vector c¡ = (c¡(1), ..., c^), where each element of the c¡ vector denotes
an element of the compensation plan, such as fixed pay, commission, or bonus. Each
element of B is also a finite-dimensional vector, bj = (bj(1), ..., bj(q)), where each element
of the bj vector denotes a behavioral characteristic that the agent will be evaluated on by
the principal, such as experience, motivation, or communication skill. The elements c¡
and bj are detailed in Section 5.
Let G be the set of mappings from the set of behavioral profiles B to the set of
compensation plans, C. Two or more compensation plans could conceivably be
associated with one particular behavioral profile bj of an agent. A particular mapping
g in G specifies a knowledge base K <= B C.
Let S:K*0*E-> R denote the total satisfaction function of the agency, where
E denotes the effort level of the agent, and 9 represents exogenous risk. Let SA denote
the satisfaction of the agent, and SP, the satisfaction of the principal (defined on the same
domain). SA and SP are both "functions" of other variables such as compensation plans,
output, agents effort, agents private information, and so on.
SA = SA(Output,C),


I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
/^\
Gary J. jt^ehler, Chairman
Professor of Decision and
Information Sciences
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Dvid E. M. Sappington
Lanzilotti-McKethan Professor
of Economics
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
1
I *-
tbii'C ^ t \ I L
Richard A. Elnicki
Professor of Decision and
Information Sciences
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Anthal Majthay
Associate Professor of
Decision and Information
Sciences


195
important elements of compensation plans. The reasons that the traditional models fail
are their strong methodological assumptions and lack of a framework which deals with
complex behavioral and motivational factors, and their influence in inducing effort
selection in the agent. Model 3 attempts to remove this inadequacy.
The results of this research are dependent on the informational assumptions of the
principal and the agent. It is not suggested that the traditional theory is always wrong.
In some cases (i.e. for the informational assumptions of some principal), both theories
may agree on their recommendations for optimal compensation plans. However, this
research does present several significant counter-examples to traditional agency wisdom.
Sec. 9.5 contains the details.
Models 4 through 7 have comparatively more realism. These models simulate a
multi-agent, multi-period, and dynamic agency models which include contracts contingent
on the characteristics of the agents. The antecedents are not point estimates as in the
earlier studies, but interval estimates. This made it possible to use specialization and
generalization operators as learning mechanisms in addition to genetic operators.
Further, while these models followed the basic LEN model (as did the previous models),
the agents who enter the agency all have different risk aversions and reservation
welfares.
Models 4 and 5 have only two elements of compensation each, while Models 6
and 7 have six each. This enables one to study the effect of complex contracts as
opposed to simple contracts. Moreover, in Models 5 and 7, the principal evaluates the
agents individually. Performance of an agent is not compared to that of the others. As


106
1: very high, 2: high, 3: average, 4: low, 5: very low.
Table 9.1 provides details that capture the above characterizations.
The information on each variable in Table 9.1 is specified as a discrete probability
distribution. Table 9.1 lists the means and standard deviations of the variables associated
with the agents characteristics and the agents personal variables. In experiment 4, the
situation is non-informative. All the variables have discrete uniform distribution, with
mean 3.00 and standard deviation \ 2 1.414. Experiment 5 is provided complete and
perfect information, and so the standard deviation is 0.00.
9.3 Details of Experiments
In this Section we discuss rule representation, inference method, calculation of
satisfaction, details of the genetic learning algorithm, and statistics captured for analysis.
9.3.1 Rule Representation
A rule has the following format:
IF < antecedent > THEN < consequent >.
The antecedent values in the "IF" part of a rule are conditions that occur or are satisfied,
and the consequent variables are assigned values from the "THEN" part of the rule
correspondingly. The antecedent and consequent of a rule are conjunctions of several
variables. Let b¡ be the i-th antecedent (denoting a behavioral variable), and Cj denote
the j-th consequent (denoting a compensation variable). The antecedent of a rule is then
given by A=i,..,m and the consequent by A=i,...,n> where A denotes conjunction. Hence,


34
exploited and irrelevant information, even if assumed, would be eliminated from the
solution.
The technique has been used in artificial intelligence (see for example, [Lippman,
1988; Jaynes, 1991; Kane, 1991]), and in solving problems in business and economics
(see for example, [Jaynes, 1991; Grandy, 1991; Zellner, 1991]).
4,2 Examples
We will see how the principle is used in solving problems involving some type
of prior information which is used as a constraint on the problem. For simplicity, we
will deal with problems involving one random variable 0 having n values, and call the
associated probabilities p¡. For all the problems, the goal is to choose a probability
distribution from among many possible ones which has the maximum entropy.
No prior information whatsoever. The problem may be formulated using the
Lagrange multiplier X for the single constraint as:
n n
Max g( iPi)) = £ Pi In pi + X £ pi 1 .
(Pj] i -1 [i -1
The solution is obtained as follows:Hence, p¡ = 1/n, i = l,...,n is the MaxEnt
assignment, which confirms the intuition on the non-informative prior.
Suppose the expected value of 0 is We have two constraints in this problem:
the first is the usual constraint on the probabilities summing to one; the second is the
given information expected value of 0 is jue. We use the Lagrange multipliers X, and
X2 for the two constraints respectively. The problem statement follows:


145
TABLE 9.32: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 5 Eigenvalues of the Correlation Matrix
Total = 6 Average = 0.375
Factor
1
2
3
4
5
6
Eigenvalue
1.175433
1.073561
1.020839
0.975691
0.924350
0.830127
Difference
0.101872
0.052722
0.045148
0.051341
0.094223
0.830127
Proportion
0.1959
0.1789
0.1701
0.1626
0.1541
0.1384
Cumulative
0.1959
0.3748
0.5450
0.7076
0.8616
1.0000
TABLE 9.33: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 5 Factor Pattern
FACTOR
1
2
3
4
5
6
X
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
GSS
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
OMS
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
M
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
PQ
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
L
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
BP
0.73332
0.17248
0.01164
-0.17230
0.08274
0.62915
S
-0.34869
0.55123
0.04419
-0.37155
0.65919
0.00508
BO
0.56837
0.47214
-0.34889
-0.05745
-0.10818
-0.56330
TP
-0.26373
0.32667
-0.63371
0.58018
0.00086
0.29247
B
-0.27872
0.59673
0.33776
-0.14045
-0.64230
0.14099
SP
0.21404
0.23289
0.61754
0.66957
0.24233
-0.10746
Notes: Final Communality Estimates total 6.0 and are as fol
BO, TP, B, and SP; 0.0 for the rest of the variables.
ows: 1.0 for BP, S,


183
TABLE 10.41: Correlation of LP and CP with Agents Satisfaction at Termination
(Model 6)
SD[QUIT]
SD[FIRED]
E[ALL]
SD[ALL]
LP
+
+
CP
+
+
TABLE 10.42: Correlation of LP and CP with Agency Interactions (Model 6)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E[NORMAL]
E[ALL]
SD[ALL]
LP
-
-
+
-
-
-
CP
+
+
+
TABLE 10.43: Correlation of LP and CP with Rule Activation (Model 6)
E[QUIT]
SD[QUIT]
E[FIRED]
E[ALL]
SD[ALL]
LP
-
-
-
-
-
CP
-
TABLE 10.44: Correlation of LP and CP with Rule Activation in the Final Iteration
(Model 6)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E[ALL]
SD[ALL]
LP
-
-
-
-
CP
+
+


207
Barr, A., Cohen, P.R., and Feigenbaum, E.A. (1989). The Handbook of Artificial
Intelligence IV. Addison-Wesley Publishing Company, Reading, MA.
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Barr, A., and Feigenbaum, E.A. (1982). The Handbook of Artificial Intelligence II.
William Kaufman, Los Altos, CA.
Berg, S., and Tschirhart, J. (1988a). Natural Monopoly Regulation: Principles and
Practice. Cambridge University Press, New York.
Berg, S., and Tschirhart, J. (1988b). "Factors Affecting the Desirability of Traditional
Regulation." Working Paper, Public Utilities Research Center, University of
Florida, Gainesville, FL.
Besanko, D., and Sappington, D. (1987). Designing Regulatory Policy with Limited
Information. Harwood Academic Publishers, London.
Blickle, M. (1987). "Information Systems and the Design of Optimal Contracts." In
Agency Theory, Information, and Incentives; Bamberg, G. and Spremann, K.
(eds.), Springer-Verlag, Berlin, pp. 93-103.
Blumer, A., Ehrenfeucht, A., Haussler, D., and Warmuth, M.K. (1989). "Leamability
and the Vapnik-Chervonenkis Dimension." JACM 36(4), pp. 929-965.
Brown, S.J., and Sibley, D.S. (1986). The Theory of Public Utility Pricing. Cambridge
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Buchanan, B.G., and Feigenbaum, E.A. (1978). "DENDRAL and META-DENDRAL:
Their Application Dimension." Artificial Intelligence 11, pp. 5-24.
Buchanan, B.G., Mitchell, T.M., Smith, R.G., and Johnson, C.R. Jr. (1977). "Models
of learning systems." In Belzer, J., Holzman, A.G., and Kent, A. (eds.),
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Campbell, J.P., and Pritchard, R.D. (1976). "Motivation Theory in Industrial and
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Cannon, W.B. (1939). The Wisdom of the Body. Norton, New York.
Child, D. (1990). The Essentials of Factor Analysis. Cassell, London.


218
Vogelsang, I., and Finsinger, J. (1979). "A Regulatory Adjustment Process for Optimal
Pricing by Multiproduct Monopoly Firms." Bell Journal of Economics 10, pp.
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Kaufmann, San Mateo, CA.
Williams, A.J. (1986). "Decision Analysis for Computer Strategy Planning." In
Computer Assisted Decision Making, Mitra, G. (ed.), North-Holland, New York.
Winograd, T. (1972). Understanding Natural Language. Academic Press, New York.
Winograd, T. (1973). "A Procedural Model of Language Understanding." In Computer
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L.H. (eds.), Kluwer Academic Publishers, Boston, MA, pp. 17-31.


191
TABLE 10.67 -- continued
MODEL #
4
5
6
7
DESCRIPTION
Non-
Discriminatory
Discriminatory
Non-
Discri minatory
Discriminatory
COMPENSATION
ELEMENTS
2
2
6
6
VARIABLES
78
86
94
102
MEAN AGENT FAC
:tors
Agents who Quit
221
128
102
-60
Fired Agents
3380
1320
904
570
Normal Agents
38
2620
572
65
All Agents
584
436
185
-20
MEAN SATISFACTION OF AGENTS
Agents who Quit
-223
-221
-66
-65
Fired Agents
-240
-300
-57
-66
Normal Agents
-189
-166
-50
-64
All Agents
-228
-215
-63
-65
MEAN NUMBER OF INTERACTIONS (NORMALIZED)
Agents who Quit
2.3597
2.0180
3.9383
3.8724
Fired Agents
5.5558
3.5605
7.5252
5.8540
Normal Agents
2.8700
1.9850
5.7950
5.5150


199
be specified by knowledge bases. This makes it possible to apply learning to
these knowledge bases, the same as was done for the principal.
4. Inclusion of the cost of human resource management for the principal. This cost
might be included either in the computation of rule fitnesses, or in the firing rules
of the principal. Coupled with a learning mechanism, this would ensure that the
principal learns the correct criteria, and to change the criteria in response to the
exogenous environment.
5. The type of simulation involved in the study of the models is discrete-event. The
time from the acceptance of a contract to the sharing of the output is one
indestructible time slice. In reality, there is a small probability for an agent to
resign, or for the principal to fire an agent, before the completion of the contract
period. This may be a desirable extension to the models above, and would be a
step towards achieving continuous simulation.
12,2 Behavior and Motivation Theory
As was pointed out in Chapter 9, further research is necessary in order to unveil
the cause-effect relationships among the elements of the behavioral models, and their
influence in unearthing good contracts in the learning process. This might shed insight
into the correlations observed among the various elements of compensation in Model 3.
Further research varying the "functional" assumptions must be carried out if any clear
pattern is to emerge. This would also help estimate the robustness of the model (the
change in the degree and direction of the correlations when the functional specifications


184
TABLE 10.45: Correlation of LP and CP with Principals Satisfaction and Least
Squares (Model 6)
E[SATP]
SD[SATP]
LASTSATP2
BEH-LS3
EST-LS4
LP
-
+
-
CP
+
+
+
1 SATP: Principals Satisfaction
2 Principals Satisfaction at Termination
3 Least Squares Deviation from Agents True Behavior
4 Least Squares Deviation from Principals Estimate of Agents Behavior
TABLE 10.46: Correlation of Agents Factors with Agents Satisfaction (Model 6)
i
AGENTS SATISFACTION
2
3
3
5
5
E[ALL]
SD[ALL]
2
+
3
-
3
+
5
-
5
+
E[ALL]
-
SD[ALL]
+
1 This column denotes Agents Factors
2 Standard Deviation of Factor/Satisfaction of Agents who Quit
3 Mean Factor/Satisfaction of Agents who were Fired
4 Standard Deviation of Factor/Satisfaction of Agents who were Fired
5 Mean Factor/Satisfaction of Agents who remained Active (Normal)
6 Standard Deviation of Factor/Satisfaction of Agents who remained Active (Normal)


4
bases contain, for example, information about the agents characteristics and pattern of
behavior under different compensation schemes; in other words, they deal with the issues
of hidden characteristics and induced effort or behavior. Given the expected behavior
pattern of an agent, a related research issue is the study of the effect of using
distributions that have maximum entropy with respect to the expected behavior.
Trial compensation schemes, which come from the specified knowledge bases, are
presented to the agent(s). Upon acceptance of the contract and realization of the output,
the actual performance of the agent (in terms of output or the total welfare) is evaluated,
and the associated compensation schemes are assigned proportional credit. Periodically,
iterations of the genetic algorithm will be used to create a new knowledge base that
enriches the current one.
Chapter 2 begins with an introduction to artificial intelligence, expert systems,
and machine learning. Chapter 3 describes genetic algorithms. Chapter 4 covers the
origin of the Maximum Entropy Principle and its formulation. Chapter 5 deals with a
survey of the principal-agent problem, where a few basic models are presented, along
with some of the main results of the research.
Chapter 6 examines the traditional methodology used in attacking the principal-
agent problem, and measures to cover the inadequacies are proposed. One of the basic
assumptions of the economic theory-the assumption of risk attitudes and utilityis
circumvented by directly dealing with the knowledge-based models of the agent and the
principal. To this end, a brief look at some of the ideas from behavior and motivation
theory is taken in Chapter 7.


65
Information prvate to the principal:
Utility of residuum, UP.
Information private to the agent:
(a) selection of effort given the compensation;
(b) utility of welfare;
(c) disutility of effort.
Timing:
(a) the principal offers a contract (r,s) to the agent;
(b) the agents effort e is induced by the compensation scheme;
(c) a state of nature occurs;
(d) the agents effort and the state of nature give rise to output;
(e) sharing of the output takes place.
Payoffs:
7TP = UP[q (r + sq)]
= UP[e(r,s) + 0O (r + s(e(r,s) + 0o))]
= UA[r + sq d(e(r,s))]
= UA[r + s(e(r,s) + 0O) d(e(r,s))],
where e(r,s) is the function which induces effort based on compensation, and 0O
is the realized state of nature.


10.43: Correlation of LP and CP with Rule Activation (Model 6) 183
10.44: Correlation of LP and CP with Rule Activation in the Final Iteration
(Model 6) 183
10.45: Correlation of LP and CP with Principals Satisfaction and Least Squares
(Model 6) 184
10.46: Correlation of Agents Factors with Agents Satisfaction (Model 6) .... 184
10.47: Correlation of Principals Satisfaction with Agents Factors and Agents
Satisfaction (Model 6) 185
10.48: Correlation of Principals Factor with Agents Factor (Model 6) 185
10.49: Correlation of LP and CP with Simulation Statistics (Model 7) 185
10.50: Correlation of LP and CP with Compensation Offered to Agents (Model
7) ; 185
10.51: Correlation of LP and CP with Compensation in the Principals Final
Knowledge Base (Model 7) 186
10.52: Correlation of LP and CP with the Movement of Agents (Model 7) .... 186
10.53: Correlation of LP with Agent Factors (Model 7) 186
10.54: Correlation of LP and CP with Agents Satisfaction (Model 7) 186
10.55: Correlation of LP and CP with Agents Satisfaction at Termination (Model
7) 187
10.56: Correlation of LP and CP with Agency Interactions (Model 7) 187
10.57: Correlation of LP and CP with Rule Activation (Model 7) 187
10.58: Correlation of LP with Rule Activation in the Final Iteration (Model 7) . 187
10.59: Correlation of LP and CP with Payoffs from Agents (Model 7) 188
10.60: Correlation of LP and CP with Principals Satisfaction (Model 7) 188
10.61: Correlation of Agent Factors with Agent Satisfaction (Model 7) 188
xiii


APPENDIX
FACTOR ANALYSIS
We use the SAS procedures (PROC FACTOR) which uses Principal Components
Method to extract factors from the final rule population (Guertin and Bailey, 1970). We
also subject the data to Kaisers Varimax rotation, which is employed to avoid skewed
distribution of variance explained by the factors. In the initial "direct" solution, the first
factor accounts for most of the variance, followed in decreasing order by the rest of the
factors. In the "derived" solution (i.e. after rotation), variables load either maximum or
close to zero. This enables the factors to stand out more sharply. By the Kaiser
criterion, factors whose eigenvalues are greater than one are retained since they are
deemed to be significant. The size of a sample (or the size of the population)
approximates the degrees of freedom for testing significance of factor loadings. Using
500 degrees of freedom (the population size) and a relatively stringent 1 % significance
level, the critical value of correlation is 0.115. The critical value of a factor loading,
fc, is given by the Burt-Banks formula (Child, 1990):
f
C
N
n
n+l-r'
204


115
The three parameters which can be controlled in learning with genetic algorithms
are the mating probability (MATE), the mutation probability (MUTATE), and the
number of iterations (ITER). From trial simulations, a mating probability of 0.6, a
mutation probability of 0.01, and 200 iterations for each run were deemed satisfactory,
and were hence kept constant in all the experiments.
9.3.5 Statistics Captured for Analysis
The following statistics were collected for each simulation:
(1) Average fitness of the principals knowledge base;
2) Variance of knowledge base fitness;
(3) Maximum fitness over all iterations of a run;
(4) Entropy of fitnesses; and
(5) Iteration when maximum fitness was first achieved.
These statistics are averaged across 10 runs for each experiment. The satisfaction
index of the rules are normalized to the interval [0,1] to give fitness levels. Entropy is
defined as the Shannon entropy, given by the formula
En{fi) = £ f1 In flt
i=1
where f¡ is the fitness of the i-th rule in the knowledge base, and In is the natural
logarithm. The maximum entropy possible is ln(Number of Rules) and corresponds to
the entropy of a distribution which occurs as the solution to a problem without any
constraints (or information). In all the experiments, the possible maximum entropy is


TABLE OF CONTENTS
ACKNOWLEDGMENTS iii
LIST OF TABLES viii
ABSTRACT xv
1 OVERVIEW 1
2 EXPERT SYSTEMS AND MACHINE LEARNING 6
2.1 Introduction 6
2.2 Expert Systems 8
2.3 Machine Learning 10
2.3.1 Introduction 10
2.3.2 Definitions and Paradigms 14
2.3.3 Probably Approximately Close Learning 21
3 GENETIC ALGORITHMS 23
3.1 Introduction 23
3.2 The Michigan Approach 26
3.3 The Pitt Approach 27
4 THE MAXIMUM ENTROPY PRINCIPLE 28
4.1 Historical Introduction 28
4.2 Examples 34
5 THE PRINCIPAL-AGENT PROBLEM 38
5.1Introduction 38
5.1.1 The Agency Relationship 38
5.1.2 The Technology Component of Agency 40
5.1.3 The Information Component of Agency 40
5.1.4 The Timing Component of Agency 42
v


138
TABLE 9.22: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 3 Varimax Rotated Factor Pattern
Factor
1 2 3
4
5
X
0.96928
-0.08142
-0.03918
0.03545
0.04428
D
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
-0.04055
0.04253
0.97181
0.16514
-0.02720
GSS
-0.25455
0.32873
0.10890
-0.08646
0.03277
OMS
-0.08603
0.93594
0.04323
-0.13317
0.11829
M
0.00000
0.00000
0.00000
0.00000
0.00000
PQ
0.00000
0.00000
0.00000
0.00000
0.00000
L
0.00000
0.00000
0.00000
0.00000
0.00000
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
BP
0.03686
-0.12283
0.16709
0.96833
-0.01802
S
-0.01604
0.03958
-0.08037
-0.03568
0.06811
BO
-0.05005
0.00008
0.00895
0.01872
0.06265
TP
0.07511
0.01390
0.06546
0.07241
-0.06475
B
0.04250
0.10437
-0.02704
-0.01793
0.97700
SP
0.02553
0.04427
0.07087
0.06923
0.13070
Factor
6
7
8
9
10
X
-0.01562
0.02692
-0.05402
0.07670
-0.19835
D
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
RISK
-0.08227
0.07314
0.00945
0.06551
0.08735
GSS
0.04743
0.00360
0.01355
0.00660
0.89680
OMS
0.04351
0.05169
-0.00050
0.01576
0.27965
M
0.00000
0.00000
0.00000
0.00000
0.00000
PQ
0.00000
0.00000
0.00000
0.00000
0.00000
L
0.00000
0.00000
0.00000
0.00000
0.00000
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
BP
-0.03644
0.07236
0.02019
0.07353
-0.07257
S
0.98027
-0.02612
-0.00494
0.15086
0.03751
BO
-0.00482
-0.00515
0.99439
-0.06454
0.01048
TP
0.15371
-0.04981
-0.06857
0.97448
0.00496
B
0.06843
0.13345
0.06613
-0.06398
0.02754
SP
-0.02605
0.98358
-0.00542
-0.04843
0.00392
Notes: Final Communality Estimates total 10.0 and are as follows: 0.0 for D, A,
M, PQ, L, and OPC; 1.0 for the rest of the variables.


80
Result:
Result 4.1: The following is a characterization of optimal functions:
Aq\e\V)
where X, p(£), and p(£) are Lagrange multipliers for the three constraints in (P)
respectively.
5.3.5 Model G: Some General Results
Result G.l (Wilson. 1968L Suppose that both the principal and the agent are risk
averse having linear risk tolerance functions with the same slope, and the disutility of the
agents effort is constant. Then the optimal sharing rule is a non-constant function of the
output.
Result G.2. In addition to the assumptions of result G.l, also suppose that the
agents effort has negative marginal utility. Let c,(q) be a sharing rule (or compensation
scheme) which is linear in the output q, and let (^(q) = k be a constant sharing rule.
Then, c, dominates Cj.
The two results above deal with conditions when observation of the output is
useful. Suppose Y is a public information system that conveys information about the
output. So, compensation schemes can be based on Y alone. The value of Y, denoted
W(Y) (following model 1), is defined as: W(Y) = maxc£c EUP[q c(y)], subject to IRC


134
TABLE 9.16: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 2 -Varimax Rotated Factor Pattern
Factor
1
2
3
4
5
6
7
X
0.03492
0.99126
0.02196
-0.01687
0.01069
0.01925
-0.03964
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
0.02987
-0.01676
-0.04298
0.99302
0.02126
-0.00162
-0.04582
GSS
0.12998
0.08431
-0.09124
0.06914
-0.05572
0.05292
0.02567
OMS
-0.00638
0.01924
0.04137
-0.00161
-0.03958
0.99160
0.01619
M
0.98841
0.03512
-0.02218
0.03018
0.02264
-0.00653
-0.02308
PQ
-0.02223
0.02208
0.98938
-0.04343
0.01497
0.04168
0.02901
L
-0.01908
0.03370
0.08208
-0.03191
-0.00782
-0.07776
0.01142
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
BP
-0.01095
0.04783
0.02059
0.02922
0.04601
0.03992
0.00344
S
0.02705
0.05363
-0.01922
0.00868
-0.01382
-0.03522
0.00210
BO
0.03723
-0.01392
-0.00442
0.00168
-0.00869
-0.02235
-0.02816
TP
0.02208
0.01055
0.01474
0.02112
0.99503
-0.03917
-0.02333
B
0.03185
-0.01912
0.01580
-0.04609
0.03829
0.03085
-0.01322
SP
-0.02242
-0.03903
0.02838
-0.04535
-0.02323
0.01596
0.99633
Factor
8
9
10
11
12
13
X
0.05425
-0.01391
-0.01919
0.03347
0.04754
0.08050
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
0.00873
0.00165
-0.04594
-0.03152
0.02887
0.06572
GSS
0.01523
0.01885
0.00031
-0.05231
0.01946
0.97603
OMS
-0.03559
-0.02242
0.03091
-0.07707
0.03965
0.05044
M
0.02757
0.03741
0.03224
-0.01900
-0.01107
0.12505
PQ
-0.01954
-0.00444
0.01591
0.08190
0.02059
-0.08759
L
0.00709
-0.02679
0.05532
0.98880
0.02057
-0.05035
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
BP
0.02113
-0.10936
-0.03162
0.02050
0.98915
0.01871
S
0.99514
-0.00501
0.05916
0.00695
0.02076
0.01446
BO
-0.00505
0.99110
0.04331
-0.02656
-0.10871
0.01810
TP
-0.01382
-0.00867
0.03796
-0.00765
0.04522
-0.05255
B
0.05972
0.04336
0.99208
0.05475
-0.03138
0.00032
SP
0.00209
-0.02757
-0.01314
0.01116
0.00340
0.02406
are as follows: 0.0 for D, A,
'lotes:
and OPC;
1.0 for the rest of the variables.


192
TABLE 10.67 -- continued
MODEL if
4
5
6
7
DESCRIPTION
Non-
Discriminatory
Discriminatory
Non-
Discriminatory
Discriminatory
COMPENSATION
ELEMENTS
2
2
6
6
VARIABLES
78
86
94
102
All Agents
2.5100
2.0958
4.2363
4.1423
Principals
Satisfaction
-332.2
(129.7)
-406.2
(161.1)
-227.7
(105.5)
-234.6
(121.9)
Principals Factor
2.8789
(7.6635)
1.8123
(5.5003)
-0.1291
(5.9218)
0.2479
(5.8992)


125
TABLE 9.1: Characterization of Agents
PERSONAL VARIABLE
EXP1
MEAN
(SD)
EXP2
MEAN
(SD)
EXP3
MEAN
(SD)
EXP5
MEAN
(SD)
COMPANY
ENVIRONMENT, CE
3.40
(0.66)
3.40
(0.66)
4.50
(0.50)
5.00
(0.00)
WORK
ENVIRONMENT, WE
3.60
(0.80)
3.60
(0.80)
4.60
(0.49)
5.00
(0.00)
STATUS INDEX, SI
4.20
(0.98)
4.20
(0.98)
4.70
(0.46)
5.00
(0.00)
ABILITIES AND
TRAITS, AT
3.51
(1.16)
1.46
(0.74)
3.73
(1.18)
4.11
(0.74)
PROB. (EFFORT ->
REWARD), PPER
2.90
(0.70)
2.90
(0.70)
4.60
(0.66)
4.00
(0.00)
BEHAVIORAL VARIABLE
EXPERIENCE, X
3.65
(0.78)
1.40
(0.66)
1.40
(0.66)
3.00
(0.00)
EDUCATION, D
2.00
(0.00)
1.00
(0.00)
4.20
(0.40)
4.00
(0.00)
AGE, A
5.00
(0.00)
1.00
(0.00)
3.00
(0.00)
3.00
(0.00)
RISK
2.10
(1.38)
2.10
(1.38)
3.90
(0.94)
4.00
(0.00)
GENERAL SOCIAL
SKILLS, GSS
3.00
(1.55)
1.70
(0.78)
3.80
(0.87)
4.00
(0.00)
MANAGERIAL
SKILLS, OMS
4.05
(0.67)
1.40
(0.66)
3.40
(0.92)
5.00
(0.00)
MOTIVATION, M
3.60
(0.66)
1.50
(0.50)
4.90
(0.30)
5.00
(0.00)
PHYSICAL
QUALITIES, PQ
3.60
(1.28)
2.3
(1.1)
4.60
(0.49)
5.00
(0.00)
COMMUNICATION
SKILLS, L
3.95
(0.59)
1.50
(0.67)
4.30
(0.64)
4.00
(0.00)
OTHERS, OPC
2.77
(0.61)
1.30
(0.64)
4.00
(0.78)
4.00
(0.00)


A KNOWLEDGE-INTENSIVE MACHINE-LEARNING APPROACH
TO THE PRINCIPAL-AGENT PROBLEM
By
KIRAN K. GARIMELLA
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1993

To my mother, Dr. Seeta Garimella

ACKNOWLEDGMENTS
I thank Prof. Gary Koehler, chairman of the DIS department, a guru to me in the
deepest sense of the word who made it possible for me to grow intellectually and
experience the richness and fulfillment of an active mind.
I also want to thank Prof. Selcuk Erenguc for encouraging me at all times; Prof.
Harold Benson who taught me care, caution, and clarity in thinking by patiently teaching
me proof techniques in mathematics; Prof. David E.M. Sappington for giving me
invaluable lessons, by his teaching and example, on research techniques, for writing
papers and books that are replete with elegance and clarity, and for ensuring that my
research is meaningful and interesting from an economists perspective; Prof. Sanford
V. Berg, for providing valuable suggestions in agency theory; and Prof. Richard Elnicki,
Prof. Antal Majthay, and Prof. Ira Horowitz for their advice and help with the research.
I thank Prof. Malay Ghosh, Department of Statistics, and Prof. Scott
McCullough, Department of Mathematics, for their guidance in statistics and
mathematics.
I also thank the administrative staff of the DIS department for helping me in
numerous ways and making my work extremely pleasant.
I thank my wife, Raji, for her patience and understanding while I put in long and
erratic hours.
in

I cannot conclude without expressing my deepest sense of gratitude to my mother,
Dr. Seeta Garimella, who constantly encouraged me in ways too numerous to recount
and made it possible for me to pursue my studies in the land of my dreams.
IV

TABLE OF CONTENTS
ACKNOWLEDGMENTS iii
LIST OF TABLES viii
ABSTRACT xv
1 OVERVIEW 1
2 EXPERT SYSTEMS AND MACHINE LEARNING 6
2.1 Introduction 6
2.2 Expert Systems 8
2.3 Machine Learning 10
2.3.1 Introduction 10
2.3.2 Definitions and Paradigms 14
2.3.3 Probably Approximately Close Learning 21
3 GENETIC ALGORITHMS 23
3.1 Introduction 23
3.2 The Michigan Approach 26
3.3 The Pitt Approach 27
4 THE MAXIMUM ENTROPY PRINCIPLE 28
4.1 Historical Introduction 28
4.2 Examples 34
5 THE PRINCIPAL-AGENT PROBLEM 38
5.1Introduction 38
5.1.1 The Agency Relationship 38
5.1.2 The Technology Component of Agency 40
5.1.3 The Information Component of Agency 40
5.1.4 The Timing Component of Agency 42
v

5.1.5 Limited Observability, Moral Hazard, and Monitoring 44
5.1.6 Informational Asymmetry, Adverse Selection, and Screening 45
5.1.7 Efficiency of Cooperation and Incentive Compatibility 47
5.1.8 Agency Costs 47
5.2 Formulation of the Principal-Agent Problem 48
5.3 Main Results in the Literature 62
5.3.1 Model 1: The Linear-Exponential-Normal Model 63
5.3.2 Model 2 68
5.3.3 Model 3 72
5.3.4 Model 4: Communication under Asymmetry 77
5.3.5 Model G: Some General Results 80
6 METHODOLOGICAL ANALYSIS 82
7 MOTIVATION THEORY 87
8 RESEARCH FRAMEWORK 92
9 MODEL 3 97
9.1 Introduction 97
9.2 An Implementation and Study 101
9.3 Details of Experiments 106
9.3.1 Rule Representation 106
9.3.2 Inference Method 110
9.3.3 Calculation of Satisfaction Ill
9.3.4 Genetic Learning Details 114
9.3.5 Statistics Captured for Analysis 115
9.4 Results 116
9.5 Analysis of Results 118
10 REALISTIC AGENCY MODELS 149
10.1 Characteristics of Agents 157
10.2 Learning with Specialization and Generalization 158
10.3 Notation and Conventions 160
10.4 Model 4: Discussion of Results 161
10.5 Model 5: Discussion of Results 163
10.6 Model 6: Discussion of Results 164
10.7 Model 7: Discussion of Results 165
10.8 Comparison of the Models 167
10.9 Examination of Learning 172
11 CONCLUSION 194
vi

12 FUTURE RESEARCH 198
12.1 Nature of the Agency 198
12.2 Behavior and Motivation Theory 199
12.3 Machine Learning 200
12.4 Maximum Entropy 203
APPENDIX FACTOR ANALYSIS 204
REFERENCES 206
BIOGRAPHICAL SKETCH 219
Vll

LIST OF TABLES
Table page
9.1: Characterization of Agents 125
9.2: Iteration of First Occurrence of Maximum Fitness 126
9.3: Learning Statistics for Fitness of Final Knowledge Bases 126
9.4: Entropy of Final Knowledge Bases and Closeness to the Maximum 126
9.5: Frequency (as Percentage) of Values of Compensation Variables in the Final
Knowledge Base in Experiment 1 127
9.6: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 1 127
9.7: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 1 128
9.8: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 1 128
9.9: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 1 Factor Pattern 129
9.10: Experiment 1 Varimax Rotation 130
9.11: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 2 131
9.12: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 2 131
9.13: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 2 131
viii

9.14: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 2 Eigenvalues of the Correlation Matrix 132
9.15: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 2 Factor Pattern 133
9.16: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 2 -Varimax Rotated Factor Pattern 134
9.17: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 3 135
9.18: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 3 135
9.19: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 3 135
9.20: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 3 Eigenvalues of the Correlation Matrix 136
9.21: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 3 Factor Pattern 137
9.22: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 3 Varimax Rotated Factor Pattern 138
9.23: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 4 139
9.24: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 4 139
9.25: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 4 139
9.26: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 4 Eigenvalues of the Correlation Matrix 140
9.27: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 4 Factor Pattern 141
9.28: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 4 Varimax Rotated Factor Pattern 143
IX

9.29: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 5 144
9.30: Range, Mean and Standard Deviation of Values of Compensation Variables
in the Final Knowledge Base in Experiment 5 144
9.31: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 5 144
9.32: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 5 Eigenvalues of the Correlation Matrix 145
9.33: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 5 Factor Pattern 145
9.34: Factor Analysis (Principal Components Method) of the Final Knowledge
Base of Experiment 5 Varimax Rotated Factor Pattern 146
9.35: Summary of Factor Analytic Results for the Five Experiments 146
9.36: Expected Factor Identification of Compensation Variables for the Five
Experiments Derived from the Direct Factor Analytic Solution 147
9.37: Expected Factor Identification of Compensation Variables for the Five
Experiments Derived from the Varimax Rotated Factor Analytic
Solution 147
9.38: Expected Factor Identification of Behavioral and Risk Variables for the
Five Experiments Derived from the Direct Factor Pattern 148
9.39: Expected Factor Identification of Behavioral and Risk Variables for the
Five Experiments Derived from Varimax Rotated Factor Analytic
Solution 148
10.1: Correlation of LP and CP with Simulation Statistics (Model 4) 174
10.2: Correlation of LP and CP with Compensation Offered to Agents (Model
4) 174
10.3: Correlation of LP and CP with Compensation in the Principals Final KB
(Model 4) 174
10.4: Correlation of LP and CP with the Movement of Agents (Model 44 174
x

10.5: Correlation of LP with Agent Factors (Model 4) 174
10.6: Correlation of LP and CP with Agents Satisfaction (Model 4) 175
10.7: Correlation of LP and CP with Agents Satisfaction at Termination (Model
4) 175
10.8: Correlation of LP and CP with Agency Interactions (Model 4) 175
10.9: Correlation of LP with Rule Activation (Model 4) 175
10.10: Correlation of LP with Rule Activation in the Final Iteration (Model 4) . 175
10.11: Correlation of LP and CP with Principals Satisfaction and Least Squares
(Model 4) 175
10.12: Correlation of Agent Factors with Agent Satisfaction (Model 4) 176
10.13: Correlation of Principals Satisfaction with Agent Factors (Model 4) ... 176
10.14: Correlation of Principals Satisfaction with Agents Satisfaction (Model
4) 176
10.15: Correlation of Principals Last Satisfaction with Agents Last Satisfaction
(Model 4) 176
10.16: Correlation of Principals Factor with Agent Factors (Model 4) 177
10.17: Correlation of LP and CP with Simulation Statistics (Model 5) 177
10.18: Correlation of LP and CP with Compensation Offered to Agents (Model
5) 177
10.19: Correlation of LP and CP with Compensation in the Principals Final
Knowledge Base (Model 5) 177
10.20: Correlation of LP and CP with the Movement of Agents (Model 5) .... 177
10.21: Correlation of LP with Agent Factors (Model 5) 178
10.22: Correlation of LP and CP with Agents Satisfaction (Model 5) 178
10.23: Correlation of LP and CP with Agents Satisfaction at Termination (Model
5) 178
xi

10.24: Correlation of LP and CP with Agency Interactions (Model 5) 178
10.25: Correlation of LP with Rule Activation (Model 5) 178
10.26: Correlation of LP with Rule Activation in the Final Iteration (Model 5 . 179
10.27: Correlation of LP and CP with Payoffs from Agents (Model 5) 179
10.28: Correlation of LP and CP with Principals Satisfaction, Principals Factor
and Least Squares (Model 5) 179
10.29: Correlation of Agent Factors with Agent Satisfaction (Model 5) 179
10.30: Correlation of Principals Satisfaction with Agent Factors (Model 5) ... 180
10.31: Correlation of Principals Satisfaction with Agents Satisfaction (Model
5) 180
10.32: Correlation of Principals Last Satisfaction with Agents Last Satisfaction
(Model 5) 180
10.33: Correlation of Principals Satisfaction with Outcomes from Agents (Model
5) 181
10.34: Correlation of Principals Factor with Agents Factors (Model 5) 181
10.35: Correlation of LP and CP with Simulation Statistics (Model 6) 181
10.36: Correlation of LP and CP with Compensation Offered to Agents (Model
6) 181
10.37: Correlation of LP and CP with Compensation in the Principals Final
Knowledge Base (Model 6) 182
10.38: Correlation of LP and CP with the Movement of Agents (Model 6) .... 182
10.39: Correlation of LP and CP with Agent Factors (Model 6) 182
10.40: Correlation of LP and CP with Agents Satisfaction (Model 6) 182
10.41: Correlation of LP and CP with Agents Satisfaction at Termination (Model
6) 183
10.42: Correlation of LP and CP with Agency Interactions (Model 6) 183
xii

10.43: Correlation of LP and CP with Rule Activation (Model 6) 183
10.44: Correlation of LP and CP with Rule Activation in the Final Iteration
(Model 6) 183
10.45: Correlation of LP and CP with Principals Satisfaction and Least Squares
(Model 6) 184
10.46: Correlation of Agents Factors with Agents Satisfaction (Model 6) .... 184
10.47: Correlation of Principals Satisfaction with Agents Factors and Agents
Satisfaction (Model 6) 185
10.48: Correlation of Principals Factor with Agents Factor (Model 6) 185
10.49: Correlation of LP and CP with Simulation Statistics (Model 7) 185
10.50: Correlation of LP and CP with Compensation Offered to Agents (Model
7) ; 185
10.51: Correlation of LP and CP with Compensation in the Principals Final
Knowledge Base (Model 7) 186
10.52: Correlation of LP and CP with the Movement of Agents (Model 7) .... 186
10.53: Correlation of LP with Agent Factors (Model 7) 186
10.54: Correlation of LP and CP with Agents Satisfaction (Model 7) 186
10.55: Correlation of LP and CP with Agents Satisfaction at Termination (Model
7) 187
10.56: Correlation of LP and CP with Agency Interactions (Model 7) 187
10.57: Correlation of LP and CP with Rule Activation (Model 7) 187
10.58: Correlation of LP with Rule Activation in the Final Iteration (Model 7) . 187
10.59: Correlation of LP and CP with Payoffs from Agents (Model 7) 188
10.60: Correlation of LP and CP with Principals Satisfaction (Model 7) 188
10.61: Correlation of Agent Factors with Agent Satisfaction (Model 7) 188
xiii

10.62: Correlation of Principals Satisfaction with Agent Factors (Model 7) ... 188
10.63: Correlation of Principals Satisfaction with Agents Satisfaction (Model
7) 189
10.64: Correlation of Principals Last Satisfaction with Agents Last Satisfaction
(Model 7) 189
10.65: Correlation of Principals Satisfaction with Outcomes from Agents (Model
7) 189
10.66: Correlation of Principals Factor with Agents Factor (Model 7) 189
10.67: Comparison of Models 190
10.68: Probability Distributions for Models 4, 5, 6, and 7 193
xiv

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
A KNOWLEDGE-INTENSIVE MACHINE-LEARNING APPROACH
TO THE PRINCIPAL-AGENT PROBLEM
By
Kiran K. Garimella
August 1993
Chairperson: Gary J. Koehler
Major Department: Decision and Information Sciences
The objective of the research is to explore an alternative approach to the solution
of the principal-agent problem, which is extremely important since it is applicable in
almost all business environments. It has been traditionally addressed by the optimization-
analytical framework. However, there is a clearly recognized need for techniques that
allow the incorporation of behavioral and motivational characteristics of the agent and
the principal that influence their selection of effort and payment levels.
The alternative proposed is a knowledge-intensive, machine-learning approach,
where all the relevant knowledge and the constraints of the problem are taken into
account in the form of knowledge-bases.
Genetic algorithms are employed for learning, supplemented in later models by
specialization and generalization operators. A number of models are studied in order of
increasing complexity and realism. Initial studies are presented that provide counter-
xv

examples to traditional agency theory and that emphasize the need for going beyond the
traditional framework. The new framework is more robust, easily extensible in a
modular manner, and yields contracts tailored to the behavioral characteristics of
individual agents.
Factor analysis of final knowledge bases after extensive learning shows that
elements of compensation besides basic pay and share of output play a greater role in
characterizing good contracts. The learning algorithms tailor contracts to the behavioral
and motivational characteristics of individual agents. Further, neither did perfect
information yield the highest satisfaction nor did the complete absence of information
yield the least satisfaction. This calls into question the traditional agency wisdom that
more information is always desirable.
Studies of other models study the effect of two different policies of evaluating
agents performance by the principal-individualized (discriminatory) evaluation versus the
relative (nondiscriminatory) evaluation. The results suggest guidelines for employing
different types of models to simulate different agency environments.
xvi

CHAPTER 1
OVERVIEW
The basic research addressed by this dissertation is the theory and application of
machine learning to assist in the solution of decision problems in business. Much of the
earlier research in machine learning was devoted to addressing specific and ad-hoc
problems or to fill a gap or make up for some deficiency in an existing framework,
usually motivated by developments in expert systems and statistical pattern recognition.
The first applications were to technical problems such as knowledge acquisition, coping
with a changing environment and filtering of noise (where filtering and optimal control
were considered inadequate because of poorly understood domains), data or knowledge
reduction (where the usual statistical theory is inadequate to express the symbolic
richness of the underlying domain), and scene and pattern analysis (where the classical
statistical techniques fail to take into account pertinent prior information; see for
example, Jaynes, 1986a).
The initial research was concerned with gaining an understanding of learning in
extremely simple toy world models, such as checkers (Samuel, 1963), SHRDLU blocks
world (Winograd, 1972), and various discovery systems. The insights gained by such
research soon influenced serious applications.
1

2
The underlying domains of most of the early applications were relatively well
structured, whether they were the stylized rules of checkers and chess or the digitized
images of visual sensors. Our research focus is on importing these ideas into the area
of business decisionmaking.
Genetic algorithms, a relatively new paradigm of machine learning, deals with
adaptive processes modeled on ideas from natural genetics. Genetic algorithms use the
ideas of parallelism, randomized search, fitness criteria for individuals, and the formation
of new exploratory solutions using reproduction, survival and mutation. The concept is
extremely elegant, powerful, and easy to work with from the viewpoint of the amount
of knowledge necessary to start the search for solutions.
A related issue is maximum entropy. The Maximum Entropy Principle is an
extension of Bayesian theory and is founded on two other principles: the Desideratum of
Consistency and Maximal-Noncommitment. While Bayesian analysis begins by assuming
a prior, the Maximum Entropy Principle seeks distributions that maximize the Shannon
entropy and at the same time satisfy whatever constraints may apply. The justification
for using Shannon entropy comes from the works of Bernoulli, Laplace, Jeffreys, and
Cox on the one hand, and from the works of Maxwell, Boltzmann, Gibbs, and Shannon
on the other; the principle has been extensively championed by Jaynes and is only just
now penetrating into economic analysis.
Under the maximum entropy technique, the task of updating priors based on data
is now subsumed under the general goal of maximizing entropy of distributions given any
and all applicable constraints, where the data (or sufficient statistics on the data) play the

3
role of constraints. Maximum entropy is related to machine learning by the fact that the
initial distributions (or assumptions) used in a learning framework, such as genetic
algorithms, may be maximum entropy distributions. A topic of research interest is the
development of machine learning algorithms or frameworks that are robust with respect
to maximum entropy. In other words, deviation of initial distributions from maximum
entropy distributions should not have any significant effect on the learning algorithms (in
the sense of departure from good solutions).
The overall goal of the research is to present an integrated methodology involving
machine learning with genetic algorithms in knowledge bases and to illustrate its use by
application to an important problem in business. The principal-agent problem was
chosen for the following reasons: it is widespread, important, nontrivial, and fairly
general so that different models of the problem can be investigated, and information-
theoretic considerations play a crucial role in the problem. Moreover, a fair amount of
interest over the problem has been generated among researchers in economics, finance,
accounting, and game theory, whose predominant approach to the problem is that of
constrained optimization. Several analytical insights have been generated, which should
serve as points of comparison to results that are expected from our new methodology.
The most important component of the new proposed methodology is information
in the form of knowledge bases, coupled with strength of performance of the individual
pieces of knowledge. These knowledge bases, the associated strengths, their relation to
one another, and their role in the scheme of things are derived from the individuals prior
knowledge and from the theory of human behavior and motivation. These knowledge

4
bases contain, for example, information about the agents characteristics and pattern of
behavior under different compensation schemes; in other words, they deal with the issues
of hidden characteristics and induced effort or behavior. Given the expected behavior
pattern of an agent, a related research issue is the study of the effect of using
distributions that have maximum entropy with respect to the expected behavior.
Trial compensation schemes, which come from the specified knowledge bases, are
presented to the agent(s). Upon acceptance of the contract and realization of the output,
the actual performance of the agent (in terms of output or the total welfare) is evaluated,
and the associated compensation schemes are assigned proportional credit. Periodically,
iterations of the genetic algorithm will be used to create a new knowledge base that
enriches the current one.
Chapter 2 begins with an introduction to artificial intelligence, expert systems,
and machine learning. Chapter 3 describes genetic algorithms. Chapter 4 covers the
origin of the Maximum Entropy Principle and its formulation. Chapter 5 deals with a
survey of the principal-agent problem, where a few basic models are presented, along
with some of the main results of the research.
Chapter 6 examines the traditional methodology used in attacking the principal-
agent problem, and measures to cover the inadequacies are proposed. One of the basic
assumptions of the economic theory-the assumption of risk attitudes and utilityis
circumvented by directly dealing with the knowledge-based models of the agent and the
principal. To this end, a brief look at some of the ideas from behavior and motivation
theory is taken in Chapter 7.

5
Chapter 8 describes the basic research model. Elements of behavior and
motivation theory and knowledge bases are incorporated. A research strategy to study
agency problems is proposed. The use of genetic algorithms periodically to enrich the
knowledge bases and to carry out learning is suggested. An overview of the research
models, all of which incorporate many features of the basic model, is presented.
Chapter 9 describes Model 3 in detail. Chapter 10 introduces Models 4 through
7 and describes each in detail. Chapter 11 provides a summary of the results of Chapters
9 and 10. Directions for future research are covered in Chapter 12.

CHAPTER 2
EXPERT SYSTEMS AND MACHINE LEARNING
2.1 Introduction
The use of artificial intelligence in a computerized world is as revolutionary as
the use of computers is in a manual world. One can make computers intelligent in the
same sense as man is intelligent. The various techniques of doing this compose the body
of the subject of artificial intelligence. At the present state of the art, computers are at
last being designed to compete with man on his own ground on something like equal
terms. To put it in another way, computers have traditionally acted as convenient tools
in areas where man is known to be deficient or inefficient, namely, doing complicated
arithmetic very quickly, or making many copies of data (i.e., files, reports, etc.).
Learning new things, discovering facts, conjecturing, evaluating and judging
complex issues (for example, consulting), using natural languages, analyzing and
understanding complex sensory inputs such as sound and light, and planning for future
action are mental processes that are peculiar to man (and to a lesser extent, to some
animals). Artificial intelligence is the science of simulating or mimicking these mental
processes in a computer.
The benefits are immediately obvious. First, computers already fill some of the
gaps in human skills; second, artificial intelligence fills some of the gaps that computers
6

7
themselves suffer (i.e., human mental processes). While the full simulation of the human
brain is a distant dream, limited application of this idea has already produced favorable
results.
Speech-understanding problems were investigated with the help of the HEARSAY
system (Erman et al., 1980, 1981; and Hayes-Roth and Lesser, 1977). The faculty of
vision relates to pattern recognition and classification and analysis of scenes. These
problems are especially encountered in robotics (Paul, 1981). Speech recognition
coupled with natural language understanding as in the limited system SHRDLU
(Winograd, 1973) can find immediate uses in intelligent secretary systems that can help
in data management and correspondence associated with business.
An area that is commercially viable in large business environments that involve
manufacturing and any other physical treatment of objects is robotics. This is a proven
area of artificial intelligence application, but is not yet cost effective for small business.
Several robot manufacturers have a good order book position. For a detailed survey see
for example, Engelberger, 1980.
An interesting viewpoint to the application of artificial intelligence to industry and
business is that presented by decision analysis theory. Decision analysis helps managers
to decide between alternative options and assess risk and uncertainty in a better way than
before, and to carry out conflict management when there are conflicts among objectives.
Certain operations research techniques are also incorporated, as for example, fair
allocation of resources that optimize returns. Decision analysis is treated in Fishbum
(1981), Lindley (1971), Keeney (1984) and Keeney and Raiffa (1976). In most

8
applications of expert systems, concepts of decision analysis find expression (Phillips,
1986). Manual application of these techniques is not cost effective, whereas their use
in certain expert systems, which go by the generic name of Decision Analysis Expert
Systems, leads to quick solutions of what were previously thought to be intractable
problems (Conway, 1986). Several systems have been proposed that range from
scheduling to strategy planning. See for example, Williams (1986).
2,2 Expert Systems
The most fascinating and economically justifiable area of artificial intelligence is
the development of expert systems. These are computer systems that are designed to
provide expert advice in any area. The kind of information that distinguishes an expert
from a nonexpert forms the central idea in any expert system. This is perhaps the only
area that provides concrete and conclusive proof of the power of artificial intelligence
techniques. Many expert systems are commercially viable and motivate diverse sources
of funding for research into artificial intelligence. An expert system incorporates many
of the techniques of artificial intelligence, and a positive response to artificial intelligence
depends on the reception of expert systems by informed laymen.
To construct an expert system, the knowledge engineer works with an expert in
the domain and extracts knowledge of relevant facts, rules, rules-of-thumb, exceptions
to standard theory, and so on. This is a difficult task and is known variously as
knowledge acquisition or mining. Because of the complex nature of the knowledge and
the ways humans store knowledge, this is bound to be a bottleneck to the development

9
of the expert system. This knowledge is codified in the form of several rules and
heuristics. Validation and verification runs are conducted on problems of sufficient
complexity to see that the expert system does indeed model the thinking of the expert.
In the task of building expert systems, the knowledge engineer is helped by several tools,
such as EMYCIN, EXPERT, OPS5, ROSIE, GURU, etc.
The net result of the activity of knowledge mining is a knowledge base. An
inference system or engine acts on this knowledge base to solve problems in the domain
of the expert system. An important characteristic of expert systems is the ability to
justify and explain their line of reasoning. This is to create credibility during their use.
In order to do this, they must have a reasonably sophisticated input/output system.
Some of the typical problems handled by expert systems in the areas of business,
industry, and technology are presented in Feigenbaum and McCorduck (1983) and Mitra
(1986). Important cases where expert systems are brought in to handle the problems are
1. Capturing, replicating, and distributing expertise.
2. Fusing the knowledge of many experts.
3. Managing complex problems and amplifying expertise.
4. Managing knowledge.
5. Gaining a competitive edge.
As examples of successful expert systems, one can consider MYCIN, designed
to diagnose infectious diseases (Shortliffe, 1976); DENDRAL, for interpretation of
molecular spectra (Buchanan and Feigenbaum, 1978); PROSPECTOR, for geological
studies (Duda et al., 1979; Hart, 1978); and WHY, for teaching geography (Stevens and

10
Collins, 1977). For a more exhaustive treatment, see, for example Stefik et al. (1982),
Barr and Feigenbaum (1981, 1982), Cohen and Feigenbaum (1982), and Barr et al.
(1989).
2,3 Machine Learning
2.3.1 Introduction
One of the key limitations of computers as envisaged by early researchers is the
fact that they must be told in explicit detail how to solve every problem. In other words,
they lack the capacity to learn from experience and improve their performance with time.
Even in most expert systems today, there is only some weak form of implicit learning,
such as learning by being told, rote memorizing, and checking for logical consistency.
The task of machine learning research is to make up for this inadequacy by incorporating
learning techniques into computers.
The abstract goals of machine learning research are broadly
1. To construct learning algorithms that enable computers to learn.
2. To construct learning algorithms that enable computers to learn in the same way
as humans learn.
In both cases, the functional goals of machine learning research are as follows:
1. To use the learning algorithms in application domains to solve nontrivial
problems.
To gain a better understanding of how humans learn, and the details of human
cognitive processes.
2.

11
When the goal is to come up with paradigms that can be used to solve problems,
several subsidiary goals can be proposed:
1. To see if the learning algorithms do indeed perform better than humans do in
similar situations.
2. To see if the learning algorithms come up with solutions that are intuitively
meaningful for humans.
3. To see if the learning algorithms come up with solutions that are in some way
better or less expensive than some alternative methodology.
It is undeniable that humans possess cognitive skills that are superior not only to
other animals but also to most learning algorithms that are in existence today. It is true
that some of these algorithms perform better than humans in some limited and highly
formalized situations involving carefully modeled problems, just as the simplex method
consistently produces solutions superior to those possible by a human being. However,
and this is the crucial issue, humans are quick to adopt different strategies and solve
problems that are ill-structured, ill-defined, and not well understood, for which there
does not exist any extensive domain theory, and that are characterized by uncertainty,
noise, or randomness. Moreover, in many cases, it seems more important to humans to
find solutions to problems that satisfy some constraints rather than to optimize some
"function." At the present state of the art, we do not have a consistent, coherent and
systematic theory of what these constraints are. These constraints are usually understood
to be behavioral or motivational in nature.

12
Recent research has shown that it is also undeniable that humans perform very poorly in
the following respects:
* they do not solve problems in probability theory correctly ;
* while they are good at deciding cogency of information, they are poor at judging
relevance (see Raiffa, accident witnesses, etc.);
* they lack statistical sophistication;
* they find it difficult to detect contradictions in long chains of reasoning;
* they find it difficult to avoid bias in inference and in fact may not be able to
identify it.
(See for example, Einhorn, 1982; Kahneman and Tversky, 1982a, 1982b, 1982c, 1982d;
Lichtenstein et al., 1982; Nisbett et al., 1982; Tversky and Kahneman, 1982a, 1982b,
1982c, 1982d.)
Tversky and Kahneman (1982a) classify, for example, several misconceptions in
probability theory as follows:
* insensitivity to prior probability of outcomes;
* insensitivity to sample size;
* misconceptions of chance;
* insensitivity to predictability;
* the illusion of validity;
* misconceptions of regression.

13
The above inadequacies on the part of humans pertain to higher cognitive
thinking. It goes without saying that humans are poor at manipulating numbers quickly,
and are subject to physical fatigue and lack of concentration when involved in mental
activity for a long time. Computers are, of course, subject to no such limitations.
It is important to note that these inadequacies usually do not lead to disastrous
consequences in most everyday circumstances. However, the complexity of the modem
world gives rise to intricate and substantial problems, solutions to which forbid
inadequacies of the above type.
Machine learning must be viewed as an integrated research area that seeks to
understand the learning strategies employed by humans, incorporate them into learning
algorithms, remove any cognitive inadequacies faced by humans, investigate the
possibility of better learning strategies, and characterize the solutions yielded by such
research in terms of proof of correctness, convergence to optimality (where meaningful),
robustness, graceful degradation, intelligibility, credibility, and plausibility.
Such an integrated view does not see the different goals of machine learning
research as separate and clashing; insights in one area have implications for another.
For example, insights into how humans learn help spot their strengths and weaknesses,
which motivates research into how to incorporate the strengths into algorithms and how
to cover up the weaknesses; similarly, discovering solutions from machine learning
algorithms that are at first nonintuitive to humans motivates deeper analysis of the
domain theory and of the human cognitive processes in order to come up with at least
plausible explanations.

14
2.3.2 Definitions and Paradigms
Any activity that improves performance or skills with time may be defined as
learning. This includes motor skills and general problem-solving skills. This is a highly
functional definition of learning and may be objected to on the grounds that humans learn
even in a context that does not demand action or performance. However, the functional
definition may be justified by noting that performance can be understood as improvement
in knowledge and acquisition of new knowledge or cognitive skills that are potentially
usable in some context to improve actions or enable better decisions to be taken.
Learning may be characterized by several criteria. Most paradigms fall under
more than one category. Some of these are
1. Involvement of the learner.
2. Sources of knowledge.
3. Presence and role of a teacher.
4. Access to an oracle (learning from internally generated examples).
5. Learning "richness."
6. Activation of learning:
(a) systematic;
(b) continuous;
(c) periodic or random;
(d) background;
(e) explicit or external (also known as intentional);

15
(f) implicit (also known as incidental);
(g) call on success; and
(h) call on failure.
When classified by the criterion of the learners involvement, the standard is the
degree of activity or passivity of the learner. The following paradigms of learning are
classified by this criterion, in increasing order of learner control:
1. Learning by being told (learner only needs to memorize by rote);
2. Learning by instruction (learner needs to abstract, induce, or integrate to some
extent, and then store it);
3. Learning by examples (learner needs to induce to a great extent the correct
concept, examples of which are supplied by the instructor);
4. Learning by analogy (learner needs to abstract and induce to a greater degree in
order to learn or solve a problem by drawing the analogy. This implies that the
learner already has a store of cases against which he can compare the analogy and
that he knows how to abstract and induce knowledge);
5. Learning by observation and discovery (here the role of the learner is greatest;
the learner needs to focus on only the relevant observations, use principles of
logic and evidence, apply some value judgments, and discover new knowledge
either by using induction or deduction).
The above learning paradigms may also be classified on the basis of richness of
knowledge. Under this criterion, the focus is on the richness of the resulting knowledge,
which may be independent of the involvement of the learner. The spectrum of learning

16
is from "raw data" to simple functions, complicated functions, simple rules, complex
knowledge bases, semantic nets, scripts, and so on.
One fundamental distinction can be made from observation of human learning.
The most widespread form of human learning is incidental learning. The learning
process is incidental to some other cognitive process. Perception of the world, for
example, leads to formation of concepts, classification of objects in classes or primitives,
the discovery of the abstract concepts of number, similarity, and so on (see for example,
Rand 1967). These activities are not indulged in deliberately. As opposed to incidental
learning, we have intentional learning, where there is a deliberate and explicit effort to
learn. The study of human learning processes from the standpoint of implicit or explicit
cognition is the main subject of research in psychological learning. (See for example,
Anderson, 1980; Craik and Tulving, 1975; Glass and Holyoak, 1986; Hasher and Zacks,
1979; Hebb, 1961; Mandler, 1967; Reber, 1967; Reber, 1976; Reber and Allen, 1978;
Reber et al., 1980).
A useful paradigm for the area of expert systems might be learning through
failure. The explanation facility ensures that the expert system knows why it is correct
when it is correct, but it needs to know why it is wrong when it is wrong, if it must
improve performance with time. Failure analysis helps in focussing on deficient areas
of knowledge.
Research in machine learning raises several wider epistemological issues such as
hierarchy of knowledge, contextuality, integration, conditionality, abstraction, and
reduction. The issue of hierarchy arises in induction of decision trees (see for example,

17
Quinlan, 1979; Quinlan, 1986; Quinlan, 1990); contextuality arises in learning semantics,
as in conceptual dependency (see for example, Schank, 1972; Schank and Colby, 1973),
learning by analogy (see for example, Buchanan et al., 1977; Dietterich and Michalski,
1979), and case-based reasoning (Riesbeck and Schank, 1989); integration is fundamental
to forming relationships, as in semantic nets (Quillian, 1968; Anderson and Bower, 1973;
Anderson, 1976; Norman, et al., 1975; Schank and Abelson, 1977), and frame-based
learning (see for example, Minsky, 1975); abstraction deals with formation of universal
or classes, as in classification (see for example, Holland, 1975), and induction of
concepts (see for example, Mitchell, 1977; Mitchell, 1979; Valiant, 1984; Haussler,
1988); reduction arises in the context of deductive learning (see for example, Newell
and Simon, 1956; Lenat, 1977), conflict resolution (see for example, McDermott and
Forgy, 1978), and theorem-proving (see for example, Nilsson, 1980). For an excellent
treatment of these issues from a purely epistemological viewpoint, see for example Rand
(1967) and Peikoff (1991).
In discussing real-world examples of learning, it is difficult or meaningless to look
for one single paradigm or knowledge representation scheme as far as learning is
concerned. Similarly, there could be multiple teachers: humans, oracles, and an
accumulated knowledge that acts as an internal generator of examples.
In analyzing learning paradigms, it is useful to look at least three aspects, since
they each have a role in making the others possible:
1. Knowledge representation scheme.
2. Knowledge acquisition scheme.

18
3. Learning scheme.
At the present time, we do not yet have a comprehensive classification of learning
paradigms and their systematic integration into a theory. One of the first attempts in this
direction was taken by Michalski, Carbonell, and Mitchell (1983).
An extremely interesting area of research in machine learning that will have far-
reaching consequences for such a theory of learning is multistrategy systems, which try
to combine one or more paradigms or types of learning based on domain problem
characteristics or to try a different paradigm when one fails. See for example Kodratoff
and Michalski (1990). One may call this type of research meta-learning research,
because the focus is not simply on rules and heuristics for learning, but on rules and
heuristics for learning paradigms. Here are some simple learning heuristics, for
example:
LH1: Given several "isa" relationships, find out about relations between the properties.
(For example, the observation that "Socrates is a man" motivates us to find out
why Socrates should indeed be classified as a man, i.e., to discover that the
common properties are "rational animal" and several physical properties.)
LH2: When an instance causes an existing heuristic with certainty to be revised
downwards, ask for causes.
LH3: When an instance that was thought to belong to a concept or class but later turns
out not to belong to it, find out what it does belong to.
LH4: If X isa Y1 and X isa Y2, then find the relationship between Y1 and Y2, and
check for consistency. (This arises in learning by using semantic nets).

19
LH5: Given an implication, find out if it is also an equivalence.
LH6: Find out if any two or more properties are semantically the same, the opposite,
or unrelated.
LH7: If an object possesses two or more properties simultaneously from the same class
or similar classes, check for contradictions, or rearrange classes hierarchically.
LH8: An isa-tree in a semantic net creates an isa-tree with the object as a parent; find
out in which isa-tree the parent object occurs as a child.
We can contrast these with meta-rules or meta-heuristics. A meta-rule is also a
rule which says something about another rule. It is understood that meta-rules are watch
dog rules that supervise the firing of other rules. Each learning paradigm has a set of
rules that will lead to learning under that paradigm. We can have a set of meta-rules for
learning if we have a learning system that has access to several paradigms of learning
and if we are concerned with what paradigm to select at any given time. Learning meta
rules help the learner to pick a particular paradigm because the learner has knowledge
of the applicability of particular paradigms given the nature and state of a domain or
given the underlying knowledge-base representation schema.
The following are examples of meta-rules in learning:
ML1: If several instances of a domain-event occur,
then use generalization techniques.
ML2: If an event or class of events occur a number of times with little or no change on
each occurrence,
then use induction techniques.

20
ML3: If a problem description similar to the problem on hand exists in a different
domain or situation and that problem has a known solution,
then use leaming-by-analogy techniques.
ML4: If several facts are known about a domain including axioms and production rules,
then use deductive learning techniques.
ML5: If undefined variables or unknown variables are present and no other learning rule
was successful,
then use the leaming-from-instruction paradigm.
In all cases of learning, meta-rules dictate learning strategies, whether explicitly as in a
multi-strategy system, or implicitly as when the researcher or user selects a paradigm.
Just as in expert systems, the learning strategy may be either goal directed or
knowledge directed. Goal-directed learning proceeds as follows:
1. Meta-rules select learning paradigm(s).
2. Learner imposes the learning paradigm on the knowledge base.
3. The structure of the knowledge base and the characteristics of the paradigm
determine the representation scheme.
4. The learning algorithm(s) of the paradigm(s) execute(s).
Knowledge directed learning, on the other hand, proceeds as follows:
1. The learner examines the available knowledge base.
2. The structure of the knowledge base limits the extent and type of learning, which
is determined by the meta-rules.
The learner chooses an appropriate representation scheme.
3.

21
4. The learning algorithm(s) of the chosen learning paradigm(s) execute(s).
2.3.3 Probably Approximately Close Learning
Early research on inductive inference dealt with supervised learning from
examples (see for example, Michalski, 1983; Michalski, Carbonell, and Mitchell, 1983).
The goal was to learn the correct concept by looking at both positive and negative
examples of the concept in question. These examples were provided in one of two ways:
either the learner obtained them by observation, or they were provided to the learner by
some external instructor. In both cases, the class to which each example belonged was
conveyed to the learner by the instructor (supervisor, or oracle). The examples provided
to the learner were drawn from a population of examples or instances. This is the
framework underlying early research in inductive inference (see for example, Quinlan,
1979; Quinlan, 1986: Angluin and Smith 1983).
Probably Approximately Close Identification (or PAC-ID for short) is a powerful
machine-learning methodology that seeks inductive solutions in a supervised
nonincremental learning environment. It may be viewed as a multiple-criteria learning
problem in which there are at least three major objectives:
(1) to derive (or induce) the correct solution, concept or rule, which is as close as we
please to the optimal (which is unknown);
(2) to achieve as high a degree of confidence as we please that the solution so derived
above is in fact as close to the optimal as we intended;
(3) to ensure that the "cost" of achieving the above two objectives is "reasonable."

22
PAC-ID therefore replaces the original research direction in inductive machine
learning (seeking the true solution) by the more practical goal of seeking solutions close
to the true one in polynomial time. The technique has been applied to certain classes of
concepts, such as conjunctive normal forms (CNF). Estimates of necessary distribution
independent sample sizes are derived based on the error and confidence criteria; the
sample sizes are found to be polynomial in some factor such as the number of attributes.
Applications to science and engineering have been demonstrated.
The pioneering work on PAC-ID was by Valiant (1984, 1985) who proposed the
idea of finding approximate solutions in polynomial time. The ideas of characterizing
the notion of approximation by using the concept of functional complexity of the
underlying hypothesis spaces, introducing confidence in the closeness to optimality, and
obtaining results that are independent of the underlying probability distribution with
which the supervisory examples are generated (by nature or by the supervisor), compose
the direction of the latest research. (See for example, Haussler, 1988; Haussler, 1990a;
Haussler, 1990b; Angluin, 1987; Angluin, 1988; Angluin and Laird, 1988; Blumer,
Ehrenfeucht, Haussler, and Warmuth, 1989; Pitt and Valiant, 1988; and Rivest, 1987).
The theoretical foundations for the mathematical ideas of learning convergence
with high confidence are mainly derived from ideas in statistics, probability, statistical
decision theory, and fractal theory. (See for example, Vapnik, 1982; Vapnik and
Chervonenkis, 1971; Dudley, 1978; Dudley, 1984; Dudley, 1987; Kolmogorov and
Tihomirov, 1961; Kullback, 1959; Mandelbrot, 1982; Pollard, 1984; Weiss and
Kulikowski, 1991).

CHAPTER 3
GENETIC ALGORITHMS
3.1 Introduction
Genetic classification algorithms are learning algorithms that are modeled on the
lines of natural genetics (Holland, 1975). Specifically, they use operators such as
reproduction, crossover, mutation, and fitness functions. Genetic algorithms make use
of inherent parallelism of chromosome populations and search for better solutions through
randomized exchange of chromosome material and mutation. The goal is to improve the
gene pool with respect to the fitness criterion from generation to generation.
In order to use the idea of genetic algorithms, problems must be appropriately
modeled. The parameters or attributes that constitute an individual of the population
must be specified. These parameters are then coded. The simulation begins with a
random generation of an initial population of chromosomes, and the fitness of each is
calculated. Depending on the problem and the type of convergence desired, it may be
decided to keep the population size constant or varying across iterations of the
simulation.
Using the population of an iteration, individuals are selected randomly according
to their fitness level to survive intact or to mate with other similarly selected individuals.
For mating members, a crossover point is randomly determined (an individual with n
23

24
attributes has n-1 crossover points), and the individuals exchange their "strings," thus
forming new individuals. It may so happen that the new individuals are exactly the same
as the parents. In order to introduce a certain amount of richness into the population,
a mutation operator with extremely low probability is applied to the bits in the individual
strings, which randomly changes each bit. After mating, survival, and mutation, the
fitness of each individual in the new population is calculated. Since the probability of
survival and mating is dependent on the fitness level, more fit individuals have a higher
probability of passing on their genetic material.
Another factor plays a role in determining the average fitness of the population.
Portions of the chromosome, called genes or features, act as determinants of qualities of
the individual. Since in mating, the crossover point is chosen randomly, those genes that
are shorter in length are more likely to survive a crossover and thus be carried from
generation to generation. This has important implications for modeling a problem and
will be mentioned in the chapter on research directions.
The power of genetic algorithms (henceforth, GAs) derives from the following
features:
1. It is only necessary to know enough about the problem to identify the
essential attributes of the solution (or "individual"); the researcher can work
in comparative ignorance of the actual combinations of attribute values that
may denote qualities of the individual.
2. Excessive knowledge cannot harm the algorithm; the simulation may be
started with any extra knowledge the researcher may have about the problem,

25
such as his beliefs about which combinations play an important role. In such
cases, the simulation may start with the researchers population and not a
random population; if it turns out that the whole or some part of this
knowledge is incorrect or irrelevant, then the corresponding individuals get
low fitness values and hence have a high probability of eventually
disappearing from the population.
3. The remarks in point 2 above apply in the case of mutation also. If mutation
gives rise to a useless feature, that individual gets a low fitness value and
hence has a low probability of remaining in the population for a long time.
4. Since GAs use many individuals, the probability of getting stuck at local
optima is minimized.
According to Holland (1975), there are essentially four ways in which genetic
algorithms differ from optimization techniques:
1. GAs manipulate codings of attributes directly.
2. They conduct search from a population and not from a single point.
3. It is not necessary to know or assume extra simplifications in order to
conduct the search; GAs conduct the search "blindly." It must be noted
however, that randomized search does not imply directionless search.
4. The search is conducted using stochastic operators (random selection
according to fitness) and not by using deterministic rules.

26
There are two important models for GAs in learning. One is the Pitt approach,
and the other is the Michigan approach. The approaches differ in the way they define
individuals and the goals of the search process.
3.2 The Michigan Approach
The knowledge base of the researcher or the user constitutes the genetic
population, in which each rule is an individual. The antecedents and consequents of each
rule form the chromosome. Each rule denotes a classifier or detector of a particular
signal from the environment. Upon receipt of a signal, one or more rules fire,
depending on the signal satisfying the antecedent clauses. Depending on the success of
the action taken or the consequent value realized, those rules that contributed to the
success are rewarded, and those rules that supported a different consequent value or
action are punished. This process of assigning reward or punishment is called credit
assignment.
Eventually, rules that are correct classifiers get high reward values, and their
proposed action when fired carries more weight in the overall decision of selecting an
action. The credit assignment problem is the problem of how to allocate credit (reward
or punishment). One approach is the bucket-brigade algorithm (Holland, 1986).
The Michigan approach may be combined with the usual genetic operators to
investigate other rules that may not have been considered by the researcher.

27
3.3 The Pitt Approach
The Pitt Approach, by De Jong (see for example, De Jong, 1988), considers the
whole knowledge base as one individual. The simulation starts with a collection of
knowledge bases. The operation of crossover works by randomly dichotomizing two
parent knowledge bases (selected at random) and mixing the dichotomized portions across
the parents to obtain two new knowledge bases. The Pitt approach may be used when
the researcher has available to him a panel of experts or professionals, each of whom
provides one knowledge base for some decision problem at hand. The crossover operator
therefore enables one to consider combinations of the knowledge of the individuals, a
process that resembles a brainstorming session. This is similar to a group decision
making approach. The final knowledge base or bases that perform well empirically
would then constitute a collection of rules obtained from the best rules of the original
expertise, along with some additional rules that the expert panel did not consider before.
The Michigan approach will be used in this research to simulate learning on one
knowledge base.

CHAPTER 4
THE MAXIMUM ENTROPY PRINCIPLE
4.1 Historical Introduction
The principle of maximum entropy was championed by E.T. Jaynes in the 1950s
and has gained many adherents since. There are a number of excellent papers by E.T.
Jaynes explaining the rationale and philosophy of the maximum entropy principle. The
discussion of the principle essentially follows Jaynes (1982, 1983, 1986a, 1986b, and
1991).
The maximum entropy principle may be viewed as "a natural extension and
unification of two separate lines of development. . The first line is identified with the
names Bernoulli, Laplace, Jeffreys, Cox; the second with Maxwell, Boltzmann, Gibbs,
Shannon." (Jaynes, 1983).
The question of approaching any decision problem with some form of prior
information is historically known as the Principle of Insufficient Reason (so named by
James Bernoulli in 1713). Jaynes (1983) suggests the name Desideratum of Consistency,
which may be formally stated as follows:
(1) a probability assignment is a way of describing a certain state of knowledge;
i.e., probability is an epistemological concept, not a metaphysical one;
28

29
(2) when the available evidence does not favor any one alternative among others,
then the state of knowledge is described correctly by assigning equal
probabilities to all the alternatives;
(3) suppose A is an event or occurrence for which some favorable cases out of
some set of possible cases exist. Suppose also that all the cases are equally
likely. Then, the probability that A will occur is the ratio of the number of
cases favorable to A to the total number of equally possible cases. This idea
is formally expressed as
Pr [a] Number of cases favorable to A
N Number of equally possible cases '
In cases where Pr[] is difficult to estimate (such as when the number of cases is
infinite or impossible to find out), Bernoullis weak law of large numbers may be
applied, where
Pi [A]
M Number of cases favorable to A
N Total number of equally likely cases
Number of times A occurs
Number of trials
m
n '
Limit theorems in statistics show that given (M,N) as the true state of nature, the
observed frequency f(m,n) = m/n approaches Pr[A] = P(M,N) = M/N as the number
of trials increase.

30
The reverse problem consists of estimating P(M,N) by f(m,n). For example, the
probability of seeing m successes in n trials when each trial is independent with
probability of success p, is given by the binomial distribution:
P(m \ n, = P(m | n,p) = (n]pm(l-p)n'm.
N \ml
The inverse problem would then consist of finding Pr[M] given (m,N,n). This problem
was given a solution by Bayes in 1763 as follows: Given (m,n), then
Pi[p < ^ < p + dp] = P(dp | m,n)
(n + 1)!
ml (n m) !
pm (l p)n m dp.
which is the Beta distribution.
These ideas were generalized and put into the form they are today, known as the
Bayes theorem, by Laplace as follows: When there is an event E with possible causes
C¡, and given prior information I and the observation E, the probability that a particular
cause C¡ caused the event E is given by
, v P(E\Ci) P(Ci\l)
PiCAE.I) = ^ E-
5^- P(E\Cj) P[Cj\l)
which result has been called "learning by experience" (Jaynes, 1978).
The contributions of Laplace were rediscovered by Jeffreys around 1939 and in
1946 by Cox who, for the first time, set out to study the "possibility of constructing a
consistent set of mathematical rules for carrying out plausible, rather than deductive,
reasoning." (Jaynes, 1983).

31
According to Cox, the fundamental result of mathematical inference may be
described as follows: Suppose A, B, and C represent propositions, AB the proposition
"Both A and B are true", and -|A the negation of A. Then, the consistent rules of
combination are:
P(AB | C) = P(A | BC) P(B | C), and
P(A | B) + P(->A|B) = 1.
Thus, "Cox proved that any method of inference in which we represent degrees of
plausibility by real numbers, is necessarily either equivalent to Laplaces, or
inconsistent." (Jaynes, 1983).
The second line of development starts with James Clerk Maxwell in the 1850s
who, in trying to find the probability distribution for the velocity direction of spherical
molecules after impact, realized that knowledge of the meaning of the physical
parameters of any system constituted extremely relevant prior information. The
development of the concept of entropy maximization started with Boltzmann who
investigated the distribution of molecules in a conservative force field in a closed system.
Given that there are N molecules in the closed system, the total energy E remains
constant irrespective of the distribution of the molecules inside the system. All positions
and velocities are not equally likely. The problem is to find the most probable
distribution of the molecules. Boltzmann partitioned the phase space of position and
momentum into a discrete number of cells Rk, where 1 < k < s. These cells were
assumed to be such that the k-th cell is a region which is small enough so that the energy
of a molecule as it moves inside that region does not change significantly, but which is

32
also so large that a large number Nk of molecules can be accommodated in it. The
problem of Boltzmann then reduces to the problem of finding the best prediction of Nk
for any given k in 1, ,s.
The numbers Nk are called the occupation numbers. The number of ways a given
set of occupation numbers will be realized is given by the multinomial coefficient
W(Nk)
AT!
N2l ... Ngl
The constraints are given by
(1)
S
E = E Nk Ek> and
k = 1
" E "*
k = 1
Since each set {Nk} of occupation numbers represents a possible distribution, the
problem is equivalently expressed as finding the most probable set of occupation numbers
from the many possible sets. Using Stirlings approximation of factorials
n\
sj2nn
n
in equation (1) yields
log W
The right hand
- E .
k 1 V
N,
(2)
side of (2) is the familiar Shannon entropy formula for the
distribution specified by probabilities which are approximated by the frequencies Nk/N,
k = 1, ..., s. In fact, in the limit as N goes to infinity,

33
lim
N-* oo
N'1 log W = -Y 7 log
^ N
N
= H.
Distributions of higher entropy therefore have higher multiplicity. In other words,
Nature is likely to realize them in more ways. If W, and W2 are two distributions, with
corresponding entropies of H, and H2, then the ratio W2/W[ is the relative preference of
W2 over Wj. Since W2/W, ~ exp[N(H2 H,)], when N becomes large (such as the
Avogadro number), the relative preference "becomes so overwhelming that exceptions
to it are never seen; and we call it the Second Law of Thermodynamics." (Jaynes, 1982).
The problem may now be expressed in terms of constrained optimization as
follows:
/ AT \
V
Maximize log W = -N Y
[Nk] * 1 ^ N/
M4
subject to
S
E Nk Ek = E> and
k = 1
s
E N* = N-
k 1
The solution yields surprisingly rich results which would not be attainable even
if the individual trajectories of all the molecules in the closed spaces were calculated.
The efficiency of the method reveals that in fact, such voluminous calculations would
have canceled each other out, and were actually irrelevant to the problem. A similar
idea is seen in the chapter on genetic algorithms, where ignorance can be seemingly

34
exploited and irrelevant information, even if assumed, would be eliminated from the
solution.
The technique has been used in artificial intelligence (see for example, [Lippman,
1988; Jaynes, 1991; Kane, 1991]), and in solving problems in business and economics
(see for example, [Jaynes, 1991; Grandy, 1991; Zellner, 1991]).
4,2 Examples
We will see how the principle is used in solving problems involving some type
of prior information which is used as a constraint on the problem. For simplicity, we
will deal with problems involving one random variable 0 having n values, and call the
associated probabilities p¡. For all the problems, the goal is to choose a probability
distribution from among many possible ones which has the maximum entropy.
No prior information whatsoever. The problem may be formulated using the
Lagrange multiplier X for the single constraint as:
n n
Max g( iPi)) = £ Pi In pi + X £ pi 1 .
(Pj] i -1 [i -1
The solution is obtained as follows:Hence, p¡ = 1/n, i = l,...,n is the MaxEnt
assignment, which confirms the intuition on the non-informative prior.
Suppose the expected value of 0 is We have two constraints in this problem:
the first is the usual constraint on the probabilities summing to one; the second is the
given information expected value of 0 is jue. We use the Lagrange multipliers X, and
X2 for the two constraints respectively. The problem statement follows:

35
dg
dp i
- 1 In pi + X = 0
In pi = X 1
p. = e1'1 V i = 1, .... n,
dg =
ax
E Pi = 1
i = i
E eX_1 = 1
i = 1
n ex_1 = 1
n Pi = 1
- p¡ = 2 v
i = 1.
. ,n.
n
n
n
~ E Piln Pi + K
i = 1
E ^i-1
i = 1
+ ^2
E <0iPi"^e
i = i
(Pil
This can be solved in the usual way by taking partial derivatives of g() w.r.t. p¡, )
X2, and equating them to zero. We obtain:
Pi = e
and
E 0ieA20i = ne E
i = 1 i = 1
Writing
= e 2,
i y and
x

36
we get
n n
£ <9j |i) x = 0
= 1
which is a polynomial in x, whose roots can be determined numerically.
For example, let n = 3, 9 take values {1,2,3}, /e = 1.25. Solving as above and
taking the appropriate roots, we obtain
X, 2.2752509, X2 -1.5132312, giving
p, 0.7882, p2 = 0.1671, and p3 0.0382.
Partial knowledge of probabilities. Suppose we know p¡, i = l,...,k. Since we
have n-1 degrees of freedom in choosing p¡, assume k < n-2 to make the example non
trivial. Then, the problem may be formulated as:
n
n
max g( {pA )
{Pi}
- Pi In P + A.
i C+1
E Pi + Q 1 '
= k*l
k
where g = ^2 Pi-
i = 1
Solving, we obtain
Pi
1 q
n k'
V i
k+1,
n.
This is again fairly intuitive: the remaining probability 1-q is distributed non-
informatively over the rest of the probability space. For example, if n = 4, p, = 0.5,
and p2 = 0.3, then k = 2, q = 0.8, and p3 = p4 = (1 0.8)/(4 2) = 0.2/2 = 0.1.
Note that the first case is a special case of the last one, with q = k = 0.

37
The technique can be extended to cover prior knowledge expressed in the form
of probabilistic knowledge bases by using two key MaxEnt solutions: non-informativeness
(as covered in the last example above), and statistical independence of two random
variables given no knowledge to the contrary (in other words, given two probability
distributions f and g over two random variables X and Y respectively, and no further
information, the MaxEnt joint probability distribution h over X*Y is obtained as h =
f*g).

CHAPTER 5
THE PRINCIPAL-AGENT PROBLEM
5.1 Introduction
5.1.1 The Agency Relationship
The principal-agent problem arises in the context of the agency relationship in
social interaction. The agency relationship occurs when one party, the agent, contracts
to act as a representative of another party, the principal, in a particular domain of
decision problems.
The principal-agent problem is a special case of a dynamic two-person game. The
principal has available to her a set of possible compensation schemes, out of which she
must select one that both motivates the agent and maximizes her welfare. The agent also
must choose a compensation scheme which maximizes his welfare, and he does so by
accepting or rejecting the compensation schemes presented to him by the principal. Each
compensation package he considers implicitly influences him to choose a particular
(possibly complex) action or level of effort. Every action has associated with it certain
disutilities to the agent, in that he must expend a certain amount of effort and/or expense.
It is reasonable to assume that the agent will reject outright any compensation package
which yields less than that which can be obtained elsewhere in the market. This
assumption is in turn based on the assumptions that the agent is knowledgeable about his
38

39
"reservation constraint", and that he is free to act in a rational manner. The assumption
of rationality also applies to the principal. After agreeing to a contract, the agent
proceeds to act on behalf of the principal, which in due course yields a certain outcome.
The outcome is not only dependent on the agents actions but also on exogenous factors.
Finally the outcome, when expressed in monetary terms, is shared between the principal
and the agent in the manner decided upon by the selected compensation plan.
The specific ways in which the agency relationship differs from the usual
employer-employee relationship are (Simon, 1951):
(1) The agent does not recognize the authority of the principal over specific tasks the
agent must do to realize the output.
(2) The agent does not inform the principal about his "area of acceptance" of
desirable work behavior.
(3) The work behavior of the agent is not directly (or costlessly) observable by the
principal.
Some of the first contributions to the analysis of principal-agent problems can be
found in Simon (1951), Alchian & Demsetz (1972), Ross (1973), Sitglitz (1974), Jensen
& Meckling (1976), Shavell (1979a, 1979b), Holmstrom (1979, 1982), Grossman & Hart
(1983), Rees (1985), Pratt & Zeckhauser (1985), and Arrow (1986).
There are three critical components in the principal-agent model: the technology,
the informational assumptions, and the timing. Each of these three components is
described below.

40
5.1.2 The Technology Component of Agency
The technology component deals with the type and number of variables involved
(for example, production variables, technology parameters, factor prices, etc.), the type
and the nature of functions defined on these variables (for example, the type of utility
functions, the presence of uncertainty and hence the existence of probability distribution
functions, continuity, differentiability, boundedness, etc.), the objective function and the
type of optimization (maximization or minimization), the decision criteria on which
optimization is carried out (expected utility, weighted welfare measures, etc.), the nature
of the constraints, and so on.
5.1.3 The Information Component of Agency
The information component deals with the private information sources of the
principal and the agent, and information which is public (i.e. known to both the parties
and costlessly verifiable by a third party, such as a court). This component of the model
addresses the question, "who knows what?". The role of the informational assumption
in agency is as follows:
(a) it determines how the parties act and make decisions (such as offer payment
schemes or choose effort levels),
(b) it makes it possible to identify or design communication structures,
(c) it determines what additional information is necessary or desirable for
improved decision making, and

41
(d) it enables the computation of the cost of maintaining or establishing
communication structures, or the cost of obtaining additional information.
For example, one usual assumption in the principal-agent literature is that the
agents reservation level is known to both parties. As another example of the way in
which additional information affects the decisions of the principal, note that the principal,
in choosing a set of compensation schemes for presenting to the agent, wishes to
maximize her welfare. It is in her interest, therefore, to make the agent accept a payment
scheme which induces him to choose an effort level that will yield a desired level of
output (taking into consideration exogenous risk). The principal would be greatly
assisted in her decision making if she had knowledge of the "function" which induces the
agent to choose an effort level based on the compensation scheme, and also knowledge
of the hidden characteristics of the agent such as his utility of income, disutility of effort,
risk attitude, reservation constraint, etc. Similarly, the agent would be able to take better
decisions if he were more aware of his risk attitude, disutility of effort and exogenous
factors. Any information, even if imperfect, would reduce either the magnitude or the
variance of risk or both. However, better information for the agent does not always
imply that the agent will choose an act or effort level that is also optimal for the
principal. In some cases, the total welfare of the agency may be reduced as a result
(Christensen, 1981).
The gap in information may be reduced by employing a system of messages from
the agent to the principal. This system of messages may be termed a "communication
structure" (Christensen, 1981). The agent chooses his action by observing a signal from

42
his private information system after he accepts a particular compensation scheme from
the principal subject to its satisfying the reservation constraint. This signal is caused by
the combination of the compensation scheme, an estimate of exogenous risk by the agent
based on his prior information or experience, and the agents knowledge of his risk
attitude and disutility of action. The communication structure agreed upon by both the
principal and the agent allows the agent to send a message to the principal. It is to be
noted that the agency contract can be made contingent on the message, which is jointly
observable by both the parties. The compensation scheme considers the message(s) as
one (some) of the factors in the computation of the payment to the agent, the other of
course being the output caused by the agents action. Usually, formal communication
is not essential, as the principal can just offer the agent a menu of compensation
schemes, and allow the agent to choose one element of the menu.
5.1.4 The Timing Component of Agency
Timing deals with the sequence of actions taken by the principal and the agent,
and the time when they commit themselves to specific decisions (for example, the agent
may choose an effort level before or after observing some signal about exogenous risk).
Below is one example of timing (T denotes time):
Tl. The principal selects a particular compensation scheme from a set of possible
compensation schemes.
T2. The agent accepts or rejects the suggested compensation scheme depending on
whether it satisfies his reservation constraint or not.

43
T3. The agent chooses an action or effort level from a set of possible actions or effort
levels.
T4. The outcome occurs as a function of the agents actions and exogenous factors
which are unknown or known only with uncertainty.
Another example of timing is when a communication structure with signals and
messages is involved (Christensen, 1981):
Tl. The principal designs a compensation scheme.
T2. Formation of the agency contract.
T3. The agent observes a signal.
T4. The agent chooses an act and sends a message to the principal.
T5. The output occurs from the agents act and exogenous factors.
Variations in the principal-agent problems are caused by changes in one or more
of these components. For example, some principal-agent problems are characterized by
the fact that the agent may not be able to enforce the payment commitments of the
principal. This situation occurs in some of the relationships in the context of regulation.
Another is the possibility of renegotiation or review of the contract at some future date.
Agency theory, dealing with the above market structure, gives rise to a variety
of problems caused by the presence of factors such as the influence of externalities,
limited observability, asymmetric information, and uncertainty (Gjesdal, 1982).

44
5.1.5 Limited Observability. Moral Hazard, and Monitoring
An important characteristic of principal-agent problems limited observability of
the agents actions gives rise to moral hazard. Moral hazard is a situation in which one
party (say, the agent) may take actions detrimental to the principal and which cannot be
perfectly and/or costlessly observed by the principal (see for example, [Holmstrom,
1979]). Formally, perfect observation might very well impose "infinite" costs on the
principal. The problem of unobservability is usually addressed by designing monitoring
systems or signals which act as estimators of the agents effort. The selection of
monitoring signals and their value is discussed for the case of costless signals in Harris
and Raviv (1979), Holmstrom (1979), Shavell (1979), Gjesdal (1982), Singh (1985), and
Blickle (1987). Costly signals are discussed for three cases in Blickle (1987).
On determining the appropriate monitoring signals, the principal invites the agent
to select a compensation scheme from a class of compensation schemes which she, the
principal, compiles. Suppose the principal determines monitoring signals s,, ..., sn, and
has a compensation scheme c(q, s,, ..., sj, where q is the output, which the agent
accepts. There is no agreement between the principal and the agent as to the level of the
effort e. Since the signals s¡, i = 1, ..., n determine the payoff and the effort level e of
the agent (assuming the signals have been chosen carefully), the agent is thereby induced
to an effort level which maximizes the expected utility of his payoff (or some other
decision criterion). The only decision still in the agents control is the choice of how
much payoff he wants; the assumption is that the agent is rational in an economic sense.
The principals residuum is the output q less the compensation c(*)- The principal

45
structures the compensation scheme c(*) in such a way as to maximize the expected
utility of her residuum (or some other decision criterion). In this manner, the principal
induces desirable work behavior in the agent.
It has been observed that "the source of moral hazard is not unobservability but
the fact that the contract cannot be conditioned on effort. Effort is noncontractible."
(Rasmusen, 1989). This is true when the principal observes shirking on the part of the
agent but is unable to prove it in a court of law. However, this only implies that a
contract on effort is imperfectly enforceable. Moral hazard may be alleviated in cases
where effort is contracted, and where both limited observability and a positive probability
of proving non-compliance exist.
5.1.6 Informational Asymmetry. Adverse Selection, and Screening
Adverse selection arises in the presence of informational asymmetry which causes
the two parties to act on different sets of information. When perfect sharing of
information is present and certain other conditions are satisfied, first-best solutions are
feasible (Sappington and Stiglitz, 1987). Typically however, adverse-selection exists.
While the effect of moral hazard makes itself felt when the agent is taking actions
(say, production or sales), adverse selection affects the formation of the relationship, and
may give rise to inefficient (in the second-best sense) contracts. In the information-
theoretic approach, we can think of both being caused by lack of information. This is
variously referred to as the dissimilarity between private information systems of the agent

46
and the firm, or the unobservability or ignorance of "hidden characteristics" (in the latter
sense, moral hazard is caused by "hidden effort or actions").
In the theory of agency, the hidden characteristic problem is addressed by
designing various sorting and screening mechanisms, or communication systems that pass
signals or messages about the hidden characteristics (of course, the latter can also be used
to solve the moral hazard problem).
On the one hand, the screening mechanisms can be so arranged as to induce the
target party to select by itself one of the several alternative contracts (or "packages").
The selection would then reveal some particular hidden characteristic of the party. In
such cases, these mechanisms are called "self-selection" devices. See, for example,
Spremann (1987) for a discussion of self-selection contracts designed to reveal the agents
risk attitude. On the other hand, the screening mechanisms may be used as indirect
estimators of the hidden characteristics, as when aptitude tests and interviews are used
to select agents.
The significance of the problem caused by the asymmetry of information is related
to the degree of lack of trust between the parties to the agency contract which, however,
may be compensated for by observation of effort. However, most real life situations
involving an agency relationship of any complexity are characterized not only by a lack
of trust but also by a lack of observability of the agents effort. The full context to the
concept of information asymmetry is the fact that each party in the agency relationship
is either unaware or has only imperfect knowledge of certain factors which are better
known to the other party.

47
5.1.7 Efficiency of Cooperation and Incentive Compatibility
In the absence of asymmetry of information, both principal and agent would
cooperatively determine both the payoff and the effort or work behavior of the agent.
Subsequently, the "game" would be played cooperatively between the principal and the
agent. This would lead to an efficient agreement termed the first-best design of
cooperation. First-best solutions are often absent not merely because of the presence of
externalities but mainly because of adverse selection and moral hazard (Spremann, 1987).
Let F = { (c,e) }, where compensation c and effort e satisfy the principals and
the agents decision criteria respectively. In other words, F is the set of first-best
designs of cooperation, also called efficient designs with respect to the principal-agent
decision criteria. Now, suppose that the agents action e is induced as above by a
function I: 1(c) = e. Let S = { (c,I(c)) } i.e. S denotes the set of designs feasible
under information asymmetry. If it were not the case that F D S = 0, then efficient
designs of cooperation would be easily induced by the principal. Situations where this
occurs are said to be incentive compatible. In all other cases, the principal has available
to her only second-best designs of cooperation, which are defined as those schemes that
arise in the presence of information asymmetry.
5.1.8 Agency Costs
There are three types of agency costs (Schneider, 1987):
(1) the cost of monitoring the hidden effort of the agent,
(2) the bonding costs of the agent, and

48
(3) the residual loss, defined as the monetary equivalent of the loss in welfare of the
principal caused by the actions taken by the agent which are non-optimal with
respect to the principal.
Agency costs may be interpreted in the following two ways:
(1) they may be used to measure the "distance" between the first-best and the second-
best designs;
(2) they may be looked upon as the value of information necessary to achieve second-
best designs which are arbitrarily close to the first-best designs.
Obviously, the value of perfect information should be considered as an upper
bound on the agency costs (see for example, [Jensen and Meckling, 1976]).
5.2 Formulation of the Principal-Agent Problem
The following notation and definitions will be used throughout:
D: the set of decision criteria, such as (maximin, minimax, maximax, minimin,
minimax regret, expected value, expected loss,...}. We use A G D.
AP: the decision criterion of the principal.
Aa: the decision criterion of the agent.
UP: the principals utility function.
UA: the agents utility function.
C: the set of all compensation schemes. We use c G C.
E: the set of actions or effort levels of the agent. We use e G E.
0: a random variable denoting the true state of nature.

49
0P: a random variable denoting the principals estimate of the state of nature.
0A: a random variable denoting the agents estimate of the state of nature.
q: output realized from the agents actions (and possibly the state of nature).
qP: monetary equivalent of the principals residuum. Note that qp = q c(*)>
where c may depend on the output and possibly other variables.
Output/outcome. The goal or purpose of the agency relationship, such as sales,
services or production, is called the output or the outcome.
Public knowledge/information. Knowledge or information known to both the
principal and the agent, and also a third enforcement party, is termed public knowledge
or information. A contract in agency can be based only on public knowledge (i.e.
observable output or signals).
Private knowledge/information. Knowledge or information known to either the
principal or the agent but not both is termed private knowledge or information.
State of nature. Any events, happenings, occurrences or information which are
not in the control of the principal or the agent and which affect the output of the agency
directly through the technology constitute the state of nature.
Compensation. The economic incentive to the agent to induce him to participate
in the agency is called the compensation. This is also called wage, payment or reward.
Compensation scheme. The package of benefits and output sharing rules or
functions that provide compensation to the agent is called the compensation scheme.
Also called contract, payment function or compensation function.

50
The word "scheme" is used here instead of "function" since complicated
compensation packages will be considered as an extension later on. In the literature, the
word "scheme" may be seen, but it is used in the sense of "function", and several nice
properties are assumed for the function (such as continuity, differentiability, and so on).
Depending on the contract, the compensation may be negative a penalty for the agent.
Typical components of the compensation functions considered in the literature are rent
(fixed and possibly negative), and share of the output.
The principals residuum. The economic incentive to the principal to engage in
the agency is the principals residuum. The residuum is the output (expressed in
monetary terms) less the compensation to the agent. Hence, the principal is sometimes
called the residual claimant.
Payoff. Both the agents compensation and the principals residuum are called
the payoffs.
Reservation welfare (of the agent). The monetary equivalent of the best of the
alternative opportunities (with other competing principals, if any) available to the agent
is known as the reservation welfare of the agent. Accordingly, it is the minimum
compensation that induces an agent to accept the contract, but not necessarily induce him
to his best effort level. Also known as reservation utility or individual utility, it is
variously denoted in the literature as m or .
Disutility of effort. The cost of inputs which the agent must supply himself when
he expends effort contributes to disutility, and hence is called the disutility of effort.

51
Individual rationality constraint (IRC). The agents (expected) utility of net
compensation (compensation from the principal less his disutility of effort) must be at
least as high as his reservation welfare. This constraint is also called the participation
constraint.
When a contract violates the individual rationality constraint, the agent rejects it
and prefers unemployment instead. Such a contract is not necessarily "bad", since
different individuals have different levels of reservation welfare. For example,
financially independent individuals may have higher than usual reservation welfare levels,
and might very well prefer leisure to work even when contracts are attractive to most
other people.
Incentive compatibility constraint (ICQ. A contract will be acceptable to the
agent if it satisfies his decision criterion on compensation, such as maximization of
expected utility of net compensation. This constraint is called the incentive compatibility
constraint.
Development of the problem: Model 1. We develop the problem from simple
cases involving the least possible assumptions on the technology and informational
constraints, to those having sophisticated assumptions. Corresponding models from the
literature are reviewed briefly in section 1.3.
A. Technology:
(a) fixed compensation, C s set of fixed compensations, U C;

(b) output q = q(e); assume q(0) = 0;
(c) existence of nonseparable utility functions;
(d) decision criterion: maximization of utility;
(e) no uncertainty in the state of nature.
B. Public information:
(a) compensation scheme, c;
(b) range of possible outputs, Q;
(c) .
Information private to the principal: UP
Information private to the agent:
(a) UA;
(b) disutility of effort, d;
(c) range of effort levels, e.
C. Timing:
(1) the principal makes an offer of fixed wage
(2) the agent either rejects or accepts the offer;
(3) if he accepts it, exerts effort level e;
(4)output q(e) results;

53
(5) sharing of output according to contract.
D. Payoffs:
Case 1: Agent rejects contract, i.e. e = 0;
TTp = UP[q(e)] = UP[q(0)] = UP[0].
*A = UA[U].
Case 2: Agent accepts contract;
TTp = UP[q(e) c].
*a = UA[c d(e)].
E. The principals problem:
(Ml.PI) Maxc e c maxq e Q UP[q c]
such that
c > U. (IRC)
Suppose C* Q C is the solution set of M1.P1. The principal picks c £ C* and offers
it to the agent.
The agents problem:
(M1.A1) For a given c\
Maxe e E UA[c* d(e)].
Suppose E* Q E is the solution set of Ml.Al. The agent selects e* 6 E*.

54
F. The solution:
(a) the principal offers c* E C* to the agent;
(b) the agent accepts the contract;
(c) the agent exerts effort e*(c*) E E;
(d) output q(e*(c*)) occurs;
(e) payoffs:
Tp = UP[q(e*(0) c*];
xA = UA[c* d(e*(c*))].
Notes:
1. The agent accepts the contract in F.b since IRC is present in Ml.PI, and C*
is nonempty since U E C.
2. Effort of the agent is a function of the offered compensation.
3. Since one of the informational assumptions was that the principal does not
know the agents utility function, is a compensation rather than the agents
utility of compensation, so UA() is meaningful.
G. Variations:
1. The principal offers C* to the agent instead of a c* E C*. The agents problem
then becomes:
(M1.A2) Maxc* 6 c* maxe e E UA[c* d(e)].
The first three steps in the solution then become:
(a) the principal offers C* to the agent;

55
(b) the agent accepts the contract;
(c) the agent picks an effort level e* which is a solution to M1.A2 and reports
the corresponding c* (or its index if appropriate) to the principal.
2. The agent may decide to solve an additional problem: from among two or more
competing optimal effort levels, he may wish to select a minimum effort level.
Then, his problem would be:
(Ml.A3) Min e* d(e*)
such that
e* G argmaxe 6 E UA[c* d(e)].
Example:
Let E = (e,, 63},
C* = {cc2,c3}.
Suppose,
Ci(q(e,)) = 5, d(e,) = 2;
C2(q(e2)) = 6, dfe) = 3;
c3(q(e3)) = 6, d(e,) = 4;
The net compensation to the agent in choosing the three effort levels is 3, 3, and
2 respectively. Assuming d(e) is monotone increasing in e, the agent chooses e!
to e2, and so prefers compensation c, to C2.

56
3. We assumed U is public knowledge. If this were not so, then the agent has to
test all offers to see it they are at least as high as the utility of his reservation
welfare. The two problems then become:
(M1.P2) Maxc 6 c maxq 6 Q UP[q c]
and
(M1.A4) Maxe6EUA[c*-d(e)]
such that
c* ^ UA[U], (IRC)
c* E argmax M1.P2.
In this case, there is a distinct possibility of the agent rejecting an offer of the
principal.
4. Note that in most realistic situations, a distinction must be made between the
reservation welfare and the agents utility of the reservation welfare. Otherwise,
merely using IRC with the reservation welfare in Ml.PI may not satisfy the
agents constraint. On the other hand, = UA() implies knowledge of UA by
the principal, a complication which yields a completely different model.
When U ^ UA(U), the following two problems occur:
(M1.P3) Maxc 6 c maxq 6 Q UP(q c)
such that
c > .
(M1.A5) Maxe e E UA(c* d(e))

57
such that
c* ^ UA(U), (IRC)
c argmax M1.P3.
In other words, the principal solves her problem the best way she can, and hopes
the solution is acceptable to the agent.
5. Negotiation. Negotiation of a contract can occur in two contexts:
(a) when there is no solution to the initial problem, the agent may communicate
to the principal his reservation welfare, and the principal may design new
compensation schemes or revise her old schemes so that a solution may be
found. This type of negotiation also occurs in the case of problems M1.P3
and M1.A5.
(b) The principal may offer c* E argmaxc 6 c Ml .PI. The agent either accepts
it or does not; if he does not, then the principal may offer another optimal
contract, if any. This interaction may continue until either the agent accepts
some compensation scheme or the principal runs out of optimal
compensations.
Development of the problem: Model 2. This model differs from the first by
incorporating uncertainty in the state of nature, and conditioning the compensation
functions on the output.

A. Technology:
(a) presence of uncertainty in the state of nature;
(b) compensation scheme c = c(q);
(c) output q = q(e,0);
(d) existence of known utility functions for the agent and the principal;
(e) disutility of effort for the agent is monotone increasing in effort e;
B. Public information:
(a) presence of uncertainty, and range of 0;
(b) output function q;
(c) payment functions c;
(d) range of effort levels of the agent.
Information private to the principal:
(a) the principals utility function;
(b) the principals estimate of the state of nature.
Information private to the agent:
(a) the agents utility function;
(b) the agents estimate of the state of nature;
(c) disutility of effort;
(d)reservation welfare;

59
C. Timing:
(a) the principal determines the set of all compensation schemes that maximize
her expected utility;
(b) the principal presents this set to the agent as the set of offered contracts;
(c) the agent picks from this set of compensation schemes a compensation
scheme that maximizes his net compensation, and a corresponding effort
level;
(d) a state of nature occurs;
(e) an output results;
(f) sharing of the output takes place as contracted.
D. Payoffs:
Case 1: Agent rejects contract, i.e. e = 0;
xP = UP[q(e,0)] = UP[q(O,0)].
tta = UA[U],
Case 2: Agent accepts contract;
xP = UP[q(e,0) c(q)].
tTa = UA[c(q) d(e)].

60
E. The principals problem:
(M2.P) Maxcec MaxeE E9p Up[q(e,e) -c(q(e,Q))]
where the expectation E( ) is given by (assuming the usual regularity conditions)
0
Up[q(e,d) c(g(e, 0) ) ] f- (0) c?0
0p
where
/
0 6 [0, 0] and
f(0) is the distribution assigned by the principal.
The agents problem:
(M2.A) Maxcec MaxeeE Ee* UA[c(q(e,d) ) d(e) ]
subject to
E**[c(q(e,Q)) -d(e)] Z, (IRC)
c e argmax(M2. P) .
where the expectation E( ) is given as usual by
UA[q(e,Q) c(g(e,0))] £ (0) d0.
e,
/

61
F. The solution:
(a) The agent selects c E C\ and a corresponding effort e* which is a solution
to M2.A;
(b) a state of nature 6 occurs;
(c) output q(e*,0) is generated;
(d) payoffs:
tp = UP[q(e*,0) c*(q(e\0))];
= UA[c*(q(e*,0)) d(e*)].
Development of the problem: Model 3. In this model, the strongest possible
assumption is made about information available to the principal: the principal has
complete knowledge of the utility function of the agent, his disutility of effort, and his
reservation welfare. Accordingly, the principal is able to make an offer of compensation
which satisfies the decision criterion of the agent and his constraints. In other words,
the two problems are treated as one. The assumptions are as in model 2, so only the
statement of the problem will be given below.
The problem:
Marcee, e-E E Up[q(e*,Q) c(g(e\0) ) ]
subject to
E UA[c(q(e\0) ) d(e') ] ^ U, (IRC)
e* e argmax {MaxeeE¡ c6C E UA[c (q(e, 6) ) -d(e)]). (ICC)

62
5.3 Main Results in the Literature
Several results from basic agency models will be presented using the framework
established in the development of the problem. The following will be presented for each
model:
Technology,
Information,
Timing,
Payoffs, and
Results.
It must be noted that the literature rarely presents such an explicit format; rather,
several assumptions are often buried within the results, or implied or just not stated.
Only by trying an algorithmic formulation is it possible to unearth unspecified
assumptions. In many cases, some of the factors are assumed for the sake of formal
completeness, even though the original paper neither mentions nor uses those factors in
its results. This type of modeling is essential when the algorithms are implemented
subsequently using a knowledge-intensive methodology.
One recurrent example of incomplete specification is the treatment of the agents
individual rationality constraint (IRC). The principal has to pick a compensation which
satisfies IRC. However, some consistency in using IRC is necessary. The agents
reservation welfare U is also a compensation (albeit a default one). The agent must

63
check one of two constraints to verify that the offered compensation indeed meets his
reservation welfare:
c > U or UA(c) > UA(U).
If the principal picks a compensation which satisfies c > U, it is not necessary that
UA(c) > UA(U) be also satisfied. However, using UA(c) > U for the IRC, where
is treated "as if it were UA(), implies knowledge of the agents utility on the part
of the principal.
The difference between the two situations is of enormous significance if the
purpose of analysis is to devise solutions to real-world problems. In the literature, this
distinction is conveniently overlooked. If all such vagueness in the technological,
informational and temporal assumptions was to be systematically eliminated, the analysis
might change in a way not intended in the original literature. Hence, the main results
in the literature will be presented as they are.
5.3.1 Model 1: The Linear-Exponential-Normal Model
This name of the model (Spremann, 1987) derives from the nature of three crucial
parameters: the payoff functions are linear, the utility functions are exponential, and the
exogenous risk has a normal distribution. Below is a full description.
Technology:
(a) compensation is the sum of a fixed rent r and a share s of the output q: c(q)
= r + sq;

64
(b) presence of uncertainty in the state of nature, denoted by 0, where 0 ~
(c) the set of effort levels of the agent, E = [0,A]; effort is induced by
compensation;
(d) output q = q(e,0) = e + 0;
(e) the agents disutility of effort is d s d(e) = e2;
(0 the principals utility UP is linear (the principal is risk neutral);
(g) the agent has constant risk aversion a > 0, and his utility is
UA(w) = -exp(-aw), where w is his net compensation (also called the
wealth);
(h) the certainty equivalent of wealth, denoted V, is defined as:
V(w) = U '[Ee(U(w))], where U denotes the utility function, Ee is the
expectation with respect to 0; as usual, subscripts P or A on V denote the
principal or the agent respectively;
(i) the decision criterion is maximization of expected utility.
Public information:
(a) compensation scheme c(q; r,s);
(b) output q;
(c) distribution of 0;
(d) agents reservation welfare ;
(e)agents risk aversion a.

65
Information prvate to the principal:
Utility of residuum, UP.
Information private to the agent:
(a) selection of effort given the compensation;
(b) utility of welfare;
(c) disutility of effort.
Timing:
(a) the principal offers a contract (r,s) to the agent;
(b) the agents effort e is induced by the compensation scheme;
(c) a state of nature occurs;
(d) the agents effort and the state of nature give rise to output;
(e) sharing of the output takes place.
Payoffs:
7TP = UP[q (r + sq)]
= UP[e(r,s) + 0O (r + s(e(r,s) + 0o))]
= UA[r + sq d(e(r,s))]
= UA[r + s(e(r,s) + 0O) d(e(r,s))],
where e(r,s) is the function which induces effort based on compensation, and 0O
is the realized state of nature.

66
Results:
Result 1.1: The optimal effort level of the agent given a compensation scheme
(r,s) is denoted e\ and is obtained by straightforward maximization to yield:
e* ss e*(r,s) = s/2.
This shows that the rent r and the reservation welfare have no impact on the selection
of the agents effort.
Result 1.2: A necessary and sufficient condition for IRC to be satisfied for a
given compensation scheme (r,s) is:
r V s2{1 ~ 2a2)
4
Result 1.3: The optimal compensation scheme for the principal is c* = (r*,s*),
where
1 + 2ao*
and
r* = u -
1 2ao:
4s
*2
Corollary 1.3: The agents optimal effort given a compensation scheme (r*,s*)
is (using result 1.1):
2 (1 + 2ao2)

67
Result 1.4: Suppose 2ao2 > 1. Then, an increase in share s requires an increase
in rent r (in order to satisfy IRC).
To see this, suppose we increase the share s by 5,
s0 = s + 8, 0 < 5 < 1-s. From Result 1.2, for IRC to hold we need,
T. Vu 2ot2)
ro 2 u 4
jj (s + 6)2(1 2oeg2)
4
-Q (1 2ao2)[52 + 2s5 + 62]
4
jj (1 2o2)2 (2sb + d2)(l 2a o2)
4 4
(2sb + 62)(1 2ao2)
4
^ r ( v 1 < 2a a2).
Result 1.5: The welfare attained by the agent is U, while the principals welfare
is given by:
v.
4 s *

68
Result 1.6: The principal prefers agents with lower risk aversion. This is
immediate from the fact that the principals welfare is decreasing in the agents risk
aversion for a given a2 and .
Result 1.7: Fixed fee arrangements are non-optimal, no matter how large the
agents risk aversion. This is immediate from the fact that
5* = > 0 V a > 0.
1 + 2ao2
Result 1.8: It is the connection between unobservability of the agents effort and
his risk aversion that excludes first-best solutions.
5.3.2 Model 2
This model (Gjesdal, 1982) deals with two problems:
(a) choosing an information system, and
(b) designing a sharing rule based on the information system.
Technology:
(a) presence of uncertainty, 9;
(b) finite effort set of the agent; effort has several components, and is hence
treated as a vector;
(c) output q is a function of the agents effort and the state of nature 6; the
range of output levels is finite;

69
(d) presence of a finite number of public signals;
(e) presence of a set of public information systems (i.e. signals), including non-
informative and randomized systems, the output being treated as one of the
informative information systems;
(f) costlessness of public information systems;
(g) compensation schemes are based on signals about effort or output or both.
Public information:
(a) distribution of the state of nature, 9;
(b) output levels;
(c) common information systems which are non-informative and randomizing;
(d) UA.
Information private to the principal: utility function, UP.
Information private to the agent: disutility of effort.
Timing:
(a) principal offers contract based on observable public information systems,
including the output;
(b) agent chooses action;
(c) signals from the specified public information systems are observed;
(d) agent gets paid on the basis of the signal;
(e) a state of nature occurs;

(f) output is observed;
(g) principal keeps the residuum.
70
Special technological assumptions: Some of these assumptions are used in only some of
the results; other results are obtained by relaxing them.
(a) The joint probability distribution function on output, signals, and actions is
twice-differentiable in effort, and the marginal effects on this distribution of
the different components of effort are independent.
(b) The principals utility function UP is trice differentiable, increasing, and
concave.
(c) The agents utility function UA is separable, with the function on the
compensation scheme (or sharing rule as it is known) being increasing and
concave, and the function on the effort being concave.
Results:
Result 2.1: There exists a marginal incentive informativeness condition which is
essentially sufficient for marginal value given a signal information system Y. When
information about the output is replaced by signals about the output and/or the agents
effort, marginal incentive informativeness is no longer a necessary condition for marginal
value since an additional information system Z may be valuable as information about
both the output and the effort.

71
Result 2.2: Information systems having no marginal insurance value but having
marginal incentive informativeness may be used to improve risk sharing, as for example,
when the signals which are perfectly correlated with output on the agents effort are
completely observable.
Result 2.3: Under the assumptions of result 2.2, when the output alone is
observed, it must be used for both incentives and insurance. If the effort is observed as
well, then a contract may consist of two parts: one part is based on the effort, and takes
care of incentives; the other part is based on output, and so takes care of risk-sharing.
For example, consider auto insurance. The principal (the insurer) cannot observe
the actions taken by the driver (such as care, caution and good driving habits) to avoid
collisions. However, any positive signals of effort can be the basis of discounts on
insurance premiums, as for example when the driver has proof of regular maintenance
and safety check up for the vehicle or undergoes safe driving courses. Also factors such
as age, marital status and expected usage are taken into account. The "output" in this
case is the driving history, which can be used for risk- sharing; another indicator of risk
which may be used is the locale of usage (country lanes or heavy city traffic). This
example motivates result 2.4, a corollary to results 2.2 and 2.3.
Result 2,4: Information systems having no marginal incentive informativeness
but having marginal insurance value may be used to offer improved incentives.
Result 2.5: If the uncertainty in the informative signal system is influenced by
the choices of the principal and the agent, then such information systems may be used
for control in decentralized decision-making.

72
5.3.3 Model 3
Holmstroms model (Holmstrom, 1979) examines the role of imperfect
information under two conditions: (i) when the compensation scheme is based on output
alone, and (ii) when additional information is used. The assumptions about technology,
information and timing are more or less standard, as in the earlier models. The model
specifically uses the following:
(a) In the first part of the model, almost all information is public; in the second
part, asymmetry is brought in by assuming extra knowledge on the part of
the agent.
(b) output is a function of the agents effort and state of nature: q == q(e,0), and
3q/3e > 0.
(c) The agents utility function is separable in compensation and effort, where
UA(c) is defined on compensation, and d(e) is the disutility defined on effort.
(d) Disutility of effort d(e) is increasing in effort.
(e) The agent is risk averse, so that UA < 0.
(f) The principal is weakly risk neutral, so that Up < 0.
(g) Compensation is based on output alone.
(h) Knowledge of the probability distribution on the state of nature 0 is public.
(i) Timing: The agent chooses effort before the state of nature is observed.
The problem:
(P) Maxc6C eeE E[UP(q c(q))]

73
such that
E[UA(c(q),e)] > U, (IRC)
e e argmaxe.6E E[UA(c(q), e)]. (ICC)
To obtain a workable formulation, two further assumptions are made:
(a) There exists a distribution induced on output and effort by the state of
nature, denoted F(q,e), where q = q(e,0). Since 3q/de > 0 by assumption,
it implies 3F(q,e)/3e < 0. For a given e, assume 3F(q,e)/de < 0 for some
range of values q.
(b) F has density function f(q,e), where (denoting fc s= df/de) fe and f^. are well
defined for all (q,e).
The ICC constraint in (P) is replaced by its first order condition using f, and the
following formulation is obtained:
(P) Maxc{EC>eeE f UP(q c(q)) f(q,e) dq
such that
[UA(c(q)) d(e)] f(q,e) dq > U, (IRC)
UA(c(q)) fe(q,e) dq = d(e). (ICC)
Results:
Result 3.1: Let X and / be the Lagrange multipliers for IRC and ICC in (P)
respectively. Then, the optimal compensation schemes are characterized as follows:

a.e.[c,c\,
1A
U'M ~ cm + fe(q,e)
V'Mq)) q>e)
where c is the agents wealth, and "c is the principals wealth plus the output (these form
the lower and upper bounds). If the equality in the above characterization does not hold,
then c(q) = c or "c depending on the direction of inequality.
Result 3.2: Under the given assumptions and the characterization in result 3.1,
/i > 0; this is equivalent to saying that the principal prefers the agent increase his effort
given a second-best compensation scheme as in the above result 3.1. The second-best
solution is strictly inferior to a first-best solution.
Result 3.3: |fe|/f is interpreted as a benefit-cost ratio for deviation from optimal
risk sharing. Result 3.1 states that such deviation must be proportional to this ratio
taking individual risk aversion into account. From Result 3.2, incentives for increased
effort are preferable to the principal. The following compensation scheme accomplishes
this (where cF(q) denotes the first-best solution for a given X):
c(q) > cF(q), if the marginal return on effort is positive to the agent;
c(q) < cF(q), otherwise.
Result 3.4: Intuitively, the agent carries excess responsibility for the output. This
is implied by result 3.3 and the assumptions on the induced distribution f.
A previous assumption is now modified as follows: Compensation c is a function
of output and some other signal y which is public knowledge. Associated with this is a
joint distribution F(q,y,e) (as above), with f(q,y,e) the corresponding density function.

75
Result 3.5: An extension of result 3.1 on the characterization of optimal
compensation schemes is as follows:
X + \i.
Aq,y,e)
Up(q c(q,y))
U'Mqj))
where X and n are as in result 3.1.
Result 3.6: Any informative signal, no matter how noisy it is, has a positive value
if costlessly obtained and administered into the contract.
Note: This result is based on rigorous definitions of value and informativeness of signals
(Holmstrom, 1979).
In the second part of this model, an assumption is made about additional
knowledge of the state of nature revealed to the agent alone, denoted z. This introduces
asymmetry into the model. The timing is as follows:
(a) the principal offers a contract c based on the output and an observed signal
y;
(b) the agent accepts the contract;
(c) the agent observes a signal z about 9;
(d) the agent chooses an effort level;
(e) a state of nature occurs;
(f) agents effort and state of nature yield an output;
(g) sharing of output takes place.

76
We can think of the signal y as information about the state of nature which both
parties share and agree upon, and the signal z as special post-contract information about
the state of nature received by the agent alone.
For example, a salesmans compensation may be some combination of percentage
of orders and a fixed fee. If both the salesman and his manager agree that the economy
is in a recession, the manager may offer a year-long contract which does not penalize the
salesman for poor sales, but offers above subsistence level fixed fee to motivate loyalty
to the firm on the part of the salesman, and a clause thrown in which transfers a larger
share of output than normal to the agent (i.e. incentives for extra effort in a time of
recession).
Now suppose the salesman, as he sets out on his rounds, discovers that the
economy is in an upswing, and that his orders are being filled with little effort on his
part. Then the agent may continue to exert little effort, realize high output, get a higher
share of output in addition to a higher initial fixed fee as his compensation.
In the case of asymmetric information, the problem is formulated as follows:
(PA) Maxc(qy)ec>e(z)eE \ UP(q c(q,y))f(q,y|z,e(z))p(z)dqdydz
such that
UA(c(q,y))f(q,y|z,e(z))p(z)dqdydz- ) d(e(z))pzdz > , (IRC)
e(z) £ argmaxc.eE j UA(c(q,y))f(q,y |z,e)dqdy d(e) V z (ICC)
where p(z) is the marginal density of z, d(e(z)) is the disutility of effort e(z).
Let X and i(z)p(z) be the Lagrange multipliers for (IRC) and (ICC) in (PA) respectively.

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Result 3.7: The extension of result 3.1 on the characterization of optimal
compensation schemes to the problem (PA) is:
Up(q c(q,y)) + /\x(z).fe(q,y\z,e(z))P() U(c(q,y)) ffiq,y\z,e(z))p(z)dz
The interpretation of result 3.7 is similar to that of result 3.1. Analogous to result 3.2,
n(z) ^ 0, and /x(z) < 0 for some z and fx(z) > 0 for other z, which implies, as in
result 3.2, that result 3.7 characterizes solutions which are second-best.
5.3.4 Model 4: Communication under Asymmetry
This model (Christensen, 1981) attempts an analysis similar to model 3, and
includes communication structures in the agency. The special assumptions are as
follows:
(a) There is a set of messages M that the agent uses to communicate with the
principal; compensation is based on the output and the message picked by
the agent; hence, the message is public knowledge.
(b) There is a set of signals about the environment; the agent chooses his effort
level based on the signal he observes; the agent also selects his compensation
scheme at this time by selecting an appropriate message to communicate to
the principal; selection of the message is based on the effort.

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(c) Uncertainty is with respect to the signals observed by the agent; the
distribution characterizing this uncertainty is public knowledge; the joint
density is defined on output and signal conditioned on the effort:
f(q£ |e) = f(q|£,e)*f(|).
(d) Both parties are Savage(1954)-rational.
(e) The principals utility of wealth is UP, with weak risk-aversion; in particular,
Up > 0 and UP < 0.
(i) The agents utility of wealth is separable into UA defined on compensation
and disutility of effort. The agent has positive marginal utility for money,
and he is strictly risk-averse; i.e. UA > 0, UA < 0, and d' > 0.
Timing:
(a) The principal and the agent determine the set compensation schemes, based
on the output and the message sent to the principal by the agent; the
principal is committed to this set of compensation schemes;
(b) the agent accepts the compensation scheme if it satisfies his reservation
welfare;
(c) the agent observes a signal £;
(d) the agent picks an effort level based on £;
(e) the agent sends a message m to the principal; this causes a compensation
scheme from the contracted set to be chosen;
(f) output occurs;

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(g) sharing of output takes place.
Note that in the timing, (d) and (e) could be interchanged in this model without affecting
anything.
The following is the principals problem:
(P) Find (c*(q,m),e*(£,m),m*(£)) such that c* G C, e* G E, and
m* G M solves:
Maxc(q,m),e),m(i) E[UP(q c(q,m))]
such that
E[UA(c(q,m)) d(e)] > , (IRC)
e(£) G argmaxe.£E E[UA(c(q,m(£))) d(e) (self-selection of action),
m(0 G argmaxm.6M E[UA(c(q,m))-d(e(£,m))|£] (self-selection of
message),
where e(£,m) is the optimal act given that £ is observed and m is reported.
The following assumptions are used for analyzing the problem in the above formulation:
(a) UP( ) and UA( ) d( ) are concave and twice continuously differentiable in
all arguments.
(b) Compensation functions are piecewise continuous and differentiable a.e.(£).
(c) The density function f is twice differentiable a.e.
(d) Regularity conditions enable differentiation under the integral sign.
(e) Existence of an optimal solution is assumed.

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Result:
Result 4.1: The following is a characterization of optimal functions:
Aq\e\V)
where X, p(£), and p(£) are Lagrange multipliers for the three constraints in (P)
respectively.
5.3.5 Model G: Some General Results
Result G.l (Wilson. 1968L Suppose that both the principal and the agent are risk
averse having linear risk tolerance functions with the same slope, and the disutility of the
agents effort is constant. Then the optimal sharing rule is a non-constant function of the
output.
Result G.2. In addition to the assumptions of result G.l, also suppose that the
agents effort has negative marginal utility. Let c,(q) be a sharing rule (or compensation
scheme) which is linear in the output q, and let (^(q) = k be a constant sharing rule.
Then, c, dominates Cj.
The two results above deal with conditions when observation of the output is
useful. Suppose Y is a public information system that conveys information about the
output. So, compensation schemes can be based on Y alone. The value of Y, denoted
W(Y) (following model 1), is defined as: W(Y) = maxc£c EUP[q c(y)], subject to IRC

81
and ICC. Let Y denote a non-informative signal. Then, the two results yield a ranking
of informativeness: W(Y) > W(Y). When Q is an information system denoting perfect
observability of the output q, and the timing of the agency relationship is as in model 1
(i.e. payment is made to the agent after observing the output), then W(Q) > W(Y) as
well.

CHAPTER 6
METHODOLOGICAL ANALYSIS
The solution to the principal-agent problem is influenced by the way the model
itself is setup in the literature. Highly specialized assumptions, which are necessary in
order to use the optimization technique, contribute a certain amount of bias. As an
analogy, one may note that a linear regression model assumes implicit bias by seeking
solutions only among linear relationships between the variables; a correlation coefficient
of zero therefore implies only that the variables are not linearly correlated, not that they
are not correlated. Examples of such specialized assumptions abound in the literature,
a small but typical sample of which are detailed in the models presented in Chapter 5.
The consequences of using the optimization methodology are primarily of two.
Firstly, much of the pertinent information that is available to the principal, the agent and
the researcher must be ignored, since this information deals with variables which are not
easily quantifiable, or which can only be ranked nominally, such as those that deal with
behavioral and motivational characteristics of the agent and the prior beliefs of the agent
and principal (regarding the task at hand, the environment, and other exogenous
variables). Most of this knowledge takes the form of rules linking antecedents and
consequents, and which have associated certainty factors.
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Secondly, a certain amount of bias is introduced into the model by requiring that
the functions involved in the constraints satisfy some properties, such as differentiability,
monotone likelihood ratio, and so on. It must be noted that many of these properties are
reasonable and meaningful from the standpoint of accepted economic theory. However,
standard economic theory itself relies heavily on concepts such as utility and risk
aversion in order to explain the behavior of economic agents. Such assumptions have
been criticized on the grounds that individuals violate them; for example, it is known that
individuals sometimes violate properties of the Neumann-Morgenstem utility functions.
Decision theory addressing economic problems also uses concepts such as utility, risk,
loss, and regret, and relies on classical statistical inference procedures. However, real
life individuals are rarely consistent in their inference, lacking in statistical sophistication,
and unreliable on probability calculations. Several references to support this view are
cited in Chapter 2. If the term "rational man" as used in economic theory means that
individuals act as if they were sophisticated and infallible (in terms of method and not
merely content), then economic analysis might very well yield erroneous solutions.
Consider, as an example, the treatment of compensation schemes in the literature.
They are assumed to be quite simple, either being linear in the output, or involving a
fixed element called the rent. (See chapter 5 for details). In practice, compensation
schemes are fairly comprehensive and involved. They cover as many contingencies as
possible, provide for a variety of payment and reward criteria, specify grievance
procedures, termination, promotion, varieties of fringe benefits, support services, access
to company resources, and so on.

84
The set of all compensation schemes is in fact a set of knowledge bases consisting
of the following components (B.R. Ellig, 1982):
(1) Compensation policies/strategies of the principal;
(2) Knowledge of the structure of the compensation plans, which means specific rules
concerning short-term incentives linked to partial realization of expected output,
long-term incentives linked to full realization of expected output, bonus plans
linked to realizing more than the expected output, disutilities linked to
underachievement, and rules specifying injunctions to the agent to restrain from
activities that may result in disutilities to the principal (if any).
There are various elements in a compensation scheme, which can be classified as
financial and non-financial:
Financial elements of compensation
1. Base Pay (periodic).
2. Commission or Share of Output.
3. Bonus (annual or on special occasions).
4. Long Term Income (lump sum payments at termination).
5. Benefits (insurance, etc.).
6. Stock Participation.
7. Non-taxable or tax-sheltered values.
Nonfinancial elements of compensation
1. Company Environment.
2.
Work Environment.

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3. Items which are designed to improve productivity of agent.
4. Status or Prestige.
5. Elements of agents disutility assumed by the firm.
As another example, note that some of the important factors not considered in the
traditional treatment of the principal-agent problem are connected to the characteristics
of the agent. In a real-world situation, the principal has a great deal of behavioral
knowledge which he acquires from acting in a social context. In dealing with the
problems associated with the agency contract, he takes into account factors of the agent
such as the following:
* General social skills, which are also known as social interaction skills, networking
skills, or people skills.
* Office and managerial skills.
* Past experience or reputation.
* Motivation or enthusiasm.
* General behavioral aspects (personal habits).
* Physical qualities deemed essential or useful to the task.
* Language/communication skills.
In the light of these shortcomings of the traditional methodology, it is desirable
to see how they make their decisions in reality. It may be more fruitful to think of
people making decisions based on some underlying probabilistic knowledge bases. These
knowledge bases would capture all the rules of behavior and decision-making, such as

86
the choice of effort levels by the agent. This would also enable one to bypass the use
of utility and risk aversion as artificial explanatory variables.
In order to see how behavioral and motivational factors may be integrated into the
new approach, it is necessary to review briefly some models of motivation and behavioral
theory. This is done in Chapter 7.

CHAPTER 7
MOTIVATION THEORY
There are many models of motivation. One is drive theory (W.B. Cannon, 1939;
C.L. Hull, 1943). The main assumption in drive theory is that decisions concerning
present behavior are based in large part on the consequences, or rewards, of past
behavior. Where past actions led to positive consequences, individuals would tend to
repeat such actions; where past actions led to negative consequences or punishment,
individuals would tend to avoid repeating them. C.L. Hull (1943) defines "drive" as an
energizing influence which determined the intensity of behavior, and which theoretically
increased along with the level of deprivation. "Habit" is defined as the strength of
relationship between past stimulus and response (S-R). The strength of this relationship
depends not only upon the closeness of the S-R event to reinforcement but also upon the
magnitude and number of such reinforcements. Hence effort, or motivational force, is
a multiplicative function of magnitude and number of reinforcements.
In the context of the principal-agent model, drive theory would explain the agents
effort as arising from some past experience of deprivation (need of money) and from the
strength of feeling that effort leads to reward. So, the drive model of motivation defines
effort as follows:
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88
Effort = Drive Habit
= fd(past deprivation) fh( E( | S-R | ))
where fd is some "function" denoting drive as dependent on past deprivation,
fh is some "function" denoting habit as dependent on the sum of the strengths of
a number of instances of S-R reinforcements, and
| S-R | is the magnitude of an S-R reinforcement.
Drive theory, in its simplest form, states that individuals have basic biological
drives (eg., hunger and thirst) that must be satisfied. As these drives increase in strength,
there is an accompanying increase in tension. Tension is aversive to the organism, and
anything reducing that tension is viewed positively. The process of performing action that
achieves this is termed learning. All higher human motives are deemed to be derivatives
of this learning.
Another view is given in Instrumentality Theory which rejects the drive model
(L.W. Porter & E.E. Lawler, 1968), and emphasizes the anticipation of future events.
This emphasis provides a cognitive element ignored in most of the drive models. The
reasons for preferring instrumentality theory over other theories may be summarized as
follows:
(1) The terminology and concepts of instrumentality theory are more applicable
to the problems of human motivation; the emphasis on rationality and
cognition is appropriate for describing the behavior of managers.
(2) Instrumentality theory greatly facilitates the incorporation of motives such
as status, achievement, and power into a theory of attitudes and performance.

89
Figure 1 shows the Porter & Lawler model of the instrumentality theory of motivation.
The model parts are described below.
Value of reward describes the attractiveness of various outcomes to the individual.
The instrumentality model agrees with the drive model that rewards acquire attractiveness
as a function of their ability to satisfy the individual.
Perceived effort-reward probability refers to the subjective estimate of the
individual that increased effort will lead to the acquisition of some valued reward. This
consists of two estimates: the first is the probability that improved performance will lead
to the value reward, and the second is the probability that effort will lead to improved
performance. These two probabilities have a multiplicative relationship. Instrumentality
model makes a distinction between Effort and Performance: effort is a measure of how
hard an individual works, while performance is a measure of how effective is his effort.
Abilities and traits are included as a source of variation in this model, while other
models implicitly assume some fixed levels of abilities and traits. Abilities and traits refer
to relatively stable characteristics of the individual such as intelligence, personality
characteristics, and psychomotor skills, which are considered as boundary conditions or
limitations on performance.
Role Perception denotes an individuals definition of successful performance in
work. An appropriate definition of success is essential in determining whether or not
effort is transformed into good performance, and also in perceiving equity in reward.
Distinction is made between intrinsic and extrinsic rewards. Intrinsic rewards
are rewards that satisfy higher-order Maslow needs (A.H. Maslow, 1943; A.H. Maslow,

90
1954) and are administered by the individual to himself rather than by some external
agent. Extrinsic rewards are rewards administered by an external party such as the
principal.
Perceived equitable rewards describes the level of reward that an individual feels
is appropriate. The appropriateness of the reward is linked to role perceptions and
perception of performance.
Satisfaction is referred to as a "derivative variable". It is derived by the individual
(here, the agent) by comparing actual reward to perceived equitable reward. Satisfaction
may therefore be defined as the correspondence or correlation between actual reward and
perceived equitable reward.
Research in instrumentality theory is detailed in (Campbell and Pritchard, 1976;
Mitchell, 1974). Most of the tests of both their initial model and later versions have
yielded similar results: effort is predicted more accurately than performance. This makes
sense logically. Individuals have effort under their control but not always performance.
The environment (exogenous or random risk) plays a major role in determining if and
how effort yields levels of performance (Steers and Porter, 1983).

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FIGURE 1: THE PORTER AND LAWLER MODEL OF INSTRUMENTALITY THEORY
FIGURE 2: MODIFIED PORTER AND LAWLER MODEL

CHAPTER 8
RESEARCH FRAMEWORK
The object of the research is to develop and demonstrate an alternative
methodology for studying agency problems. To this end, we study several agency
models from a common framework described below. There are two types of issues
associated with the studies. One deals with the issues of modeling the agency problem
itself. The other deals with the issues of the method, in this case, knowledge bases,
genetic learning operators, and the operators of specialization and generalization.
The common framework for the agency problems has these elements:
1. The use of rule bases to model the information and expertise possessed by the
principal and the agent.
2. The use of probability distributions to model the uncertain nature of some of the
information.
3. Consideration of a number of elements of compensation.
4. Offering compensation to an agent based on the agents characteristics.
The common framework for the methodology for studying agency issues has these
elements:
1. Simulation of the agency interactions over a period of time.
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2. Use of learning mechanisms to capture the dynamics of agency interaction.
A number of preliminary studies were conducted in order to define and fine-tune
the two frameworks. The initial studies sought to understand the behavior of optimal
compensation schemes in a dynamic environment. These initial studies supported the
idea that learning by way of the genetic algorithm paradigm leads to quick convergence
to a relatively stable solution. Of course, genetic algorithms may find multiple stable
solutions. Further, the preliminary studies led to fixing of the genetic parameters, since
it was noticed that variations in these parameters did not contribute anything of interest.
For example, increasing mutation probability delayed convergence of the solutions, and
beyond 0.5 led to a chaotic situation. Similarly, varying the mating probability had an
effect on the speed with which the solutions were found. The nature of the solutions
were not affected. The genetic parameters were therefore fixed as follows:
* Crossover mechanism uniform one-point crossover;
* Mating probability 0.6;
* Mutation probability ranging from 0.01 to 0.001 (for different models);
* Discard worst rule and copy the best rule.
The use of generalization and specialization operators for learning in later models
will be described subsequently. Below, we give an overview of the various models
studied. The details follow in later sections.
Models 1 and 2 were preliminary studies conducted to explore the new framework
for attacking agency problems. The goal of these models, as well as Model 3, was to
demonstrate the feasibility of addressing issues in agency which the traditional theory

94
ignored (see, for example, Chapter 6 for a methodological analysis). Models 1 and 2 led
to the choice of genetic parameters (as described above), and finalizing the agency
interaction mechanism (namely, timing and information), including the Porter-Lawler
model of human behavior and motivation. While both Models 1 and 2 are more realistic
than the traditional models, they still do not capture the entire realism of an agency. The
later models capture increasing amounts of realism.
Model 3 is the first formal study. The goal of this study is to develop a model
which provides a counter-example to the traditional theory which considers fixed pay,
share of output, and exogenous risk to be important agency variables, and ignores the
role of the agents behavioral and motivational characteristics in selecting his
compensation scheme. This study tries to answer the following questions: Is there a
non-trivial and formal agency scenario where the lack of dependence of the compensation
scheme on the agents characteristics leads to a sub-optimal solution (as compared to the
standard theory)? Is there a scenario wherein consideration of other elements of
compensation lead to better results for both the principal and the agent? Is there a
scenario where, from a principals perspective, exogenous risk (which can only be
observed ex-post) plays a lesser role than other agency variables? How does certainty
of information affect the nature of the solutions? What measures may be used to
characterize good solutions, or identify important variables? The last question is
non-trivial, because all the variables used in these studies are discrete nominal valued,
and hence are not amenable to any formal measure theory. This study involves five
experiments (which differ in the information available to the principal), and the use of

95
factor analysis to study the principals knowledge base at the end of the simulation in
order to characterize good compensation schemes and identify important variables.
Models 1, 2 and 3 involve only a single agent. Models 4 and beyond capture
more realism in agency relationship. They are multi-agent, multi-period, dynamic
(agents are hired and fired all the time) models. Moreover, they closely follow one
traditional agency theory the LEN model of Spremann (see Chapter 5 for details).
Models 4 and 5 study the LEN model, while including only two elements of
compensation as in the original LEN model, and retaining the behavioral characteristics
of the agents. Model 4 studies the agency under a non-discriminatory firing policy of
the principal, while Model 5 studies exactly the same agency but with the principal
employing a discriminatory firing policy for the agents. Similarly, Models 6 and 7 are
non-discriminatory and discriminatory respectively. However, Models 6 and 7 employ
compensation variables not included in the original LEN model. These models study the
following issues:
* the nature of good compensation schemes under a demanding agency environment;
* the correlation between various variables of the agency;
* the correlation between the variables of the agency and the control variables of
the experiments;
* the effect of discriminatory firing practices by the principal
* the effect of complex compensation schemes.

96
Chapter 9 describes Model 3 in detail. Chapter 10 introduces Models 4 through
7, and describes each in detail. The conclusions are given in Chapter 11, and directions
for future research are covered in Chapter 12.

CHAPTER 9
MODEL 3
9.1 Introduction
In Model 3, utility functions are replaced by knowledge bases, machine learning
replaces estimation and inference replaces optimization. In so doing, complex contractual
structures and behavioral and motivational considerations can be directly incorporated
into the model.
In Section 2 we describe a series of experiments used to illustrate our approach.
These experiments study a realistic situation. Section 3 covers the methodology and
details of the experiments. Section 4 tabulates the results of our experiments, while
Section 5 describes and discusses the results.
Initially, the principals knowledge base reflects her current state of knowledge
about the agent (if any). The agents knowledge base reflects the way he will produce
under a contract. This knowledge base incorporates motivational and behavioral
characteristics. It includes his perception of exogenous risk, social skills, experience,
etc. The details are provided in Section 3.
The principal will refine her knowledge base through a learning mechanism.
Using the current knowledge base, the principal will use inference to determine a
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98
contract. This contract is used by the agent. The resulting output and welfare are used
by the principal to construct a "better" knowledge base through a learning procedure.
In the following we incorporate specific models and components to achieve an
implementation of our new principal-agent model. We link behavioral factors by the
model of Porter & Lawler (1968), which also incorporates the calculation of satisfaction
and subsequent effort levels by the agent. The Porter & Lawler model derives from the
instrumentality theory of motivation, which emphasizes the anticipation of future events,
unlike most models of motivation based on drive theory. The key ideas of the Porter &
Lawler model are the recognition of the appropriateness of rationality and cognition as
descriptive of the behavior of managers, and the incorporation of motives such as status,
achievement, and power as factors that play a role in attitudes and performance.
Effort is determined by the utility or value of compensation and the perceived
probability of effort leading to reward. Performance, determined by the effort level,
abilities of the agent, and role perceptions, leads to intrinsic and extrinsic rewards, which
in turn influence the satisfaction derived by the agent. A comparison of performance and
the satisfaction derived from it influences the perception of equity of reward, and
reinforces or weakens satisfaction. Performance also plays a role in the revision of the
probability of effort leading to adequate reward.
The principal and agent knowledge-bases in our model consist of rules. Each rule
has a set of antecedent variables and a set of consequent variables. The antecedent
variables are the agents behavioral characteristics and the exogenous risk, while the
consequent variables are the variables denoting the elements of compensation. The

99
knowledge-base therefore consists of rules that specify selection of compensation plans
based on the agents characteristics and the exogenous risk. A formal description
follows.
Let N denote a nominal scale. Nk denotes the k-fold nominal product. Let C Q
Nk denote the set of all compensation plans, {c,,...,cn}. Let B Nk denote the set of
all the behavioral profiles of the agent, {b1( ..., bm}. Each compensation plan c¡ is a
finite-dimensional vector c¡ = (c¡(1), ..., c^), where each element of the c¡ vector denotes
an element of the compensation plan, such as fixed pay, commission, or bonus. Each
element of B is also a finite-dimensional vector, bj = (bj(1), ..., bj(q)), where each element
of the bj vector denotes a behavioral characteristic that the agent will be evaluated on by
the principal, such as experience, motivation, or communication skill. The elements c¡
and bj are detailed in Section 5.
Let G be the set of mappings from the set of behavioral profiles B to the set of
compensation plans, C. Two or more compensation plans could conceivably be
associated with one particular behavioral profile bj of an agent. A particular mapping
g in G specifies a knowledge base K <= B C.
Let S:K*0*E-> R denote the total satisfaction function of the agency, where
E denotes the effort level of the agent, and 9 represents exogenous risk. Let SA denote
the satisfaction of the agent, and SP, the satisfaction of the principal (defined on the same
domain). SA and SP are both "functions" of other variables such as compensation plans,
output, agents effort, agents private information, and so on.
SA = SA(Output,C),

100
Sp = SP(V,Effort,C), and
S = S(SA,SP),
where V is the agents private information about the principal and her company.
Thus, S(b¡,Ci) denotes the total satisfaction derived when the agent has the
behavioral profile b¡ and the principal offers compensation plan c¡. Define fitness to be
the total satisfaction S(b;,Ci) normalized with respect to the whole knowledge base K. Let
F(g) denote the average fitness of a mapping g G G which specifies a knowledge base
1C£B*C.
1 n
Fig) = Y,s{bi'ci)' biEB' Cjtc.
n 1=1
The objective function of the principal-agent problem in our formulation is:
Max E EF-(sr) ] =E [A SibilCi)]
n 2 1
gzG
= e [- s(b, c,e, v) ]
nU.
= E S(E, C, 0, V) ] .
Our formulation of the principal-agent problem may be stated formally as:
Max E [F(gr) ] = E [S(E,C,Q)]
geG
such that
E e aigmax SA(B,C,,V),

where
C E range(g), and
V is the agents private information.
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The two constraints of the original problem (Individual Rationality and Incentive
Compatibility) are subsumed in the calculation of F. The agent, for example, selects his
effort level so as to increase his satisfaction or welfare based on his behavioral
characteristics and the compensation plan offered by the principal. It is not necessary
to check for IRC explicitly. Our model ensures that the agent, when presented with a
compensation plan that does not satisfy his IRC, picks an effort level that yields
extremely low total satisfaction. The dynamic learning process (described below)
discards all such compensation plans. In order to formalize the constraints in our new
model, it is necessary to introduce details of the functions, knowledge bases,
representation scheme for the knowledge bases, and the inference strategy. This is done
in Section 9.3.
9.2 An Implementation and Study
To both illustrate our method and to study the results of our approach, a series
of experiments were conducted. All the simulation experiments start with the same
initial set of rules for the principal, with the variables denoting agent characteristics
acting as the antecedents and the variables denoting elements of compensation acting as
consequents. This initial knowledge base of 500 rules is generated randomly, which
ensures that no initial bias is introduced into the model.

102
The agents knowledge base is varied from experiment to experiment to reflect
different behavioral characteristics, abilities, and perceptions. The experiments differ
with respect to each other in the probability distributions of the variables representing the
agents characteristics and the agents personal information about the principal.
An experiment consists of 10 runs of a sequence of 200 learning cycles including
the following steps:
1. Using her current knowledge base, the principal infers a compensation plan.
2. The agent performs under this compensation plan and an output is realized.
3. A satisfaction level is computed which reflects the total welfare of the principal
and the agent.
4. The principal notes the results of the compensation plan and revises her
knowledge base using a genetic algorithm learning method.
The following hypotheses are considered:
Hypothesis 1: Behavioral characteristics and complex compensation plans play a
significant role in determining good compensation rules.
Hypothesis 2: In the presence of complete certainty regarding behavioral
characteristics, the most important variables that explain variation in good compensation
rules are the same as those considered in the traditional principal-agent models.
Hypothesis 3: Extra information about behavioral characteristics yields better
compensation rules. Specifically, any information is better than having non-informative
pnors.

103
The experiments are designed to study the compensation rules which achieve
close-to-optimal satisfaction for the principal and the agent under different informational
assumptions. Each experiment pertains to a different agent having specific behavioral
characteristics and perception of the principal or the company.
Nine characteristics of the agent. They are: experience, education, age, general
social skills, office and managerial skills, motivation, physical qualities deemed essential
to the task, language and communication skills, and miscellaneous personal
characteristics.
The elements of compensation that are taken into account are: basic pay, share
of output or commission, bonus payments, long term payments, benefits, and stock
participation.
In the calculation of satisfaction (total welfare of the principal and the agent), we
also take into account variables that denote the agents perception or assessment of the
principal or her company. These variables may be called the agents "personal"
variables, since the principal has no information about them. The agents personal
variables we consider are: company environment, work environment, status, his own
traits and abilities, and his perceived probability of effort leading to reward.
Characterization of the agent in each of the five experiments is given below:
Agent #1 (involved in Experiment 1) is moderately experienced, has completed high
school, is above 55 years of age. His general social skills are average, but his office and
managerial skills are quite good. He has slightly above average motivation and
enthusiasm for the job, and he is more or less physically fit, but the principal is not very

104
sure about the agents health. He has good communication skills, while his other
miscellaneous personal characteristics leave something to be desired. He has a rather
pessimistic outlook about exogenous factors (economy and business conditions), but he
is not too sure of his pessimistic estimate.
His assessment of company and work environment is moderately favorable, while
he considers the companys corporate image to be rather high. His perception of his own
abilities and traits is that they are just better than average, but he feels that he is not
consistent (sometimes he does far better, sometimes far worse). He is pessimistic about
effort leading to reward, perhaps because his uninspiring characteristics and lack of good
education led to slow reward and promotion in the past.
Agent ft2 in Experiment 2 has the same assessment of personal variables as Agent
#1. However, his characteristics are more modest. He has very little experience, no
high school education, and is much below average in all other respects. He is as
pessimistic and as unsure about the exogenous variables as Agent ft 1.
Agent #3 in Experiment 3 is a college graduate in his late 20s to early 30s. He
has little experience but is very highly motivated, possesses good communication skills,
and is good in all the other characteristics. His assessment of the exogenous environment
is optimistic. Moreover, he believes the principals work and company environment is
very good, and is generally sure of his superior abilities. He believes effort will almost
always be rewarded appropriately.

105
Nothing is known about Agent #4 in Experiment 4, while everything known about
Agent #5 in Experiment 5 is known with certainty. Agent #5 is in the same age bracket
as Agent #3, while he has more experience. His office and managerial skills, motivation
and enthusiasm are of the highest. He is physically very fit, and has very good
communication skills. He perceives the principals company and work environment to
be the best in the market, and he is very certain of his superior talents. He firmly
believes that effort is always rewarded.
The nominal scales are used throughout the experiments are given below.
For the variables CE, WE, SI, AT, GSS, OMS, P, L, OPC:
1: very bad, 2: bad, 3: average, 4: good, 5: excellent.
For PPER and M (Motivation):
1: very low, 2: low, 3: average, 4: high, 5: very high.
For X (Experience):
1: none, 2: < 1 year, 3: between 1 and 5 years,
4: between 5 and 10 years, 5: more than 10 years.
For D (Education):
1: below high school, 2: high school, 3: undergraduate,
4: graduate, 5: graduate (specialization/2 or more degrees).
For A (Age):
1: < 18 years, 2: between 18 and 25 years, 3: between 25 and 35 years, 4:
between 35 and 50 years, 5: above 50 years.
For RISK:

106
1: very high, 2: high, 3: average, 4: low, 5: very low.
Table 9.1 provides details that capture the above characterizations.
The information on each variable in Table 9.1 is specified as a discrete probability
distribution. Table 9.1 lists the means and standard deviations of the variables associated
with the agents characteristics and the agents personal variables. In experiment 4, the
situation is non-informative. All the variables have discrete uniform distribution, with
mean 3.00 and standard deviation \ 2 1.414. Experiment 5 is provided complete and
perfect information, and so the standard deviation is 0.00.
9.3 Details of Experiments
In this Section we discuss rule representation, inference method, calculation of
satisfaction, details of the genetic learning algorithm, and statistics captured for analysis.
9.3.1 Rule Representation
A rule has the following format:
IF < antecedent > THEN < consequent >.
The antecedent values in the "IF" part of a rule are conditions that occur or are satisfied,
and the consequent variables are assigned values from the "THEN" part of the rule
correspondingly. The antecedent and consequent of a rule are conjunctions of several
variables. Let b¡ be the i-th antecedent (denoting a behavioral variable), and Cj denote
the j-th consequent (denoting a compensation variable). The antecedent of a rule is then
given by A=i,..,m and the consequent by A=i,...,n> where A denotes conjunction. Hence,

107
for a rule to be activated in our experiments, all the specified antecedent conditions must
be fulfilled, and the result of the activation of the rule is to yield a compensation plan
having all the specified elements. Hence, a compensation plan is dependent on the
specific characteristics of the agent and also on the exact realization of exogenous risk.
The effectiveness of each compensation plan is therefore dependent on how well it takes
into account the characteristics of the agent. It is not necessary for each rule in the
knowledge base to have all the m antecedents and all the n consequents specified.
However, we adopt a uniform representation for the knowledge base where all the rules
have full specification of all the antecedent and consequent variables.
All the variables are positionally fixed, which facilitates pattern-matching during
inference (described in Sec. 5.2 below). The antecedent variables dealing with the
agents characteristics (including exogenous risk) are listed in order below, with the
variable names in parentheses (b4 is not a behavioral variable: it represents 9, the
exogenous risk):
(1) Experience (X),
(2) Education (D),
(3) Age (A),
(4) Exogenous Risk (RISK),
(5) General Social Skills (GSS),
(6) Office and Managerial Skills (OMS),
(7) Motivation (M),
(8) Physical Qualities deemed essential to the task (PQ),

108
(9) Language and Communication Skills (L), and
(10) Miscellaneous Personal Characteristics (OPC).
The consequent variables that denote the elements of compensation plans are listed
in order below, with the variable names in parentheses:
(1) Basic Pay (BP),
(2) Share or Commission of Output (S),
(3) Bonus Payments (BO),
(4) Long Term Payments (TP),
(5) Benefits (B), and
(6) Stock Participation (SP).
We assume that each of the 10 variables representing the agents characteristics
(including exogenous risk) and the 6 variables that represent the elements of
compensation has 5 possible values. This is a convenient number of values for nominal
variables and represents one of the Likert scales.
In effect, every rule is represented as an ordered sequence of 16 integer numbers
of 1 through 5. The first ten numbers are understood to be the antecedents, and the next
six the consequents. The nominal scale linked to the consequent variables is as follows:
1: minimum; 2: low; 3: average; 4: high; 5: very high
For example, consider the following rule:
IF <2,3,1,4,5,2,3,1,4,3> THEN <3,2,4,3,2,2>
This rule means:
IF

109
Experience is less than one year, AND
Education is undergraduate, AND
Age is below 18 years, AND
Exogenous RISK is low (favorable business climate), AND
General Social Skills are excellent, AND
Office and Managerial Skills are bad (no skills at all), AND
Motivation is average, AND
Physical Qualities are very bad (frail health), AND
Communication Skills are good, AND
Other Characteristics are good
THEN
Basic Pay is average, AND
Commission is low, AND
Bonus payments are high, AND
Long term payments are average, AND
Benefits are low, AND
Stock Participation is low.
The total number of possible rules for the principal is 516 = 152,587,890,625.
The goal of each trial is to pick a small number, say 500 (= 3.2768 10"7 %) of rules
from among these 516 rules so that the final rules have very high satisfaction associated
with them.

110
9.3.2 Inference Method
The key heuristics that motivate the inference process are:
(1) compensation plans are conditional on the characteristics of the agent and the
assessment of exogenous risk;
(2) compensation plans which are close to optimal, rather than optimal, are sought.
We assume that the agent and the principal both have the same information on the
exogenous risk. At each learning episode in an experiment, the values in the rules are
changed by means of applying genetic operators (see Chapter 3 for details). The learning
algorithm ensures that rules having "robust" combinations of compensation plans survive
and refine over learning episodes. Such compensation plans are then identified as most
effective for that particular agent.
The "functional" relationship of the different variables in the inference scheme
is as follows (the subscript t denotes the learning episode or time):
Effort, = g(f1(Ct),f2(Vt),PPERt,IRt.1,PEPRO,
where C, is the compensation offered by the principal in time or learning episode
t,
where PPER denotes perceived probability of effort leading to reward,
PEPR denotes perceived equity of past reward,
PERR is perceived equity of current reward,
V, = (CE,, WE,, ST AT,), the agents private information in time t,
g is a fixed real-valued effort selection mapping,
f, is a fixed real-valued mapping of compensation, and

Ill
f2 is a fixed real-valued mapping of the agents private information;
similarly, functions f3 through f10, and h, through h3 are fixed real-valued mapping
defined on the appropriate domains;
Output, = f3(Effort RISKJ;
PERF, = f4(Outputt, Effort,);
IR, = f5(CE,, WE,, ST,);
PERR, = f6(PERF h,(C,));
Disutility, = f7(EffortJ;
PEPR, = PERR,.,;
SA, = fg(PERF IR,, h2(Q, PERR,, Effort,, RISK,, Disutility,);
Sp, = f9(0utput h3(C Output^); and
St = floC^AD SpJ.
The functions g, f, through fio and h, through h3 used in the inference scheme
to select effort levels, infer intrinsic reward, disutility, satisfactions, etc., are given in
Section 5.3 below.
9.3.3 Calculation of Satisfaction
At each learning episode, the following steps are carried out to compute the
satisfaction of the principal and the agent:
(0) the principal infers a compensation plan;
(1) the agent selects an effort level based on the compensation plan, his perception
of the principal, and other variables from the Porter & Lawler model;

112
(2) an act of nature is generated randomly according to the specified distribution of
exogenous risk;
(3) output is a function of effort and the act of nature;
(4) performance is a function of output and effort;
(5) the agents intrinsic reward is calculated;
(6) the agents perceived equity of reward is calculated;
(7) the agents disutility of effort is calculated;
(8) the agents satisfaction is a function of effort, performance, act of nature, intrinsic
reward, perceived equity of reward, compensation, and disutility of effort;
(9) the principals satisfaction is a function of output and compensation; and
(10) the total satisfaction is the sum of the satisfactions of the agent and the principal.
The functions used in inference, selection of effort by the agent, and calculation
of satisfaction are given below. The variables are multiplied by coefficients which
denote an arbitrary priority of these variables for decision-making. Any such priority
scheme may be used, or the functions replaced by knowledge-bases which help decide
in selecting or calculating values for the decision variables. These functions are kept
fixed for all the agents in the experiments. In function f,0 for example, basic pay
received the greatest weight, and terminal pay the least. Consideration of basic pay and
share of output as the most important variables in determination of effort is consistent
with the assumptions in the traditional principal-agent theory. Further, based on her
experience of most agents, the principal expects the company environment and corporate
ranking to play a more important role in the agents acceptance of contracts and in

113
selection of effort than specific behavioral traits. This is reflected in the function f20,
where the variable AT (Abilities and Traits) plays a vital role in the Porter and Lawler
model in determining effort selection. The probability distribution of AT is derived from
the probability distributions of the behavioral variables (excluding RISK, which plays a
direct role in the model) as follows:
1 10
Pr[ AT = i] = £ Pr [£>(J) = i] i = 1, ... ,5,
where b is the j-th behavioral variable, and b(4) is RISK (which is excluded).
The compensation variables enter the model in various ways, either directly as in
effort selection or indirectly as in determination of intrinsic reward. Their major role
is to induce the agent to select effort levels that lead to desired satisfaction levels.
The information available to the principal determines the weight of the different
variables in the model and their contributory effect, or the derivation of AT from the
behavioral variables. While the functions below reflect one such information system of
the principal, others are possible.
f,() = 13*BP + 12*S + 1 l*BO + 10*B + 9*SP + 8*TP;
f20 = 7*CE + 6*WE + 5*ST + 4*AT;
Effort = g() = (f,() + f2() + 3*PPER + 2*IR + PEPR)/13;
Output s f3() = Effort + RISK;
Performance, PERF = f4() = Output / Effort;
Intrinsic Reward, IR = f5() = (3*CE + 2*WE + ST)/6;
h,() = 5*S + 4*BP + 3*BO + 2*SP + B;

114
PERR = f6() = (6*PERF + h,0)/21;
Disutility of Effort, Dis = f7() = -Effort / 10;
h2() = 10*BP + 9*S + 8*BO + 7*SP + 6*B + 5*TP;
Satisfaction of the agent, SAt:
SAl = fgQ = (12*PERF+ll*IR+h20+4*PERR+3*Effort-2*RISK+Dis)/66;
h30 = BP + (S/10 Output) + BO + TP + B + SP;
Principals Satisfaction, Sp, = f9 = Output h3();
Total Satisfaction, St = f10() = SAt + Sp,.
9.3.4 Genetic Learning Details
Genetic learning by the principal requires a "fitness measure" for each rule.
Here, the fitness of a rule is the (weighted) sum of the satisfactions of the principal and
the agent, and normalized with respect to the full knowledge base. As already noted, the
satisfaction of the principal is the utility of the principals residuum, while the satisfaction
of the agent is derived from the Porter-Lawler model of motivation. The average fitness
of the knowledge base is derived, and the fitnesses of the individual rules are normalized
to the interval [0,1]. One-point crossover and mutation are then applied to the
knowledge base to yield the next generation of rules. A copy of the rule with the
maximum fitness is passed unchanged to the next knowledge base. Pilot studies for this
model showed that in no case did the maximum fitness across iterations peak after 200
iterations. Hence, 200 iterations were employed for all the experiments.

115
The three parameters which can be controlled in learning with genetic algorithms
are the mating probability (MATE), the mutation probability (MUTATE), and the
number of iterations (ITER). From trial simulations, a mating probability of 0.6, a
mutation probability of 0.01, and 200 iterations for each run were deemed satisfactory,
and were hence kept constant in all the experiments.
9.3.5 Statistics Captured for Analysis
The following statistics were collected for each simulation:
(1) Average fitness of the principals knowledge base;
2) Variance of knowledge base fitness;
(3) Maximum fitness over all iterations of a run;
(4) Entropy of fitnesses; and
(5) Iteration when maximum fitness was first achieved.
These statistics are averaged across 10 runs for each experiment. The satisfaction
index of the rules are normalized to the interval [0,1] to give fitness levels. Entropy is
defined as the Shannon entropy, given by the formula
En{fi) = £ f1 In flt
i=1
where f¡ is the fitness of the i-th rule in the knowledge base, and In is the natural
logarithm. The maximum entropy possible is ln(Number of Rules) and corresponds to
the entropy of a distribution which occurs as the solution to a problem without any
constraints (or information). In all the experiments, the possible maximum entropy is

116
therefore ln(501) 6.2166061. Addition of constraints or information (such as the
value of the mean or variance) may result in a smaller entropy. The object of
calculating the entropy of the knowledge base is to measure its informativeness. When
the fitnesses, expressed as a distribution, achieve the maximum entropy while satisfying
all the constraints of the system, the knowledge base is most informative yet maximally
non-committal (see, for example, Jaynes 1982, 1986a, 1986b, 1991). An entropy value
which is smaller than the maximum indicates some loss of information, while a larger
entropy indicates unwarranted assumption of information. The entropy values will be
compared across experiments to give an indication of the nature of the learned rules.
9.4 Results
The distribution of first iteration to achieve the maximum fitness bound is shown
in Table 9.2 (expressed as a percentage) for the experiments. The table shows that there
is more than a 38% chance of the maximum occurring within the first 30 iterations, a
50% chance of the maximum occurring within the first 60 iterations, and more than a
78% chance that it will do so within the first 120 iterations.
Learning appeared to converge quickly to the best knowledge base formed over
the 200 learning episodes. Table 9.2 only indicates the way the learning process
converges. Based on a number of pre-tests, this trend was found to be consistent.
However, it should not be taken as an exact guide in any replication of the experiments.
Since random mutations in the learning process might result in rules which are
not representative of the agent, the final knowledge base is processed to remove such

117
rules. The processing involves removal of those rules which have at least one antecedent
value (i.e. value of a behavioral variable) which is not within one standard deviation
range of the mean (given in Table 9.1). The processed knowledge bases of all the runs
of each experiment are pooled to form the final knowledge base.
Table 9.3 shows the fitness statistics for the various experiments, where MATE
= 0.6, MUTATION = 0.01 and ITER = 200 is fixed. Table 9.3 also shows the
redundancy ratio of the knowledge base of each experiment. This is the ratio of the total
number of rules to the number of distinct rules. This ratio may be greater than one
because the learning process may generate copies of highly stable rules.
Table 9.4 shows the attained Shannon entropy of normalized fitness of the final
knowledge base for each experiment. Table 9.4 also shows the theoretical maximum
entropy of fitness (defined as the natural logarithm of the number of rules), and the ratio
of the attained entropy to the maximum entropy. The fitness of each rule is multiplied
by 10000 for readability.
Tables 9.5 9.34 summarize the results of the five experiments in detail. Tables
9.5, 9.11, 9.17, 9.23, and 9.29 show the frequency of values of the compensation
variables in the final knowledge base. Tables 9.6, 9.12, 9.18, 9.24, and 9.30 show the
range (minimum and maximum), mean, and standard deviation of the compensation
variables. Tables 9.7, 9.13, 9.19, 9.25, and 9.31 show the results of Spearman
correlation analysis on the final knowledge base. Tables 9.8, 9.9, 9.10, 9.14, 9.15,
9.16, 9.20, 9.21, 9.22, 9.26, 9.27, 9.28, 9.32, 9.33, and 9.34 deal with factor analysis
of the final knowledge base. Tables 9.8, 9.14, 9.20, 9.26, and 9.32 list the eigenvalues

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of the correlation matrix. Tables 9.9, 9.15, 9.21, 9.27, and 9.33 show the factor pattern
of the direct solution (i.e. without rotation). Tables 9.10, 9.16, 9.22, 9.28, and 9.34
show the factor pattern of the varimax rotation.
The following rules having highest fitness in each experiment are displayed below
for illustration (the rule representation format of Section 5.1 will be used; fitnesses,
denoted FIT, are multiplied by 10,000 for convenience):
EXP 1: IF <3,2,5,2,3,4,4,4,4,3> THEN <4,1,1,1,1,1 >;
EXP 2: IF <2,1,1,2,1,1,2,2,2,1 > THEN <3,1,2,1,1,1 >;
EXP 3: IF < 1,4,3,4,3,3,5,5,4,4> THEN <5,1,3,1,1,1 >;
EXP 4: IF <2,3,3,3,3,4,3,4,3,2> THEN <5,1,1,1,1,3>;
EXP 5: IF <3,4,3,4,4,5,5,5,4,4> THEN <5,1,2,1,1,3>.
9.5 Analysis of Results
In each of the experiments, letting the process run to completion usually improved
the average fitness of the population, decreased its variance and increased its entropy.
Several exceptions to this suggest that it may be a better strategy to store those
knowledge bases generated during the learning process which possess desirable
characteristics. Low variance indicates higher certainty, while higher entropy indicates
a stable state close to a global optimum and uniformity in fitness for the rules of the
population.
Agent ft 1 provides the maximum total satisfaction, followed in decreasing order
by Agents #2, #5, #4, and #3 (Table 9.3). Interestingly, certain information did not

119
yield higher average fitness (or satisfaction) as can be seen by comparing Agents #5 and
#1; a complete non-informative prior (as in the case of Agent ft A) did not lead to lowest
average fitness (the lowest was obtained by Agent #3). Furthermore, the result in this
case is counter-intuitive when the behavioral characterizations of the different agents are
considered. Agent #5 seems to be the best bet for this principal to maximize satisfaction.
This is not the case. This result takes on added significance in view of the fact that
Agent #5 faced an environment having low exogenous risk compared to that faced by
Agent ft 1 (higher values for the risk variable in Table 9.1 denote less risk).
However, the uncertainty of the agents performance in maximizing total
satisfaction is least in the case of Agent #5 (about whom the principal has completely
certain information), while it is the highest in the case of Agent ft A (about whom the
principal has no information whatsoever). Agent ff5 is followed in increasing order of
uncertainty by Agents ft3, ft 1, #2, and ft A.
From Table 9.4, the ratio of the entropy of the normalized fitnesses of the
knowledge base to the theoretical maximum gives an indication of how close the
information content of the final knowledge base is to the theoretical maximum. It shows
that the final knowledge base of the non-informative case (Agent ttA) is least informative
(while satisfying maximal non-commitalness), while the case of certain information
(Agent #5) shows a highly informative knowledge base. This is intuitively reasonable.
Tables 9.5, 9.6, 9.11, 9.12, 9.17, 9.18, 9.23, 9.24, 9.29 and 9.30 show the
compensation recommendations for each of the five agents. The mean compensation
value for each variable including the standard deviation from the mean helps in the task

120
of deciding on a specific compensation plan. For example, Agent #1 must be given high
basic pay but as less of the other elements of compensation as possible, while Agent #2
should be given an above average(but not high) basic pay and a low amount of bonus
(Table 9.11). Only in the non-informative case (Agent #4) a definite recommendation
is made for the share of output to be as low as possible in the compensation plan offered
to him (Table 9.24). Furthermore, if standard deviation from the mean compensation
values is to be understood as the uncertainty regarding compensation, it is interesting to
observe that in the case of Agent #4, the recommendations for compensation plans is
more definitive than in the case of Agent #5 (as can be seen from comparing the standard
deviations in Tables 9.24 and 9.30).
A few correlations at the 0.1 significance level among the compensation variables
were observed (Tables 9.7, 9.13, 9.19, 9.25, and 9.31). For Agent #1, a mild positive
correlation of 0.1173 was observed between Basic Pay and Terminal Pay (Table 9.7).
For Agent ft2, mild negative correlations between Basic Pay and Bonus (-0.2396) and
between Basic Pay and Benefits (-0.1101) were observed. Bonus and Benefits were
mildly positively correlated (Table 9.13). In the case of Agent #3, the following
correlations were evident: Basic Pay and Share (-0.2124), Benefits and Share (0.2552),
Bonus and Benefits (0.3042), and Benefits and Stock Participation (0.2762) (Table 9.19).
No correlations were observed at all (at the 0.1 significance level) for Agent #4 (the non-
informative case) (Table 9.25), while Agent #5 had the most number of significant
correlations (7 out a possible 15). However, all of these correlations were, without
exception, very weak. Basic Pay formed weak negative correlations with Share (-0.0598)

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and Terminal Pay (-0.0568), and weak positive correlations with Bonus (0.1591) and
Stock Participation (0.0389). Benefits and Share were weakly positively correlated
(0.0557). Stock Participation formed weak positive correlations with Basic Pay (0.0389),
Bonus (0.0508) and Benefits (0.0605) (Table 9.31).
Without further research, the causes of these correlations cannot be known
definitely. While the compensation schemes are definitely tailored to the behavioral
characteristics of the agents, motivation theory does not enable (at the present state of
the art) to make definitive causal connections between specific behavioral patterns and
effort-inducing compensation. Directions for future research are described in Chapter
12.
Factor analysis of the final knowledge base of each experiment was carried out
to see if the knowledge base had any significant factors. A factor with eigenvalue greater
than one may be deemed to be significant since it accounts for more variation in the rules
than any one variable alone. Table 9.9 provides a summary of pertinent data from
Tables 9.8, 9.14, 9.20, 9.26, and 9.32.
The percentage of total variation accounted for by the significant factors is rather
low, the maximum being for experiment 3. Experiment 4 required the maximum number
of factors (almost as many as the number of variables, which is 16). Experiment 4 also
had the highest average eigenvalue, and Experiment 5 the lowest. The number of
significant factors was least in the case of Experiment 5, and each factor accounted for
a greater proportion of the variation than the non-informative situation of Experiment 4.

122
This suggests that the final knowledge base of Experiment 4 is comparatively highly
"fragmented" than that of Experiment 5.
Tables 9.9, 9.15, 9.21, 9.27, and 9.33 show the direct factor pattern. Variables
that load high on a factor indicate a greater role played in explaining that factor.
Moreover, each factor accounts for a small proportion of the total variation. A measure
of the explanatory power of a variable may be the expected factor identification, defined
as the sum of the products of each factor loading and the proportion of variation of that
factor, the sum being taken over the total number of factors that account for all the
variation in the population. Table 9.36 shows the expected factor identification of each
of the compensation variables for each experiment. Table 9.37 shows the expected factor
identification computed from the varimax rotated factor matrices.
Table 9.36 shows that except in Experiment 3, Basic Pay and Share did not have
the highest explanatory measure. Comparing across all the five experiments and ranking
the compensation variables, the following is the order of variables in decreasing
explanatory measure:
Benefits and stock participation (tied),
Terminal pay,
Bonus,
Basic pay (also called Rent or Fixed pay), and
Share.
A similar comparison from the data in Table 9.37 for the varimax rotated factors
yields the following ordering of the compensation variables:

Benefits and stock participation (tied),
Basic pay and terminal pay (tied),
Share, and
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Bonus.
Using the direct factor matrices, the expected factor identifications of behavioral
variables were computed (Table 9.38). These variables were ranked and ordered across
the 5 experiments. The exogenous risk variable, though not a behavioral variable, was
included to study its relative importance also. The following is the decreasing order of
explanatory power:
Experience,
Managerial skills,
General social skills,
Risk,
Physical qualities,
Communication skills,
Education,
Motivation,
Other personal skills, and
Age.
Using the varimax factor matrices, the expected factor identifications of
behavioral variables were computed (Table 9.38). These variables were ranked and

124
ordered across the 5 experiments. The following is the decreasing order of explanatory
power:
Experience, risk, and physical qualities (tied),
Managerial skills,
Motivation,
Age, and general social skills (tied),
Education,
Communication skills, and other personal skills (tied).
The above results and analysis support the hypothesis that behavioral
characteristics and complex compensation plans play a significant role in determining
good compensation rules (Hypothesis 1 in Sec. 9.2 ). However Hypothesis 2, regarding
the high relative importance of Basic Pay and Share in the case of completely certain
information (Experiment 5), has not been supported (see Sec. 9.2). The results show
that even when complete and certain information is present, it is not reasonable for the
principal to try to induce the agent to exert optimum effort by presenting a contract based
solely on Basic Pay and Share of output. Further, the results provide a counterexample
to the seemingly intuitive notion that either perfect information about the behavioral
characteristics of the agent will yield the most satisfaction or that a complete lack of
information about the agent will lead to minimum satisfaction. This suggests that
Hypothesis 3 (see Sec. 9.2) is also not supported.

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TABLE 9.1: Characterization of Agents
PERSONAL VARIABLE
EXP1
MEAN
(SD)
EXP2
MEAN
(SD)
EXP3
MEAN
(SD)
EXP5
MEAN
(SD)
COMPANY
ENVIRONMENT, CE
3.40
(0.66)
3.40
(0.66)
4.50
(0.50)
5.00
(0.00)
WORK
ENVIRONMENT, WE
3.60
(0.80)
3.60
(0.80)
4.60
(0.49)
5.00
(0.00)
STATUS INDEX, SI
4.20
(0.98)
4.20
(0.98)
4.70
(0.46)
5.00
(0.00)
ABILITIES AND
TRAITS, AT
3.51
(1.16)
1.46
(0.74)
3.73
(1.18)
4.11
(0.74)
PROB. (EFFORT ->
REWARD), PPER
2.90
(0.70)
2.90
(0.70)
4.60
(0.66)
4.00
(0.00)
BEHAVIORAL VARIABLE
EXPERIENCE, X
3.65
(0.78)
1.40
(0.66)
1.40
(0.66)
3.00
(0.00)
EDUCATION, D
2.00
(0.00)
1.00
(0.00)
4.20
(0.40)
4.00
(0.00)
AGE, A
5.00
(0.00)
1.00
(0.00)
3.00
(0.00)
3.00
(0.00)
RISK
2.10
(1.38)
2.10
(1.38)
3.90
(0.94)
4.00
(0.00)
GENERAL SOCIAL
SKILLS, GSS
3.00
(1.55)
1.70
(0.78)
3.80
(0.87)
4.00
(0.00)
MANAGERIAL
SKILLS, OMS
4.05
(0.67)
1.40
(0.66)
3.40
(0.92)
5.00
(0.00)
MOTIVATION, M
3.60
(0.66)
1.50
(0.50)
4.90
(0.30)
5.00
(0.00)
PHYSICAL
QUALITIES, PQ
3.60
(1.28)
2.3
(1.1)
4.60
(0.49)
5.00
(0.00)
COMMUNICATION
SKILLS, L
3.95
(0.59)
1.50
(0.67)
4.30
(0.64)
4.00
(0.00)
OTHERS, OPC
2.77
(0.61)
1.30
(0.64)
4.00
(0.78)
4.00
(0.00)

126
TABLE 9.2: Iteration of First Occurrence of Maximum Fitness
RANGE
PERCENTAGE
RANGE
PERCENTAGE
[1,10]
14
(100,110]
4
(10,20]
14
(110,120]
4
(20,30]
10
(120,130]
0
(30,40]
6
(130,140]
6
(40,50]
2
(140,150]
2
(50,60]
4
(150,160]
2
(60,70]
6
(160,170]
2
(70,80]
4
(170,180]
4
(80,90]
4
(180,190]
0
(90,100]
6
(190,200]
6
TABLE 9.3: Learning Statistics for Fitness of Final Knowledge Bases
Experiment
Number of
Rules
Redundancy
Ratio
Minimum
Maximum
Mean
S.D.
1
199
1.3724
13.96
27.19
20.29
2.87
2
397
1.3690
7.77
27.16
19.92
3.18
3
63
1.1455
11.09
24.66
19.71
2.42
4
74
1.1563
11.92
26.68
19.82
3.69
5
1965
5.7794
3.09
24.72
19.94
2.35
TABLE 9.4: Entropy of Final Knowledge Bases and Closeness to the Maximum
Experiment
Number of
Rules
Entropy
Maximum
Entropy
Ratio1
1
199
5.2834
5.2933
0.9981
2
397
5.9709
5.9839
0.9978
3
63
4.1355
4.1431
0.9982
4
74
4.2869
4.3041
0.9960
5
1965
7.5760
7.5833
0.9990
Ratio of Entropy to Maximum Entropy

127
TABLE 9.5: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 1
Compensation
Variables
Values of the Variable
1
2
3
4
5
Basic Pay
3.0
4.5
13.1
38.2
41.2
Share
97.5
2.0
0.5
0.0
0.0
Bonus
61.8
22.6
5.5
5.5
4.5
Terminal Pay
93.0
2.0
3.0
1.5
0.5
Benefits
82.9
9.5
1.5
3.0
3.0
Stock
Participation
74.4
18.1
6.0
1.5
0.0
TABLE 9.6: Range, Mean and Standard Deviation of Values of Compensation
Variables in the Final Knowledge Base in Experiment 1
Variable
Minimum
Maximum
Mean
S.D.
BP
1.00
5.00
4.1005025
0.9949112
S
1.00
3.00
1.0301508
0.1987219
BO
1.00
5.00
1.6834171
1.0987947
TP
1.00
5.00
1.1457286
0.5807252
B
1.00
5.00
1.3366834
0.8945464
SP
1.00
4.00
1.3467337
0.6631551

128
TABLE 9.7: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 1
(Spearman Correlation Coefficients in the first row for each variable,
Prob> j R j under Ho: Rho=0 in the second)
BP
S
BO
TP
B
SP
BP
1.00000
0.04942
0.11030
0.11728
-0.07280
0.02989
0.0
0.4882
0.1209
0.0990
0.3068
0.6752
S
0.04942
1.00000
0.03915
-0.04413
0.00558
-0.09337
0.4882
0.0
0.5830
0.5360
0.9377
0.1896
BO
0.11030
0.03915
1.00000
-0.03333
0.00579
-0.03130
0.1209
0.5830
0.0
0.6402
0.9354
0.6607
TP
0.11728
-0.04413
-0.03333
1.00000
0.02864
-0.00110
0.0990
0.5360
0.6402
0.0
0.6880
0.9877
B
-0.07280
0.00558
0.00579
0.02864
1.00000
-0.04710
0.3068
0.9377
0.9354
0.6880
0.0
0.5089
SP
0.02989
-0.09337
-0.03130
-0.00110
-0.04710
1.00000
0.6752
0.1896
0.6607
0.9877
0.5089
0.0
TABLE 9.8: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 1
(Eigenvalues of the Correlation Matrix)
Total = 11 Average = 0.6875
1
2
3
4
5
6
Eigenvalue
1.494645
1.352410
1.160236
1.116413
1.051618
1.012871
Difference
0.142235
0.192174
0.043823
0.064795
0.038747
0.080984
Proportion
0.1359
0.1229
0.1055
0.1015
0.0956
0.0921
Cumulative
0.1359
0.2588
0.3643
0.4658
0.5614
0.6535
7
8
9
10
11
12
Eigenvalue
0.931887
0.823970
0.757124
0.714118
0.584709
0.000000
Difference
0.107916
0.066847
0.043006
0.129409
0.584709
0.000000
Proportion
0.0847
0.0749
0.0688
0.0649
0.0532
0.0000
Cumulative
0.7382
0.8131
0.8819
0.9468
1.0000
1.0000
13
14
15
16
Eigenvalue
0.000000
0.000000
0.000000
0.000000
Difference
0.000000
0.000000
0.000000
0.000000
Proportion
0.0000
0.0000
0.0000
0.0000
Cumulative
1.0000
1.0000
1.0000
1.0000

129
TABLE 9.9: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 1 Factor Pattern
Factor 1
Factor 2
Factor 3
Factor 4
Factor 5
Factor 6
X
-0.38741
-0.32701
-0.33959
0.31473
-0.02677
-0.10644
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
-0.00000
0.00000
0.00000
0.00000
0.00000
-0.00000
RISK
-0.39646"
-0.13369
0.50581
0.25216
-0.11529
0.46880
GSS
0.17684
0.23305
0.28615
-0.36547
-0.61216
0.30750
OMS
-0.00000
0.00000
0.00000
-0.00000
-0.00000
0.00000
M
0.45141
0.44846
-0.30819
0.01878
-0.02665
-0.04173
PQ
0.54728
-0.53206
0.16099
0.05279
0.21852
0.00511
L
-0.00000
-0.00000
0.00000
-0.00000
-0.00000
0.00000
OPC
0.00000
-0.00000
-0.00000
0.00000
0.00000
-0.00000
BP
0.24127
0.19271
0.26919
0.66974
0.26082
0.24682
S
0.15889
0.06246
-0.59932
0.06671
0.04408
0.52285
BO
0.55605
-0.44006
0.19261
0.03879
-0.21608
-0.29675
TP
0.28107
0.47123
0.27576
-0.15331
0.47397
0.01654
B
-0.31708
-0.16489
0.12134
-0.52885
0.51514
0.06433
SP
-0.28396
0.45292
0.16366
0.24367
-0.08786
-0.50860
Factor 7
Factor 8
Factor 9
Factor 10
Factor 11
X
0.53275
0.32110
0.18254
-0.24025
0.19642
D
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
-0.00000
-0.00000
0.00000
0.00000
RISK
0.15023
0.09305
0.00794
0.48441
0.08071
GSS
0.13197
0.30346
0.03435
-0.34316
-0.03492
OMS
-0.00000
0.00000
0.00000
-0.00000
0.00000
M
0.38181
0.20000
-0.44346
0.31541
0.12412
PQ
0.21527
0.25601
0.02163
0.04990
-0.47547
L
-0.00000
0.00000
0.00000
-0.00000
0.00000
OPC
0.00000
-0.00000
-0.00000
0.00000
-0.00000
BP
-0.17272
0.06504
-0.24630
-0.38664
0.10238
S
-0.38033
0.29019
0.29471
0.12585
-0.01855
BO
-0.26496
0.16193
0.12058
0.12813
0.44320
TP
0.28937
-0.02725
0.51720
0.01514
0.14920
B
-0.15392
0.41618
-0.28532
-0.07102
0.15815
SP
-0.25267
0.47536
0.12030
0.12243
-0.20590
Notes:
Final Communality Estimates total ll.C
and are as follows: 0.0 for D,
A, OMS, L, and OPC; 1.0 for the rest of the variables.

130
TABLE 9.10: Experiment 1 Varimax Rotation
Factor 1
Factor 2
Factor 3
Factor 4
Factor 5
Factor 6
X
0.00592
-0.00592
-0.06160
-0.00152
0.03289
-0.03681
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
0.00697
0.01680
0.02680
-0.04246
0.99219
0.03829
GSS
-0.00519
-0.02315
0.99595
-0.00698
0.02638
-0.02607
OMS
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
M
0.00646
-0.06592
0.03811
0.04031
-0.08515
0.02529
PQ
-0.10498
0.00895
-0.01482
-0.00856
-0.01218
0.03838
L
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
BP
0.02878
-0.05624
-0.02624
0.01905
0.03809
0.99414
S
-0.04050
-0.01274
-0.00694
0.99688
-0.04193
0.01893
BO
-0.02424
-0.05007
0.01906
-0.01453
-0.04793
0.00752
TP
0.01929
0.00864
0.02160
-0.02133
-0.02683
0.04298
B
-0.00484
0.99454
-0.02324
-0.01282
0.01670
-0.05616
SP
0.99305
-0.00485
-0.00525
-0.04099
0.00693
0.02892
Factor 7
Factor 8
Factor 9
Factor 10
Factor 11
X
-0.07567
0.99216
-0.05006
-0.03047
0.01219
D
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
-0.02644
0.03284
-0.04665
-0.08451
-0.01179
GSS
0.02122
-0.06089
0.01826
0.03736
-0.01414
OMS
0.00000
0.00000
O.OOOO0
0.00000
0.00000
M
0.06591
-0.03072
-0.01159
0.98940
0.01758
PQ
0.02316
0.01277
0.15553
0.01808
0.98070
L
0.00000
0.00000
0.00000
0.00000
0.00000
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
BP
0.04274
-0.03658
0.00741
0.02495
0.03682
S
-0.02106
-0.00149
-0.01395
0.03942
-0.00818
BO
-0.03591
-0.05154
0.98287
-0.01188
0.15448
TP
0.99215
-0.07568
-0.03483
0.06528
0.02213
B
0.00860
-0.00589
-0.04828
-0.06490
0.00843
SP
0.01928
0.00591
-0.02373
0.00641
-0.10112
Notes: Final Communality Estimates total 11.1
3 and are as
follows: 0.0 for D,
A, OMS, L, and OPC; 1.0 for the rest of the variables.

131
TABLE 9.11: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 2
Compensation
Variable
VALUES OF THE VARIABLE
1
2
3
4
5
Basic Pay
6.5
2.0
17.1
45.3
29.0
Share
95.7
1.8
0.8
1.3
0.5
Bonus
50.1
22.7
7.6
13.4
6.3
Terminal Pay
93.7
3.3
1.3
0.5
1.3
Benefits
85.1
8.6
3.5
2.0
0.8
Stock
87.9
6.8
2.0
1.8
1.5
TABLE 9.12: Range, Mean and Standard Deviation of Values of Compensation
Variables in the Final Knowledge Base in Experiment 2
Variable
Minimum
Maximum
Mean
S.D.
BP
1.00
5.00
3.8816121
1.0582000
S
1.00
5.00
1.0906801
0.4839221
BO
1.00
5.00
2.0302267
1.2964961
TP
1.00
5.00
1.1234257
0.5617257
B
1.00
5.00
1.2468514
0.6849916
SP
1.00
5.00
1.2216625
0.7079878
TABLE 9.13: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 2
(Spearman Correlation Coefficients in the first row for each variable, Prob > ¡ R ¡
under Ho: Rho=0 in the second)
BP
S
BO
TP
B
SP
BP
1.00000
0.02951
-0.23955
0.05064
-0.11008
0.01298
0.0
0.5578
0.0001
0.3142
0.0283
0.7965
S
0.02951
1.00000
0.03275
-0.00414
0.06030
0.00038
0.5578
0.0
0.5153
0.9344
0.2307
0.9940
BO
-0.23955
0.03275
1.00000
0.01020
0.10281
-0.02808
0.0001
0.5153
0.0
0.8394
0.0406
0.5770
TP
0.05064
-0.00414
0.01020
1.00000
0.04402
-0.00848
0.3142
0.9344
0.8394
0.0
0.3817
0.8663
B
-0.11008
0.06030
0.10281
0.04402
1.00000
0.01402
0.0283
0.2307
0.0406
0.3817
0.0
0.7807
SP
0.01298
0.00038
-0.02808
-0.00848
0.01402
mwmmm
0.7965
0.9940
0.5770
0.8663
0.7807
0.0

132
TABLE 9.14: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 2 Eigenvalues of the Correlation Matrix
Factors
1
2
3
4
5
6
Eigenvalue
1.562150
1.349480
1.288563
1.186437
1.075113
1.008861
Difference
0.212669
0.060917
0.102126
0.111324
0.066252
0.039300
Proportion
0.1202
0.1038
0.0991
0.0913
0.0827
0.0776
Cumulative
0.1202
0.2240
0.3231
0.4144
0.4971
0.5747
7
8
9
10
11
12
Eigenvalue
0.969560
0.913091
0.869975
0.797047
0.744512
0.637679
Difference
0.056469
0.043117
0.072927
0.052535
0.106833
0.040147
Proportion
0.0746
0.0702
0.0669
0.0613
0.0573
0.0491
Cumulative
0.6492
0.7195
0.7864
0.8477
0.9050
0.9540
13
14
15
16
Eigenvalue
0.597532
0.000000
0.000000
0.000000
Difference
0.597532
0.000000
0.000000
Proportion
0.0460
0.0000
0.0000
0.0000
Cumulative
1.0000
1.0000
1.0000
1.0000

133
TABLE 9.15: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 2 Factor Pattern
Factor
1
2
3
4
5
6
7
X
0.23470
0.40822
0.41989
0.10143
-0.06455
-0.47522
-0.13029
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
-0.00000
-0.00000
0.00000
-0.00000
0.00000
0.00000
-0.00000
RISK
0.40696
0.10345
-0.15114
-0.43374
0.06063
0.00857
0.09780
GSS
0.71945
0.12878
0.06651
0.25299
-0.09613
-0.02708
0.21848
OMS
0.15988
0.26111
-0.23533
0.55088
0.53138
0.02406
-0.24275
M
0.52994
-0.06812
0.35756
0.04245
0.12138
-0.00603
0.43643
PQ
-0.49072
0.18271
0.19086
0.25694
0.29339
-0.29651
0.18784
L
-0.43182
0.11417
0.46917
-0.00994
-0.26917
-0.20723
0.25407
OPC
-0.00000
-0.00000
-0.00000
0.00000
0.00000
-0.00000
-0.00000
BP
0.00206
0.73317
0.02383
-0.14116
0.09366
0.15727
-0.00144
S
0.15005
0.08440
0.48987
0.00873
-0.35507
0.37735
-0.43373
BO
0.16081
-0.64356
0.15230
0.08186
0.15639
-0.23750
0.04318
TP
-0.11221
0.09559
0.22871
-0.50489
0.50146
0.27257
0.26726
B
-0.07398
-0.24228
0.54532
0.23797
0.32011
0.41360
-0.14065
SP
-0.15402
0.09822
-0.17831
0.46301
-0.29859
0.42643
0.51464
Factor
8
9
10
11
12
13
X
-0.34093
0.12914
0.28987
-0.21169
-0.06036
-0.28162
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
-0.00000
0.00000
nmoum
-0.00000
RISK
0.64290
0.27270
0.17846
-0.21469
-0.03416
-0.18056
GSS
0.03558
-0.12787
0.18071
0.00686
-0.21839
0.49158
OMS
0.14111
0.00621
0.04899
-0.09147
0.41684
0.03269
M
-0.03356
-0.10222
-0.53502
0.03731
0.16803
-0.22844
PQ
0.21954
0.40686
-0.28804
-0.04598
-0.29716
0.16419
L
0.35726
-0.28314
0.19616
0.00520
0.37074
0.12874
OPC
-0.00000
0.00000
0.00000
0.00000
0.00000
-0.00000
BP
0.05725
-0.04855
0.03755
0.62106
-0.07920
-0.09706
S
0.05131
0.43120
-0.18876
-0.00933
0.15673
0.15771
BO
0.00810
0.35568
0.28456
0.47545
0.11527
-0.02132
TP
-0.35860
0.14954
0.18191
-0.15212
0.14461
0.21390
B
0.20155
-0.28888
0.19343
-0.05661
-0.30269
-0.17940
SP
-0.10104
0.29287
0.22341
-0.05877
0.02784
-0.18570
Notes: Final Communality Estimates total 13.0 and are as follows: 0.0 for D, A,
and OPC; 1.0 for the rest of the variables.

134
TABLE 9.16: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 2 -Varimax Rotated Factor Pattern
Factor
1
2
3
4
5
6
7
X
0.03492
0.99126
0.02196
-0.01687
0.01069
0.01925
-0.03964
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
0.02987
-0.01676
-0.04298
0.99302
0.02126
-0.00162
-0.04582
GSS
0.12998
0.08431
-0.09124
0.06914
-0.05572
0.05292
0.02567
OMS
-0.00638
0.01924
0.04137
-0.00161
-0.03958
0.99160
0.01619
M
0.98841
0.03512
-0.02218
0.03018
0.02264
-0.00653
-0.02308
PQ
-0.02223
0.02208
0.98938
-0.04343
0.01497
0.04168
0.02901
L
-0.01908
0.03370
0.08208
-0.03191
-0.00782
-0.07776
0.01142
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
BP
-0.01095
0.04783
0.02059
0.02922
0.04601
0.03992
0.00344
S
0.02705
0.05363
-0.01922
0.00868
-0.01382
-0.03522
0.00210
BO
0.03723
-0.01392
-0.00442
0.00168
-0.00869
-0.02235
-0.02816
TP
0.02208
0.01055
0.01474
0.02112
0.99503
-0.03917
-0.02333
B
0.03185
-0.01912
0.01580
-0.04609
0.03829
0.03085
-0.01322
SP
-0.02242
-0.03903
0.02838
-0.04535
-0.02323
0.01596
0.99633
Factor
8
9
10
11
12
13
X
0.05425
-0.01391
-0.01919
0.03347
0.04754
0.08050
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
0.00873
0.00165
-0.04594
-0.03152
0.02887
0.06572
GSS
0.01523
0.01885
0.00031
-0.05231
0.01946
0.97603
OMS
-0.03559
-0.02242
0.03091
-0.07707
0.03965
0.05044
M
0.02757
0.03741
0.03224
-0.01900
-0.01107
0.12505
PQ
-0.01954
-0.00444
0.01591
0.08190
0.02059
-0.08759
L
0.00709
-0.02679
0.05532
0.98880
0.02057
-0.05035
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
BP
0.02113
-0.10936
-0.03162
0.02050
0.98915
0.01871
S
0.99514
-0.00501
0.05916
0.00695
0.02076
0.01446
BO
-0.00505
0.99110
0.04331
-0.02656
-0.10871
0.01810
TP
-0.01382
-0.00867
0.03796
-0.00765
0.04522
-0.05255
B
0.05972
0.04336
0.99208
0.05475
-0.03138
0.00032
SP
0.00209
-0.02757
-0.01314
0.01116
0.00340
0.02406
are as follows: 0.0 for D, A,
'lotes:
and OPC;
1.0 for the rest of the variables.

135
TABLE 9.17: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 3
COMPENSATION VARIABLE
VALUES OF THE VARIABLE
1
2
3
4
5
BASIC PAY
11.1
15.9
14.3
17.5
41.3
SHARE
92.1
6.3
0.0
1.6
0.0
BONUS
30.2
33.3
25.4
7.9
3.2
TERMINAL PAY
85.7
6.3
3.2
1.6
3.2
BENEFITS
76.2
12.7
3.2
3.2
4.8
STOCK
66.7
14.3
6.3
9.5
3.2
TABLE 9.18: Range, Mean and Standard Deviation of Values of Compensation
Variables in the Final Knowledge Base in Experiment 3
Variable
Minimum
Maximum
Mean
S.D.
BP
1.00
5.00
3.6190476
1.4416452
S
1.00
4.00
1.1111111
0.4439962
BO
1.00
5.00
2.2063492
1.0649660
TP
1.00
5.00
1.3015873
0.8731648
B
1.00
5.00
1.4761905
1.0450674
SP
1.00
5.00
1.6825397
1.1475837
TABLE 9.19: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 3
BP
S
BO
TP
B
SP
BP
1.00000
-0.21239
0.04193
0.09919
-0.06653
0.16112
0.0
0.0947
0.7442
0.4392
0.6044
0.2071
S
-0.21239
1.00000
0.13992
0.06965
0.25522
-0.06207
0.0947
0.0
0.2741
0.5875
0.0435
0.6289
BO
0.04193
0.13992
1.00000
-0.02696
0.30417
0.02454
0.7442
0.2741
0.0
0.8339
0.0154
0.8486
TP
0.09919
0.06965
-0.02696
1.00000
-0.05317
-0.09539
0.4392
0.5875
0.8339
0.0
0.6790
0.4571
B
-0.06653
0.25522
0.30417
-0.05317
0.27619
0.6044
0.0435
0.0154
0.6790
0.0
0.0284
SP
0.16112
-0.06207
0.02454
-0.09539
0.27619
1.00000
0.2071
0.6289
0.8486
0.4571
0.0284
0.0

136
TABLE 9.20: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 3 Eigenvalues of the Correlation Matrix
Factor
1
2
3
4
5
6
Eigenvalue
2.051970
1.485699
1.393947
1.302750
1.019307
0.766105
Difference
0.566272
0.091752
0.091196
0.283444
0.253202
0.134694
Proportion
0.2052
0.1486
0.1394
0.1303
0.1019
0.0766
Cumulative
TT252
0.3538
0.4932
0.6234
0.7254
0.8020
Factor
7
8
9
10
11
12
Eigenvalue
0.631411
0.529438
0.495105
0.324267
0.0000
0.0000
Difference
0.101973
0.034334
0.170837
0.324267
0.0000
0.0000
Proportion
0.0631
0.0529
0.0495
0.0324
0.0000
0.0000
Cumulative
0.8651
0.9181
0.9676
1.0000
1.0000
1.0000
Factor
13
14
15
16
Eigenvalue
0.0000
0.0000
0.0000
0.0000
Difference
0.0000
0.0000
0.0000
Proportion
0.0000
0.0000
0.0000
0.0000
Cumulative
1.0000
1.0000
1.0000
1.0000

137
TABLE 9.21: Factor Analysis (Principal Components Method) of the Final
FACTOR
1
2
3
4
5
X
-0.59074
-0.06170
-0.06894
0.46822
-0.20218
D
0.00000
0.00000
0.00000
0.00000
0.00000
A
-0.00000
0.00000
0.00000
-0.00000
-0.00000
RISK
0.10996
0.76295
0.33072
-0.11407
-0.01594
GSS
0.85184
0.10329
0.21497
-0.12037
-0.04482
OMS
0.80467
0.01491
0.07961
0.16731
-0.18963
M
-0.00000
0.00000
-0.00000
0.00000
0.00000
PQ
-0.00000
0.00000
-0.00000
0.00000
0.00000
L
-0.00000
0.00000
-0.00000
0.00000
0.00000
OPC
-0.00000
0.00000
-0.00000
0.00000
0.00000
BP
-0.39157
0.65888
0.22137
0.06324
0.23306
S
0.17892
-0.38179
0.38789
0.52832
0.35570
BO
0.13728
0.13920
-0.35713
-0.07526
0.82400
TP
-0.12358
-0.02483
0.78267
0.33425
0.10374
B
0.29624
0.09962
-0.43582
0.64893
0.08771
SP
0.10276
0.52831
-0.31264
0.45432
-0.24887
FACTOR
6
7
8
9
10
X
0.50944
0.05741
-0.05787
0.29569
0.16957
D
0.00000
0.00000
0.00000
0.00000
0.00000
A
-0.00000
0.00000
-0.00000
0.00000
-0.00000
RISK
0.19694
-0.09151
-0.48027
-0.04820
-0.05509
GSS
0.03364
-0.02060
0.09967
0.10779
0.42176
OMS
0.29181
0.03604
0.17912
0.22710
-0.33448
M
-0.00000
0.00000
-0.00000
-0.00000
0.00000
PQ
-0.00000
0.00000
0.00000
-0.00000
0.00000
L
-0.00000
0.00000
-0.00000
-0.00000
0.00000
OPC
-0.00000
0.00000
0.00000
0.00000
0.00000
BP
-0.19754
-0.26443
0.35986
0.25771
-0.01930
S
-0.35026
-0.00881
-0.28183
0.25181
-0.02289
BO
0.27700
0.26878
0.01950
0.01442
0.00576
TP
0.18578
0.19317
0.20941
-0.36516
0.00462
B
0.06503
-0.44763
0.00951
-0.27895
0.03276
SP
-0.32300
0.48794
0.01272
-0.03113
0.02641
M, PQ, L, and OPC; 1.0 for the rest of the variables.

138
TABLE 9.22: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 3 Varimax Rotated Factor Pattern
Factor
1 2 3
4
5
X
0.96928
-0.08142
-0.03918
0.03545
0.04428
D
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
-0.04055
0.04253
0.97181
0.16514
-0.02720
GSS
-0.25455
0.32873
0.10890
-0.08646
0.03277
OMS
-0.08603
0.93594
0.04323
-0.13317
0.11829
M
0.00000
0.00000
0.00000
0.00000
0.00000
PQ
0.00000
0.00000
0.00000
0.00000
0.00000
L
0.00000
0.00000
0.00000
0.00000
0.00000
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
BP
0.03686
-0.12283
0.16709
0.96833
-0.01802
S
-0.01604
0.03958
-0.08037
-0.03568
0.06811
BO
-0.05005
0.00008
0.00895
0.01872
0.06265
TP
0.07511
0.01390
0.06546
0.07241
-0.06475
B
0.04250
0.10437
-0.02704
-0.01793
0.97700
SP
0.02553
0.04427
0.07087
0.06923
0.13070
Factor
6
7
8
9
10
X
-0.01562
0.02692
-0.05402
0.07670
-0.19835
D
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
RISK
-0.08227
0.07314
0.00945
0.06551
0.08735
GSS
0.04743
0.00360
0.01355
0.00660
0.89680
OMS
0.04351
0.05169
-0.00050
0.01576
0.27965
M
0.00000
0.00000
0.00000
0.00000
0.00000
PQ
0.00000
0.00000
0.00000
0.00000
0.00000
L
0.00000
0.00000
0.00000
0.00000
0.00000
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
BP
-0.03644
0.07236
0.02019
0.07353
-0.07257
S
0.98027
-0.02612
-0.00494
0.15086
0.03751
BO
-0.00482
-0.00515
0.99439
-0.06454
0.01048
TP
0.15371
-0.04981
-0.06857
0.97448
0.00496
B
0.06843
0.13345
0.06613
-0.06398
0.02754
SP
-0.02605
0.98358
-0.00542
-0.04843
0.00392
Notes: Final Communality Estimates total 10.0 and are as follows: 0.0 for D, A,
M, PQ, L, and OPC; 1.0 for the rest of the variables.

139
TABLE 9.23: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 4
COMPENSATION
VARIABLE
VALUES OF THE VARIABLE
1
2
3
4
5
BASIC PAY
8.0
10.8
6.8
20.3
54.1
SHARE
100.0
0.0
0.0
0.0
0.0
BONUS
W7
24.3
4.1
8.1
1.4
TERMINAL PAY
82.4
5.4
5.4
4.1
2.7
BENEFITS
78.4
12.2
6.8
1.4
1.4
STOCK
82.4
14.9
1.4
0.0
1.4
TABLE 9.24: Range, Mean and Standard Deviation of Values of Compensation
Variables in the Final Knowledge Base in Experiment 4
Variable
Minimum
Maximum
Mean
S.D.
BP
1.0000
5.0000
4.0135135
1.3395281
S
1.0000
1.0000
1.0000000
0~
BO
1.0000
5.0000
1.6216216
0.9890178
TP
1.0000
5.0000
1.3918919
0.9625532
B
1.0000
5.0000
1.3513514
0.7839561
SP
1.0000
5.0000
1.2297297
0.6092281
TABLE 9.25: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 4
(Spearman Correlation Coefficients in the first row for each variable,
Prob> ¡R¡ under Ho: Rho=0 in the second)
BP
S
BO
TP
B
SP
BP
1.00000

-0.07927
-0.12735
0.17890
0.09947
0.00000
0.5020
0.2796
0.1272
0.3991
S
.
1.00000
.
.
.

0.00000
BO
-0.07927
.
1.00000
0.04158
-0.05059
-0.05058
0.5020
0.00000
0.7250
0.6686
0.6687
TP
-0.12735
.
0.04158
1.00000
-0.15591
-0.03370
0.2796
0.7250
0.00000
0.1847
0.7756
B
0.17890
.
-0.05059
-0.15591
1.00000
-0.07384
0.1272
0.6686
0.1847
0.00000
0.5318
SP
0.09947
.
-0.05058
-0.03370
-0.07384
1.00000
0.3991
0.6687
0.7756
0.5318
0.0

140
TABLE 9.26: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 4 Eigenvalues of the Correlation Matrix
Total = 15 Average = 0.9375
Factor
1
2
3
4
5
6
Eigenvalue
2.266645
1.820044
1.740554
1.392479
1.222659
1.127880
Difference
0.446601
0.079490
0.348075
0.169820
0.094779
0.081301
Proportion
0.1511
0.1213
0.1160
0.0928
0.0815
0.0752
Cumulative
0.1511
0.2724
0.3885
0.4813
0.5628
0.6380
Factor
7
8
9
10
11
12
Eigenvalue
1.046579
0.911929
0.720692
0.673039
0.590800
0.540745
Difference
0.134650
0.191237
0.047653
0.082239
0.050055
0.139484
Proportion
0.0698
0.0608
0.0480
0.0449
0.0394
0.0360
Cumulative
0.7078
0.7686
0.8166
0.8615
0.9009
0.9369
Factor
13
14
15
16
Eigenvalue
0.401261
0.330169
0.214527
0.000000
Difference
0.071092
0.115642
0.214527
Proportion
0.0268
0.0220
0.0143
0.0000
Cumulative
0.9637
0.9857
1.0000
1.0000

141
TABLE 9.27: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 4 Factor Pattern
Factor
1
2
3
4
5
X
0.39987
0.52286
-0.38231
0.31635
0.00739
D
0.65507
0.02692
0.14216
-0.45863
0.14832
A
-0.69786
-0.01735
-0.21577
-0.09847
-0.45496
RISK
-0.56345
0.48709
0.00618
0.07723
0.29746
GSS
0.12282
0.34586
0.57027
0.25255
-0.09610
OMS
-0.18220
-0.28764
0.47685
0.37232
-0.13876
M
-0.10416
0.01902
0.71620
0.06443
0.17785
PQ
0.05916
0.70795
-0.11360
0.13412
0.32138
L
-0.26565
0.09598
0.42751
-0.65510
0.17288
OPC
0.16943
0.49388
-0.14315
-0.39151
-0.43841
BP
0.66360
-0.28499
0.05754
0.13749
-0.12937
S
-0.00000
0.00000
-0.00000
0.00000
-0.00000
BO
-0.09702
-0.33988
-0.32518
-0.18613
0.66939
TP
-0.19261
-0.15261
-0.17228
0.42969
0.19808
B
0.47077
-0.02466
0.13058
0.11620
0.10372
SP
-0.05247
0.36153
0.30017
0.08792
0.06952
Factor
6
7
8
9
10
X
0.11952
-0.10795
0.17609
-0.14149
-0.19329
D
-0.15335
-0.24955
0.24565
0.01985
0.09769
A
-0.06005
0.00624
-0.11661
0.29239
0.18458
RISK
0.39016
-0.07852
-0.10355
-0.06561
-0.11007
GSS
0.13077
0.31075
0.14084
-0.09173
0.39591
OMS
0.30435
-0.27467
0.39357
-0.17861
0.10779
M
-0.27035
0.15311
-0.03593
0.09622
-0.51882
PQ
-0.25059
0.18421
-0.20210
-0.05302
0.22436
L
-0.03394
0.21155
0.01226
-0.07221
0.14553
OPC
0.03602
0.11633
0.44300
0.11891
-0.14114
BP
-0.15691
0.01890
-0.35834
-0.07636
0.12265
S
0.00000
-0.00000
0.00000
0.00000
-0.00000
BO
0.19577
-0.06597
0.22588
0.05967
0.12389
TP
-0.53566
0.27996
0.43910
0.23157
0.07421
B
0.52889
0.24791
-0.08326
0.59940
-0.00482
SP
-0.23789
-0.73091
-0.06188
0.34125
0.12271
Factor
11
12
13
14
15
X
0.32008
0.12801
-0.22099
-0.11673
0.15746
D
-0.12094
-0.17286
-0.12805
0.27294
0.16169
A
0.19543
-0.01042
0.01472
0.10009
0.25320

142
TABLE 9.27 continued
Factor
11
12
13
14
15
RISK
-0.03696
0.15517
-0.05328
0.36381
-0.06798
GSS
0.31576
-0.24533
0.01240
0.05951
-0.06948
OMS
-0.22520
0.21461
0.10693
-0.04652
0.14814
M
0.15822
-0.05462
0.14185
0.02518
0.12264
PQ
-0.29957
0.03046
0.21993
-0.09147
0.15164
L
0.06466
0.35400
-0.22578
-0.15875
0.01682
OPC
-0.00639
0.15802
0.28350
0.03033
-0.09980
BP
0.18946
0.41750
0.14451
0.18472
-0.00217
S
0.00000
-0.00000
0.00000
-0.00000
0.00000
BO
0.31328
-0.00269
0.27097
-0.03495
0.03473
TP
-0.05316
0.16795
-0.14856
0.10896
-0.06195
B
-0.12859
0.06230
-0.07108
-0.04760
0.03615
SP
0.10652
0.05874
0.01048
-0.09678
-0.11597
for the rest of the variables.

143
TABLE 9.28: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 4 Varimax Rotated Factor Pattern
FACTOR
1
2
3
4
5
X
0.03602
0.04669
0.14883
0.05089
0.00711
D
0.05774
0.09209
0.12082
0.09927
-0.08622
A
-0.10231
-0.24787
-0.14726
0.08419
0.91011
RISK
0.14759
-0.17610
0.06520
0.92643
0.07767
GSS
0.08372
0.00725
0.04552
0.01376
-0.03982
OMS
-0.16731
-0.06523
-0.08774
0.03698
-0.04746
M
-0.02422
-0.01799
-0.10685
0.02106
-0.08576
PQ
0.95101
-0.00952
0.10464
0.13279
-0.08740
L
0.00879
0.05939
-0.16568
0.07772
0.02935
OPC
0.04738
0.10469
0.13445
-0.01761
0.05144
BP
-0.03349
0.08663
0.04612
-0.21501
-0.13151
S
0.00000
0.00000
0.00000
0.00000
0.00000
BO
-0.06461
0.03125
-0.02082
0.04200
-0.04468
TP
0.05751
-0.07338
0.00566
-0.05950
0.03865
B
-0.01518
0.05088
0.03210
-0.02021
-0.11377
SP
0.07991
0.08161
0.04361
0.06382
0.03603
Notes: Final Communality Estimates total 15.0 and are as follows: 0.0 for S; 1.0
for the rest of the variables.

144
TABLE 9.29: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 5
COMPENSATION
VARIABLE
VALUES OF THE VARIABLE
1
2
3
4
5
BASIC PAY
5.9
15.6
18.0
9.7
50.7
SHARE
96.5
1.5
0.9
0.8
0.4
BONUS
43.1
oo
d
27.0
11.9
7.1
TERMINAL PAY
89.8
1.9
OO
cn
2.4
2.0
BENEFITS
70.7
18.1
3.6
3.0
4.6
STOCK
80.6
9.9
4.7
2.5
2.3
TABLE 9.30: Range, Mean and Standard Deviation of Values of Compensation
Variables in the Final Knowledge Base in Experiment 5
Variable
Minimum
Maximum
Mean
S.D.
BP
1.0000
5.0000
3.8376590
1.3484571
S
L000
5.0000
1.0692112
0.4127470
BO
1.0000
5.0000
2.2910941
1.3171851
TP
1.0000
5.0000
1.2498728
0.8092869
B
1.0000
5.0000
1.5251908
1.0241491
SP
1.0000
5.0000
1.3603053
0.8659971
TABLE 9.31: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 5
(Spearman Correlation Coefficients in the first row for each variable,
Prob> ¡R¡ under Ho: Rho=0 in the second)
BP
S
BO
TP
B
SP
BP
1.00000
-0.05978
0.15907
-0.05684
-0.00131
0.03886
0.00000
0.0080
0.0001
0.0117
0.9538
0.0850
S
-0.05978
1.00000
-0.00454
0.01208
0.05571
-0.02912
0.0080
0.00000
0.8408
0.5925
0.0135
0.1970
BO
0.15907
-0.00454
1.00000
0.02932
-0.02295
0.05081
0.0001
0.8408
0.00000
0.1930
0.3093
0.0243
TP
-0.05684
0.01208
0.02932
1.00000
-0.00354
0.00990
0.0117
0.5925
0.1939
0.00000
0.8755
0.6611
B
-0.00131
0.05571
-0.02295
-0.00354
1.00000
0.06052
0.9538
0.0135
0.3093
0.8755
0.00000
0.0073
SP
0.03886
-0.02912
0.05081
0.00990
0.06052
1.00000
0.0850
0.1970
0.0243
0.6611
0.0073
0.00000

145
TABLE 9.32: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 5 Eigenvalues of the Correlation Matrix
Total = 6 Average = 0.375
Factor
1
2
3
4
5
6
Eigenvalue
1.175433
1.073561
1.020839
0.975691
0.924350
0.830127
Difference
0.101872
0.052722
0.045148
0.051341
0.094223
0.830127
Proportion
0.1959
0.1789
0.1701
0.1626
0.1541
0.1384
Cumulative
0.1959
0.3748
0.5450
0.7076
0.8616
1.0000
TABLE 9.33: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 5 Factor Pattern
FACTOR
1
2
3
4
5
6
X
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
GSS
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
OMS
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
M
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
PQ
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
L
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
BP
0.73332
0.17248
0.01164
-0.17230
0.08274
0.62915
S
-0.34869
0.55123
0.04419
-0.37155
0.65919
0.00508
BO
0.56837
0.47214
-0.34889
-0.05745
-0.10818
-0.56330
TP
-0.26373
0.32667
-0.63371
0.58018
0.00086
0.29247
B
-0.27872
0.59673
0.33776
-0.14045
-0.64230
0.14099
SP
0.21404
0.23289
0.61754
0.66957
0.24233
-0.10746
Notes: Final Communality Estimates total 6.0 and are as fol
BO, TP, B, and SP; 0.0 for the rest of the variables.
ows: 1.0 for BP, S,

146
TABLE 9.34: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 5 Varimax Rotated Factor Pattern
FACTOR
1
2
3
4
5
6
X
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
RISK
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
GSS
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
OMS
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
M
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
PQ
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
L
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
OPC
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
BP
0.07084
-0.03061
0.02061
-0.01879
-0.01860
0.99645
S
-0.0025
7
0.01489
-0.00424
0.03512
0.99909
-0.01845
BO
0.99737
0.01480
0.00534
0.00245
-0.00259
0.07065
TP
0.01471
0.99928
-0.00697
0.00628
0.01488
-0.03035
B
0.00243
0.00629
0.01183
0.99912
0.03512
-0.01864
SP
0.00531
-0.00697
0.99967
0.01181
-0.00423
0.02042
Notes: Final Communality Estimates total 6.0 and are as follows: 1.0 for BP, S,
BO, TP, B, and SP; 0.0 for the rest of the variables.
TABLE 9.35: Summary of Factor Analytic Results for the Five Experiments
Experiment
Number of Significant
Factors (Eigenvalue >
1)
Percentage of
Total Variation
Total Factors
Average
Eigenvalue
1
6
65.35
11
0.6875
2
6
57.47
13
0.8125
3
5
72.54
10
0.6250
4
7
70.78
15
0.9375
5
3
54.50
6
0.3750

147
TABLE 9.36: Expected Factor Identification of Compensation Variables for the Five
Experiments Derived from the Direct Factor Analytic Solution
COMPENSATION
VARIABLE
EXPECTED FACTOR IDENTIFICATION
EXP 1
EXP 2
EXP 3
EXP 4
EXP 5
BASIC PAY
0.2675
0.1652
0.3053
0.2394
0.3043
SHARE
0.2350
0.2267
0.3081
0.0000
0.3371
BONUS
0.2767
0.2190
0.2325
0.2279
0.3591
TERMINAL PAY
0.2587
0.2467
0.2480
0.2400
0.3529
BENEFITS
0.2619
0.2506
0.2784
0.2104
0.3601
STOCK
0.2757
0.2385
0.2863
0.2054
0.3497
TABLE 9.37: Expected Factor Identification of Compensation Variables for the Five
Experiments Derived from the Varimax Rotated Factor Analytic Solution
COMPENSATION
VARIABLE
EXPECTED FACTOR IDENTIFICATION
EXP 1
EXP 2
EXP3
EXP 4
EXP 5
BASIC PAY
0.1212
0.0795
0.1915
0.1677
0.1667
SHARE
0.1206
0.0915
0.1177
0.0000
0.1661
BONUS
0.1017
0.0881
0.0772
0.0997
0.2095
TERMINAL PAY
0.1122
0.1032
0.1096
0.1234
0.1904
BENEFITS
0.1426
0.0907
0.1511
0.1835
0.1741
STOCK
0.1531
0.0959
0.1109
0.1272
0.1777

148
TABLE 9.38: Expected Factor Identification of Behavioral and Risk Variables for the
Five Experiments Derived from the Direct Factor Pattern
VARIABLE
EXPECTED FACTOR IDENTIFICATION
Exp 1
Exp 2
Exp 3
Exp 4
Exp 5
Risk
0.2594
0.2238
0.2490
0.2430
0.0000
Experience
0.2808
0.2518
0.2875
0.2688
0.0000
Education
0.0000
0.0000
0.0000
0.2454
0.0000
Age
0.0000
0.0000
0.0000
0.2275
0.0000
General Social Skills
0.2670
0.2117
0.2685
0.2441
0.0000
Managerial Skills
0.0000
0.2244
0.2757
0.2656
0.0000
Motivation
0.2622
0.2160
0.0000
0.1970
0.0000
Physical Qualities
0.2509
0.2667
0.0000
0.2262
0.0000
Communication
Ability
0.0000
0.2489
0.0000
0.2294
0.0000
Other Qualities
0.0000
0.0000
0.0000
0.2396
0.0000
TABLE 9.39: Expected Factor Identification of Behavioral and Risk Variables for the
Five Experiments Derived from Varimax Rotated Factor Analytic Solution
VARIABLE
EXPECTED FACTOR IDENTIFICATION
Exp 1
Exp 2
Exp 3
Exp 4
Exp 5
Risk
0.1226
0.1153
0.1919
0.0472
0.0000
Experience
0.1015
0.1300
0.2416
0.0337
0.0000
Education
0.0000
0.0000
0.0000
0.0502
0.0000
Age
0.0000
0.0000
0.0000
0.0549
0.0000
General Social Skills
0.1251
0.1016
0.1648
0.0204
0.0000
Managerial Skills
0.0000
0.1030
0.2086
0.0507
0.0000
Motivation
0.1014
0.1453
0.0000
0.0272
0.0000
Physical Qualities
0.0895
0.1260
0.0000
0.1764
0.0000
Communication
Ability
0.0000
0.0900
0.0000
0.0374
0.0000
Other Qualities
0.0000
0.0000
0.0000
0.0413
0.0000

CHAPTER 10
REALISTIC AGENCY MODELS
In this chapter we describe Models 4 through 7. These models incorporate
realism to a greater extent than previous models. The simulation design of these four
models is the same. Each model has 200 simulations conducted with a common set of
simulation parameters. The two control variables for the simulations are the number of
learning periods and the number of contract renegotiation periods. The learning periods
run from 5 to 200, while the contract renegotiation periods run from 5 to 25.
In each learning period, there are a number of contract renegotiation periods.
The principal utilizes these periods to collect data about the performance of the agents
and the usefulness of her knowledge. In each contract renegotiation period, all the agents
are offered new compensation by the principal, which they are at liberty to accept or
reject. At the end of a prespecified number of contract renegotiation periods (this
number being a control variable), the principal uses the data to initiate the learning
process. The learning paradigms are two: the genetic algorithm used in the previous
studies, and the specialization-generalization learning operator (described in Sec. 10.2
below). This learning process actually uses the data collected in the contract
renegotiation periods to change the principals knowledge base and bring it in line with
149

150
changing conditions (such as the number, characteristics and risk aversion of the agents,
and also the nature of exogenous risk).
The timing of the agency problem is as follows:
1. The principal offers a compensation scheme to an agent chosen at random. The
principal selects this scheme from out of a large number of possible ones based
on her current knowledge base and on her estimate of the agents characteristics.
2. The agent either accepts or rejects the contract according to his reservation
welfare. If the agent rejects the contract, nothing further is done. If all the
agents reject the contracts they are offered, the principal seeks a fixed number
(here, 5) of new agents. This process continues until an agent accepts a contract.
3. If an agent accepts the contract, he selects an effort level based on his
characteristics, the contract, and his private information.
4. Nature acts to render an exogenous environment level.
5. Output occurs as a function of the agents effort level and the exogenous risk.
6. Sharing of the output between the agent and the principal occurs.
7. The principal reviews the agents performance and using certain criteria either
fires him or continues to deal with him in subsequent periods.
The following are the main features common to these models:
1. The agency is multi-period a number of periods are simulated.
2. The models are all multi-agent models.
3. The agency is dynamic agents are hired and fired all the time.

151
4.Agents not only have the option of leaving during contract negotiation time, but
they may also be fired by the principal for poor performance. The performance
of the agents is evaluated only at the end of the first contract renegotiation period
after every learning episode.
Furthermore, all the models follow the basic LEN model of Spremann. The
features of the LEN model are:
1. The principal is risk neutral. So, her utility function is linear (L).
2. The agents are all risk averse. In particular, their utility functions are exponential
(E).
3. The exogenous risk is distributed normally around a mean of zero (N).
4. The agents effort is in [0,0.5].
5. The agents disutility of effort is the square root of effort.
6. The output is the sum of the agents effort and the exogenous risk.
7. The agents payoff is the compensation less the disutility of effort.
8. The principals payoff is the output less the compensation.
9. The total output of the agency is separable and is the sum of the outputs derived
from the actions of the individual agents.
10. Each agents output is determined by a random value of the exogenous risk,
which may or may not be the same as those faced by the other agents.
Features 1 to 8 are explicit in the original LEN model, while features 9 and 10 are
implicit.
The informational characteristics of the models are the same, and are as follows:

152
1. The agent knows his own characteristics and has access to his private information,
both of which affect effort selection. This information is personal to the agent
and not shared with the other agents or with the principal.
2. The principal possesses a personal knowledge base which consists of if-then rules.
These rules help the principal select compensation schemes based on her estimate
of the agents characteristics. The principal also has available to her an estimate
of the agents characteristics. Some of these estimates are exact (eg. age), while
others are close (such estimates are based on some deviation around the true
characteristics).
3. The principal can only observe the exogenous risk parameter ex-post. The
principal evaluates the performance of each agent in the light of the observed ex
post risk and may decide to fire or retain him.
4. All the agents share a common probability distribution from which their
reservation welfare is derived. This distribution (called the rw-pdf) is for a
random variable which is a sum of the values of the elements of compensation.
In Models 4 and 5, this sum ranges from 2 to 10 (since they have two elements
of compensation, and each element has 5 possible values from 1 to 5). The rw-
pdf has a peak value at 4 with probability mass 0.6. In Models 6 and 7, this sum
ranges from 6 to 30 (since they have six elements of compensation), and the rw-
pdf has a probability mass of 0.6 at its peak value of 12. For all the models, the
rw-pdf is monotonically increasing for values below the peak value, and is
monotonically decreasing for values after the peak value.

153
The experimental design is 2 X 2. The first design variable is the number of
elements of compensation, and it takes two values 2 and 6. The second design variable
is the policy of evaluation of the agents by the principal. This policy plays a role in
firing an agent for lack of adequate performance. One policy evaluates the performance
of an agent relative to the other agents. By the use of this policy, an agent is not
penalized if his performance is inadequate while the performance of the rest of the agents
is also inadequate. In this sense, it is a non-discriminatory policy. The other policy
evaluates the performance of an agent without taking into consideration the performance
of the other agents. By the use of this policy, an agent is fired if his performance is
inadequate with respect to an absolute standard set by the principal, without regard to
how the other agents have performed. In this sense, it is a discriminatory policy.
By a discriminatory policy is meant an individualized performance appraisal and
firing policy, while a non-discriminatory policy means a relative performance appraisal
and firing policy. The words "discriminatory" and "non-discriminatory" will be used in
the following discussion only in the sense defined above.
Models 4 and 5 follow the basic LEN model which has only two elements of
compensation (basic pay and share of output). In Model 4, the principal evaluates the
performance of each agent relative to the performance of the other agents, and hence
follows a non-discriminatory firing policy. In Model 5 the principal keeps track of the
output she receives from each agent and evaluates each agent on an absolute standard.
Hence, she follows a discriminatory policy. Models 6 and 7 follow the basic LEN
model, but incorporate four additional elements of compensation (bonus payments,

154
terminal pay, benefits, and stock participation), as in the previous studies. In Model 6,
the principal follows a non-discriminatory evaluation and firing policy, while in Model
7, she follows a discriminatory policy.
The two basic control variables for the simulation are the number of learning
periods and the number of contract renegotiation (or data gathering) periods. A number
of statistics are collected in these studies, and they are grouped by their ability to address
some fundamental questions:
1. The first group of statistics pertains to the simulation methodology. They
report the state of the principals knowledge base. These statistics cover the
average and maximum fitness of the rules, their variance around the mean,
and the entropy of the normalized fitnesses.
2. The second group of statistics describes the type of compensation schemes
offered to the agents by the principal throughout the life of the agency.
They report the mean and variance of each element of compensation.
3. The third group of statistics describes the composition of compensation
schemes in the final knowledge base of the principal (i.e., at the termination
of the simulation). They report the mean and variance of each element of
compensation. These statistics differ from those in group two in that they
characterize the state of the principals knowledge base, while those in the
second group also capture the compensations activated as a result of the
characteristics of the agents who participate in the agency.

155
4. The fourth group of statistics deals with the movement of agents. They
describe the mean and variance of the agents who resigned from the agency
on their own (because of the failure of the principal to meet their reservation
welfares), those who were fired by the principal (because of their inadequate
performance), and those who remained active in the agency when the
simulation terminated.
5. The fifth group of statistics deals with agent factors, which measure the
change in satisfaction of the agents as they participate in the agency. They
help answer the question, "Is the agent better off by participating in this
particular model of agency?". These statistics cover the three types of agents
- those who resigned, those who were fired, and the remaining agents who
are employed (called the "normal" agents).
6. The sixth group of statistics deals with the mean and variance of the
satisfaction of the agents, again distinguishing between resigned, fired and
normal agents. An agents satisfaction is calculated from the utility of net
income of the agent. However, the term "satisfaction" is used instead of
"utility" since the former may take into consideration some intrinsic
satisfaction levels which are measured subjectively; see, for example,
Chapter 7 on Motivation Theory.
7. The seventh group of statistics reports the mean and variance of the
satisfaction level of the agents at termination. For the agents who have
resigned, this is the satisfaction derived from an agency period just prior to

156
resignation. For the agents who have been fired, this is the satisfaction they
derived in the agency period they were fired. For normal agents, this is the
satisfaction they obtained at the termination of the simulation.
8. The eighth group of statistics covers the mean and variance of the number
of agency interactions, reporting separately for resigned, fired and normal
agents.
9. The ninth group of statistics details the mean and variance of the number of
rules that were activated for each of the three types of agents in the
principals knowledge base.
10. The tenth group of statistics describes the mean and variance of the number
of rules that were activated during the final iteration of the simulation.
11. The eleventh group of statistics deals with the principal, and report on the
mean and variance of the principals satisfaction, the principals factor
(which helps answer the question, "Is the principal better off in this agency
model?"), and the satisfaction derived by the principal at termination.
12. The twelfth group of statistics details the mean and variance of payoff
received by the principal from each of the three kinds of agents. This group
of statistics are relevant only in Models 5 and 7, since this information is
used by the principal to engage in discriminatory evaluation of the agents
performance.
13. The final group of statistics computes the fit of the principals knowledge
base with the dynamic agency environment. This fit is characterized by a

157
least squares computation between the antecedents of the principals
knowledge base and the agents true characteristics, and also between the
antecedents and the principals estimate of the agents true characteristics.
Whenever some statistic distinguishes between the three types of agents, a statistic
that includes all the agents is also computed. These statistics enable one to study the
behavior and performance of the agency along several parameters. These statistics are
used to study the appropriate correlations.
10.1 Characteristics of Agents
For the purpose of the simulation, the characteristics of the agents are generated
randomly from probability distributions. These distributions capture the composition of
the agent pool. Other distributions may be used in another agency context. For these
studies, some of the characteristics are generated independently of others, while some are
generated from conditional distributions. Education, experience and general social skills
are conditional on the age of the agent, while office and managerial skills are conditional
on the education of the agent. Each agent is an "object" consisting of the following:
1. Nine behavioral characteristics.
2. Three elements of private information.
3. Index of risk aversion, generated randomly from the uniform (0,1)
distribution.
4. A vector which plays a role in effort selection by the agent.

158
The probability distributions are detailed in Table 10.68. The index of risk
aversion is unique to the agent and is drawn from the uniform (0,1) distribution. When
the principal offers a compensation scheme, the agent draws a reservation welfare from
the associated distribution, and compares the utility of the reservation compensation with
the utility of the compensation offered by the principal (in these models, the agent does
not take into account the expected utility from future contracts). The agent rejects the
contract if the latter utility does not exceed the former.
10.2 Learning with Specialization and Generalization.
The structure of the antecedents of the principals knowledge base have been
modified. In the previous models, each antecedent was a single number between 1 and
5 inclusive. However, it is felt that more realism is captured (and the application of
other learning operators is made possible) if each antecedent is expressed as an interval
bounded inclusively by 1 and 5. This would enable the principals knowledge base to
be as precise or as general as necessary. For example, if the agents who participated in
the agency in some learning period had a wide diversity of characteristics, then the
knowledge base would be appropriately generalized so that the principal would be able
to offer contracts to as many of them as possible. Similarly, if the agents had
characteristics which were close to the others, then the principals knowledge base could
be specialized or made more precise in order to distinguish between the agents and tailor
compensation schemes appropriately.

159
This tuning and adjustment is made possible by noting the number of times each
antecedent was applicable in the process of searching for an appropriate compensation
scheme for each agent. If, during the learning episode, the count of any antecedent of
a rule exceeded some average of the counts in the knowledge base, that would imply that
that antecedent is too general and is applicable to too many agents. In such a case, the
antecedents length of interval is reduced in a systematic manner. Again, if an
antecedent in a rule had a very low count, that would imply that the antecedent of that
rule was not being used much. In such a case, the length of interval of that antecedent
would be expanded.
The process of reducing the length of an antecedents interval is called
specialization, and the process of increasing it is called generalization. A fixed step size
may be associated with each process. We choose the same step size of 0.25 for both the
processes. If 1¡ is the lower bound of an antecedent and u¡ is its upper bound, then (u¡ -
1) times the step size (0.25) is the size of the specialization and generalization step size
(S). For the above antecedent, the learning operators would act as follows:
Specialization: 1¡ <-1¡ + S; u¡ *- u¡ S.
Generalization: 1¡ *- 1¡ S; u¡ <*- u¡ + S.
The step size S is therefore proportional to the length of the interval. Updating of the
bounds of the antecedent takes place in each learning episode after the application of the
mating operator and before the application of the mutation operator of the genetic
algorithm.

160
10.3 Notation and Conventions
We use the following notation to describe the results for all the models:
The prefix E[] denotes the Mean (expected value), and the prefix SD[]
denotes the Standard Deviation;
BP: Basic Pay;
SH: Share;
BO: Bonus;
TP: Terminal Pay;
BE: Benefits;
SP: Stock Participation;
LP: Learning Periods;
CP: Contract Periods;
MAXFIT: Maximum Fitness of Rules;
AVEFIT: Average Fitness of Rules;
VARFIT: Variance of Fitness of Rules;
ENTROPY: Shannon Entropy of Normalized Fitnesses of Rules;
COMP: Total Compensation Package;
FIRED: Agents who were Fired;
QUIT: Agents who Resigned;
NORMAL: Agents who remained until the end;
ALL: All the agents;

161
Several correlations among the dependent variables, in addition to the thirteen
groups listed above, will be presented for each model. The correlations are indicated as
" + for positive correlations and as for negative correlations. All correlations are
at the 0.1 significance level. After all the models are summarized, they will be
compared and the implications will be discussed. Tables 10.1 through 10.16 cover
Model 4. Tables 10.17 through 10.34 cover Model 5, Tables 10.35 through 10.48 cover
Model 6, and Tables 10.49 through 10.66 cover Model 7. Table 10.67 compares the
four models. Sections 10.4 through 10.7 discuss the results for the four models.
10,4 Model 4: Discussion of Results
Model 4 has two elements of compensation, and the principal does not practice
discrimination in evaluating the agents. Increasing the number of learning periods tends
to result in a lower contract (by individual contract element and also by total contract)
offered to agents. Increasing the number of data collection periods during which no
evaluation of the agents occurs, results in a higher contract being offered to the agents.
In both cases, the variance of the total contract increases (Table 10.2). Interestingly
enough, in both cases, the contracts that make up the final knowledge base of the
principal show positive correlation (Table 10.3). Tables 10.2 and 10.3 together imply
that while the final knowledge base favors comparatively high contracts, the principal is
able to select only the low contracts. This affects the agents factors (which determine
if the agents are better off at termination in this agency model) adversely. In fact,
increasing the number of learning periods leaves all the agents worse off (Table 10.5).

162
However, this adverse affect is not carried through to the agents satisfactions. All the
agents seem more satisfied the longer the agency process. But the agents satisfactions
decreased on average by increasing the number of data collection periods (Table 10.6).
In other words, observability by the principal affects their satisfaction adversely. This
may be due to the fact that the principal has more data with which she can measure the
usefulness of her knowledge base (by measuring the relative importance of each of the
antecedent clauses in the rules), thus allowing her to tailor compensation schemes (which
form the consequent clauses in the rules of her knowledge base) to reward agents
accurately. Because of the fundamentally adversarial relationship between the agents and
the principal, this would decrease the mean satisfaction of the agents.
The mean agent factor for fired agents is positively correlated with the mean
satisfaction of the principal (Table 10.13). However, the agents satisfaction and the
principals satisfaction held inverse relationships, except in the case of normal agents
(Table 10.14). This is consistent with the fact that the agents who quit and those who
were fired obtained, on average, less satisfaction than the normal agents. However,
because of the extremely dynamic environment (a mean of 444 agents across all the
simulations), the overall mean satisfaction of the agents is negatively correlated with the
principals satisfaction (Table 10.67).
With increase in the length of the simulation, more agents quit and were fired.
However, the expected number of agents fired decreased. In all, a mean of 5 agents
were fired (Table 10.67).

163
10.5 Model 5: Discussion of Results
Model 5 has two elements of compensation, and the principal evaluates the
performance of agents in a discriminatory manner. The value of individual elements of
the contract as well as the value of the total contract offered to agents decreased with
increases in the number of learning periods. When the number of contract periods for
each learning period was increased, only the mean share offered to the agents increased,
but no significant results were available for the rest of the elements of contract. The
variance of the total contract increased both times (Table 10.18). The principals final
knowledge base is also consistent with this result (Table 10.19).
Increasing the number of learning periods left the agents worse off at termination,
while increasing the number of contract periods merely decreased the variance of the
agent factors (Table 10.21). However, the agents satisfaction showed positive
correlation with the number of learning periods, except for agents who were fired (Table
10.22). This positive correlation also extends to those agents who quit of their own
accord. This implies that while the satisfactions rose with more learning periods, they
did not rise high enough or in a timely way for some agents. Again, as in Model 4,
increasing observability (number of contract periods) by the principal correlated
negatively with agents satisfactions, while decreasing their variance.
In Model 5, payoff from individual agents is known, which enables the principal
to practice discrimination in firing agents. The mean payoff of agents who quit, of those
who stayed on (normal agents), and also of all the agents (considered as a whole),
showed positive correlation with the number of learning periods, while the number of

164
contract periods correlated negatively with all but normal agents. For agents who were
fired, there were no significant correlations. This implies that on the whole,
observability by the principal affects the agents payoffs adversely (Table 10.30).
The principals satisfaction also correlated negatively with the mean outcomes
from the agents (Table 10.33). Mean payoff from an agent may increase with an
increase in the number of learning periods while the outcome from that agent decreases
because the principal is offering smaller contracts.
The mean satisfaction of the two parties showed positive correlation only in the
case of agents who were fired and normal agents. There is an inverse relationship
between the mean satisfaction of the principal and the mean satisfaction of agents who
quit. This is also true in the case of all the agents (taken as a whole) (Table 10.31).
This implies that while the principals satisfaction was high, most of the contribution
came from agents who ultimately resigned from the agency, while those who were fired
used less effort and had commensurately higher contracts. This may suggest the reason
for why some agents quit and why some agents were fired. On the whole, this Model
is extremely dynamic since the total number of agents who quit (996) and the total
number of agents who were fired (16) is the highest for all the four models (Table
10.67).
10.6 Model 6: Discussion of Results
Model 6 has six elements of compensation, and the principal does not practice any
discrimination in evaluating the performance of the agents. As with the previous Models

165
4 and 5, compensation offered to agents correlated negatively with the number of
learning periods (Table 10.36). The value of compensation in the final knowledge base
of the principal also correlated negatively with both the number of learning periods and
the number of contract periods (Table 10.37).
The mean principals satisfaction correlated negatively with the mean satisfaction
of agents who quit and all the agents (considered as a whole). There were no
corresponding significant correlations between the principals satisfaction and the agents
factors (Table 10.47). The principals factor (which indicates if she is better off by
participating in this agency model) and factors of agents who were fired correlate
negatively. This of course explains why these agents were fired. The agency
environment is more stable than the previous two models. Only 234 agents quit, while
only 4 agents were fired (Table 10.67).
10.7 Model 7: Discussion of Results
Model 7 has six elements of compensation, and the principal practices
discrimination in her evaluation of the agents. As in the previous models, a higher
number of learning periods is associated with lower value of compensation packages
offered to the agents (Table 10.50). A higher number of contract periods correlates
negatively with mean basic pay, but positively with mean value of stock participation (no
significant correlations were observed at the 0.1 level for the other elements of
compensation) (Table 10.50). In the final knowledge base of the principal, the variances
of the elements of compensation showed negative correlation with the number of learning

166
periods, while the mean values for some of the elements of compensation (share of
output and stock participation) and the total contract correlated positively with the
number of contract periods (Table 10.51).
The principal has available to her (in this Model 7) the payoffs from each agent.
The mean payoff from agents who quit and all the agents taken as a whole showed
positive correlation with the number of learning periods, while there was negative
correlation for the mean payoff from fired agents. This implies that the principal
succeeded in learning to control effort selection by the agents in such a way as to
increase the payoff. This need not imply that the agents are better off, or that their mean
satisfaction is high (see discussion in the next paragraph). The number of contract
periods correlated negatively with the mean payoff from all types of agents except for
fired agents (who had no significant correlation) (Table 10.59). This may seem counter
intuitive, since having more data should lead to better control. However, collecting data
takes time. The longer it takes time, the longer the principal defers using the learning
mechanisms. This gives the agents time to get away with a smaller contribution to
payoff, while collecting commensurately larger contracts until the principal learns.
The mean agent factor for fired agents, and the mean satisfaction of agents who
quit and of normal agents, correlates negatively with the mean satisfaction of the
principal (Tables 10.62 and 10.63). The principal is also able to observe the outcomes
from each agent individually. The mean outcome from all the types of agents (except
those who were fired, for whom there are no significant correlations at the 0.1 level)

167
correlates negatively with the principals satisfaction (Table 10.65). Observability, in
this case also, is detrimental to the interests of the agents.
10.8 Comparison of the Models
Table 10.67 summarizes the key statistics of the four models. The contracts
offered to the agents by the principal are higher in value in Models 6 and 7 (than in
Models 4 and 5) where the number of elements are more (six, as compared to two in
Models 4 and 5). However, the value of the contract per element of compensation (i.e.
the normalized statistic) is the highest in Model 4 (two elements of compensation and
non-discriminatory evaluation), followed by Models 6 and 7 (Table 10.67). This
suggests that in the absence of complex contracts and individualized observability, the
principal can only offer higher contracts in an effort to second-guess the reservation
welfare of the agents and to retain the services of good agents. Again, since
observability is poor, the principal can only offer comparatively higher contracts to all
the agents. Increasing either the complexity of contracts or the observability enables the
principal to be more efficient. However, the principal must have an instrument capable
of being flexible in order to be efficient. This is not possible when the contracts are very
simple, even if the principal is able to observe each agent individually. Hence, in Model
5, the principal can only effectively punish poor performance. If she attempts to reward
good performance using only two elements of compensation (basic pay and share of
output), her own welfare is affected. Hence, the value of contracts in Model 5 is
uniformly lower than in the other models. This also leads us to expect that the

168
reservation welfare of many agents may not be met. Table 10.67 confirms this. The
number of agents who quit of their own accord is the highest of all models. Similarly,
the principal is unable to induce proper effort selection using only two elements of
compensation. However, this does not stop her from punishing (effectively and
individually) poor performers. This leads us to expect that the number of agents fired
in Model 5 would be highest of all the models. Table 10.67 again confirms this
expectation.
Agent factors indicate whether the agents were better off or worse off on the
whole in the particular agency model (with positive factors indicating better off and
negative factors indicating worse off). This is a measure of the difference in satisfaction
enjoyed by the agents normalized for number of learning periods and contract periods.
Agents were better off to a greater extent when the number of compensation elements
were two rather than six, and when the principal practiced non-discriminatory evaluation
of agents performance. This is because the principal has less scope for controlling
agents effort selection through complex contracts, and no individualized evaluation of
agents performances and hence no possibility of penalizing agents with poor
performance. Therefore, in all cases except Model 7, agents as a whole were better off.
Looking at specific types of agents, the agents who quit were better off in the
non-discriminatory cases (Models 4 and 6), and in the case of two elements of
compensation (Models 4 and 5). The same holds true for agents who were fired.
However, for normal agents, the greatest increase in satisfaction (compared across the
models) occurred in Model 5 (two elements of compensation with discriminatory

169
evaluation). This implies that the principal discriminated in favor of the normal agents,
while terminating the services of undesirable agents and forcing other agents to quit by
offering very low contracts. Normal agents suffered the most in Model 4 where the
number of elements of compensation are two, and the principal does not practice
discrimination. This means that the complexity of compensation plans is insufficient to
selectively reward good agents in Models 4 and 5, while a non-discriminatory evaluation
practice (as in Models 4 and 6) adds to the unfavorable atmosphere for the good agents.
It appears that increasing either the number of elements of compensation or practicing
a discriminatory evaluation is sufficient to selectively reward good agents (as in Models
5 and 6), but the dual approach does not help the normal agents (as in Model 7), even
though their factors are almost double when compared to Model 4.
Interestingly, the greatest increase in satisfaction is observed for the agents who
were fired for all the models. At the same time, their mean satisfaction is the lowest.
This implies that their payoff contribution to the principal is also low. In the case of two
elements of compensation and non-discrimination (Models 4 and 5), the agents who were
eventually fired took advantage of the principals inability to focus on their performance,
thereby increasing their satisfaction at a rate which was higher than that of other types
of agents. Whenever the principal had complex contracts as a manipulating tool (as in
Models 6 and 7), or whenever she had sufficient information to evaluate performances
discriminatively (as in Models 5 and 7), the factors for fired agents show a significant
decline. This implies that they were fired sooner before they could increase their own
payoffs to the extent they could in the other models.

170
The mean satisfaction of agents showed significant increase (about 70%) in
Models 6 and 7 over Models 4 and 5. Comparing with the drop in agent factors in
Models 6 and 7 over Models 4 and 5, this implies that using more elements of
compensation raises the level of satisfaction by about 70%, but does not cause a
comparatively higher rise in satisfaction as the agency progresses. When the number of
elements of compensation are two (Models 4 and 5), the mean satisfaction of agents is
higher in the discriminatory case compared to the non-discriminatory case, except (of
course) for agents who were eventually fired. However, when the number of elements
of compensation were increased to six (Models 6 and 7), all agents experienced decreased
mean satisfaction in the discrimination case (Model 7). This seems to suggest that
complexity of contracts and the practice of discrimination work at cross purposes in
satisfying all agents.
On the one hand, if the goal of the agency is to rapidly improve satisfaction levels
(or increase the rate of their improvement), then discrimination is the best policy (since
Model 5 has the highest agent factors if the factors for fired agents is ignored). Such a
goal might be reasonable for an existing agency currently suffering from low satisfaction
levels or low profit levels. A discrimination policy would get rid of shirking agents,
convey a motivational message to good agents, and increase profits by paring down the
value of contracts temporarily.
On the other hand, if the goal of the agency is to achieve a high mean satisfaction
level, attract better agents by matching the general reservation welfare, and decrease
agent turnover, then a non-discriminatory evaluation policy coupled with complex

171
contracts is the best policy (as in Model 6). Such a model would be very useful if the
cost of human resource management is a significant expense item for the principal.
Further, while a high satisfaction level is achieved in Model 6, further increase in
satisfaction is only gradual. The emphasis is not on agent factors. In many real-world
situations, if the initial satisfaction level of agents is high, further attempts to increase
that level might yield diminishing returns.
In Table 10.67, negative values for the mean satisfaction of agents occur because
the satisfaction of the agents is dependent on their risk-aversion of net income, which is
modeled as a negative exponential function which always takes negative values. Hence,
the absolute values in any model taken by themselves do not convey much information.
They must be compared with the values from the other models.
The mean satisfaction of the principal is greatest in Model 6 (six elements of
compensation with non-discriminatory evaluation), and least in Model 5 (two elements
of compensation with discriminatory evaluation). Her mean satisfaction is higher the
more complex the contracts (since this allows her to tailor compensation to a wide variety
of agents), and it is also higher if she does not practice discrimination. So, while
discrimination is good for some agents in some circumstances, it is never a desirable
policy for the principal. When complex contracts are involved, the practice of
discrimination erodes the mean satisfaction of all parties only marginally, while
decreasing agents factors significantly.
The greatest improvement in satisfaction for the principal, however, takes place
in Model 5 (two elements of compensation and discriminatory policy). The improvement

172
is marginally positive in Model 7 (complex contracts and discrimination), while it is
marginally negative in Model 6 (complex contracts and no discrimination). Hence,
depending on the goals of the agency vis-a-vis satisfaction of the principal, Model 5
(which ensures greatest rate of increase of satisfaction) or Model 6 (which ensures
highest mean satisfaction) may be chosen.
Predictably, the greatest number of agents were fired in the case of discriminatory
evaluation (Models 5 and 7), while the greatest number of agents quit in Model 5,
followed by Model 4. This implies that in Model 4, some of the agents were not
satisfied with the simple contracts offered to them (which did not meet their reservation
levels), while in Model 5, the principal forced some of the poorly performing agents to
resign by assigning them comparatively low contracts. The use of complex contracts
significantly reduces the number of agents who quit and also the number of agents who
were fired. This is because complex contracts enable the principal tailor contracts
efficiently to as many agents as possible. This ensures a more stable agency
environment.
10.9 Examination of Learning
There is no significant advantage in conducting a longer simulation in order to
increase maximum fitness of rules. Only uniformity of rule fitnesses (denoted by
entropy) is better achieved through longer simulations. Increasing the length of the
contract period increases the maximum fitness while also increasing the variance (Tables
10.1, 10.17, 10.35, and 10.49). Only in the case of Model 5 the average fitness showed

173
positive correlation with number of learning periods, but not at the 0.1 level of
significance. In all other cases, the correlation was negative, but not at the 0.1 level of
significance (except for Model 6, which showed significance). This suggests that the
models may be GA-deceptive. Further study is necessary to verify this, and suggestions
are made in Chapter 12 (Future Research). Another reason for this behavior may be due
to the fact that the functions which calculate fitness of rules do not cover all the factors
that cause the fitness to change. Of necessity, the agents private information must
remain unknown to the principals learning mechanism. Further, the index of risk
aversion of the agents is uniformly distributed in the interval (0,1). Computation of
fitness is hence not only probabilistic, but also "incomplete".

174
TABLE 10.1: Correlation of LP and CP with Simulation Statistics (Model 4)
AVEFIT
MAXFIT
VARIANCE
ENTROPY
LP
-
-
+
CP
-
+
+
-
TABLE 10.2: Correlation of LP and CP with Compensation Offered to Agents
(Model 4)
E[BP]
SD[BP]
E[SH]
SD[SH]
E[COMP]
SD[COMP]
LP
-
-
-
-
+
CP
+
+
+
+
TABLE 10.3: Correlation of LP and CP with Compensation in the Principals Final
KB (Model 4)
E[BP]
SD[BP]
E[SH]
SD[SH]
E[COMP]
SD[COMP]
LP
-
+
-
+
-
CP
+
+
+
TABLE 10.4: Correlation of LP and CP with the Movement of Agents (Model 4)
QUIT
E[QUIT]
SD[QUIT]
FIRED
E[FIRED]
SD[FIRED]
LP
+
+
+
+
-
-
CP
+
-
+
-
-
TABLE 10.5: Correlation of LP with Agent Factors (Model 4)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
SD[ALL]
LP
-
-
+
-

175
TABLE 10.6: Correlation of LP and CP with Agents Satisfaction (Model 4)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E[NORMAL]
E[ALL]
SD[ALL]
LP
+
-
+
+
+
CP
-
+
-
+
TABLE 10.7: Correlation of LP and CP with Agents Satisfaction at Termination
(Model 4)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E[ALL]
SD[ALL]
LP
-
+
+
CP
-
+
-
+
TABLE 10.8: Correlation of LP and CP with Agency Interactions (Model 4)
E[QUIT]
SD[QUIT]
SD[FIRED]
E[NORMAL]
E[ALL]
SD[ALL]
LP
-
-
+
-
-
-
CP
+
+
+
+
+
TABLE 10.9: Correlation of LP with Rule Activation (Model 4)
E[QUIT]
SD[QUIT]
E[FIRED]
E[ALL]
SD[ALL]
LP
-
-
-
-
-
TABLE 10.10: Correlation of LP with Rule Activation in the Final Iteration
(Model 4)
E[QUIT]
SD[QUIT]
E[ALL]
SD[ALL]
LP
-
-
-
-
TABLE 10.11: Correlation of LP and CP with Principals Satisfaction and Least
Squares (Model 4)
E[SATP]
SD[SATP]
LASTSATP
FACTOR
BEH-LS
EST-LS
LP
-
+
-
-
+
+
CP
+
-
+
+

176
TABLE 10.12: Correlation of Agent Factors with Agent Satisfaction (Model 4)
AGENT
FACTORS
AGENT SATISFACTION
SD[QUIT]
SD[FIRED]
SD[NORMAL]
SD[ALL]
SD[QUIT]
+
SD[FIRED]
+
SD [NORMAL]
+
SD[ALL]
+
TABLE 10.13: Correlation of Principals Satisfaction with Agent Factors (Model 4)
PRINCIPALS
SATISFACTION
AGENTS FACTORS
SD[QUIT]
E[FIRED]
SD[FIRED]
SD [NORMAL]
SD[ALL]
E[SATISFACTION]
+
+
-
+
+
SD[SATISFACTION]
-
TABLE 10.14: Correlation of Principals Satisfaction with Agents Satisfaction
(Model 4)
PRINCIPALS
SATISFACTION
AGENTS SATISFACTION
E[QUIT]
SD[QUIT]
SD[NORMAL]
E[ALL]
SD[ALL]
E[SATISFACTION]
-
+
-
+
SD[SATISFACTION]
-
+
-
+
TABLE 10.15: Correlation of Principals Last Satisfaction with Agents Last
Satisfaction (Model 4)
AGENTS
LAST
SATISFACTION
SD[FIRED]
E[NORMAL]
SD[NORMAL]
PRINCIPALS
LAST
+
SATISFACTION

177
TABLE 10.16: Correlation of Principals Factor with Agent Factors (Model 4)
TABLE 10.17: Correlation of LP and CP with Simulation Statistics (Model 5)
AVEFIT
MAXFIT
VARIANCE
ENTROPY
LP
-
-
+
CP
-
+
+
-
TABLE 10.18: Correlation of LP and CP with Compensation Offered to Agents
(Model 5)
E[BP]
SD[BP]
E[SH]
SD[SH]
E[COMP]
SD[COMP]
LP
-
-
-
-
+
CP
+
+
+
TABLE 10.19: Correlation of LP and CP with Compensation in the Principals Final
Knowledge Base (Model 5)
E[BP]
SD[BP]
E[SH]
SD[SH]
E[COMP]
SD[COMP]
LP
-
-
-
CP
+
+
+
TABLE 10.20: Correlation of LP and CP with the Movement of Agents (Model 5)
QUIT
E[QUIT]
SD[QUIT]
FIRED
E[FIRED]
SD [FIRED]
LP
+
+
+
+
-
-
CP
+
-
+
-
-

178
TABLE 10.21: Correlation of LP with Agent Factors (Model 5)
SD[QUIT]
E[FIRED]
SD[NORMAL]
SD[ALL]
LP
-
-
-
-
CP
+
+
TABLE 10.22: Correlation of LP and CP with Agents Satisfaction (Model 5)
E[QUIT]
SD[QUIT]
EfFIRED]
SD[FIRED]
SD[NORMAL]
E[ALL]
SD[ALL]
LP
+
-
-
+
-
+
-
CP
-
+
+
-
+
TABLE 10.23: Correlation of LP and CP with Agents Satisfaction at Termination
(Model 5)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
SD [NORMAL]
E[ALL]
SD[ALL]
LP
+
-
-
+
-
+
-
CP
-
+
+
-
-
+
TABLE 10.24: Correlation of LP and CP with Agency Interactions (Model 5)
E[QUIT]
SD[QUIT]
E[FIRED
SD[FIRED]
E[NORMAL]
E[ALL]
SD[ALL]
LP
-
-
-
+
-
-
-
CP
+
+
+
+
+
TABLE 10.25: Correlation of LP with Rule Activation (Model 5)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E[ALL]
SD[ALL]
LP
-
-
-
-
-
-

179
TABLE 10.26: Correlation of LP with Rule Activation in the Final Iteration
(Model 5)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E[ALL]
SD[ALL]
LP
-
-
-
-
-
-
TABLE 10.27: Correlation of LP and CP with Payoffs from Agents (Model 5)
E[QUIT]
SD[QUIT]
SD[FIRED]
E[NORMAL]
SD [NORMAL]
E[ALL]
SD[ALL]
LP
+
-
+
-
+
-
CP
-
+
+
+
-
+
TABLE 10.28: Correlation of LP and CP with Principals Satisfaction, Principals
Factor and Least Squares (Model 5)
E[SATP]
SD[SATP]
LASTSATP2
FACTOR3
BEH-LS4
EST-LS5
LP
-
-
-
+
+
CP
+
+
-
1 SATP: Principals Satisfaction
2 Principals Satisfaction at Termination
3 Principals Factor
4 Least Squares Deviation from Agents True Behavior
5 Least Squares Deviation from Principals Estimate of Agents Behavior
TABLE 10.29: Correlation of Agent Factors with Agent Satisfaction (Model 5)
AGENT
FACTORS
AGENT SATISFACTION
SD[QUIT]
SD[FIRED]
SD [NORMAL]
SD[ALL]
SD[QUIT]
+
SD[FIRED]
+
SD[NORMAL]
+
SD[ALL]
+

180
TABLE 10.30: Correlation of Principals Satisfaction with Agent Factors (Model 5)
PRINCIPALS
SATISFACTION
AGENTS FACTORS
SD[QUIT]
E[FIRED]
SD[FIRED]
SD [NORMAL]
SD[ALL]
E[SATISFACTION]
+
+
-
+
+
SD[SATISFACTION]
+
-
+
+
TABLE 10.31: Correlation of Principals Satisfaction with Agents Satisfaction
(Model 5)
PS1
AGENTS SATISFACTION
E[QUIT]
SD[QUIT]
E[FIRED]
SD [FIRED]
SD[NORMAL]
E[ALL]
SD[ALL]
T~
-
+
+
-
+
-
+
'i
-
+
-
+
1 PS: This column contains the mean and standard deviation of the Principals
Satisfaction
2 Mean Principals Satisfaction
3 Standard Deviation of Principals Satisfaction
TABLE 10.32: Correlation of Principals Last Satisfaction with Agents Last
Satisfaction (Model 5)
AGENTS LAST SATISFACTION
E[QUIT]
E[FIRED]
E[NORMAL]
SD [NORMAL]
E[ALL]
SD[ALL]
PRINCIPALS
LAST
SATISFACTION
-
+
-
+
-
+

181
TABLE 10.33: Correlation of Principals Satisfaction with Outcomes from Agents
(Model 5)
PS1
OUTCOMES FROM AGENTS
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
4
j
E[ALL]
SD[ALL]
2
-
+
-
+
-
+
-
+
5
-
-
-
-
1 PS: This column contains the mean and standard deviation of the Principals
Satisfaction
2 Mean Principals Satisfaction
3 Standard Deviation of Principals Satisfaction
4 E[NORMAL] : Mean Outcome from Normal (non-terminated) Agents
5 SD[NORMAL]
TABLE 10.34: Correlation of Principals Factor with Agents Factors (Model 5)
E[FIRED]
SD[FIRED]
SD [NORMAL]
PRINCIPALS FACTOR
+
-
+
TABLE 10.35: Correlation of LP and CP with Simulation Statistics (Model 6)
AVEFIT
MAXFIT
VARIANCE
ENTROPY
LP
-
-
-
+
CP
-
+
+
-
TABLE 10.36: Correlation of LP and CP with Compensation Offered to Agents
(Model 6)
E1
SD1
SD2
SD3
E4
SD4
SD5
E6
SD6
E7
SD7
LP
-
-
-
-
-
-
-
-
-
-
+
CP
-
+
+
+
1 BASIC PAY; 2 SHARE OF OUTPUT; 3 BONUS PAYMENTS; 4 TERMINAL
PAY
5 BENEFITS; 6 STOCK PARTICIPATION; 7 TOTAL CONTRACT

182
TABLE 10.37: Correlation of LP and CP with Compensation in the Principals
Final Knowledge Base (Model 6)
E1
SD1
SD2
SD3
SD4
SD5
SD6
SD7
LP
-
-
-
-
-
-
-
CP
-
-
-
-
-
-
1 BASIC PAY; 2 SHARE OF OUTPUT; 3 BONUS PAYMENTS; 4 TERMINAL
PAY
5 BENEFITS; 6 STOCK PARTICIPATION; 7 TOTAL CONTRACT
TABLE 10.38: Correlation of LP and CP with the Movement of Agents (Model 6)
QUIT
E[QUIT]
SD[QUIT]
FIRED
E[FIRED]
SD[FIRED]
LP
+
+
+
+
CP
+
+
-
-
TABLE 10.39: Correlation of LP and CP with Agent Factors (Model 6)
SD[QUIT]
E[NORMAL]
SD[ALL]
LP
-
-
CP
+
TABLE 10.40: Correlation of LP and CP with Agents Satisfaction (Model 6)
SD[QUIT]
SD [FIRED]
LP
+
CP
+

183
TABLE 10.41: Correlation of LP and CP with Agents Satisfaction at Termination
(Model 6)
SD[QUIT]
SD[FIRED]
E[ALL]
SD[ALL]
LP
+
+
CP
+
+
TABLE 10.42: Correlation of LP and CP with Agency Interactions (Model 6)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E[NORMAL]
E[ALL]
SD[ALL]
LP
-
-
+
-
-
-
CP
+
+
+
TABLE 10.43: Correlation of LP and CP with Rule Activation (Model 6)
E[QUIT]
SD[QUIT]
E[FIRED]
E[ALL]
SD[ALL]
LP
-
-
-
-
-
CP
-
TABLE 10.44: Correlation of LP and CP with Rule Activation in the Final Iteration
(Model 6)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E[ALL]
SD[ALL]
LP
-
-
-
-
CP
+
+

184
TABLE 10.45: Correlation of LP and CP with Principals Satisfaction and Least
Squares (Model 6)
E[SATP]
SD[SATP]
LASTSATP2
BEH-LS3
EST-LS4
LP
-
+
-
CP
+
+
+
1 SATP: Principals Satisfaction
2 Principals Satisfaction at Termination
3 Least Squares Deviation from Agents True Behavior
4 Least Squares Deviation from Principals Estimate of Agents Behavior
TABLE 10.46: Correlation of Agents Factors with Agents Satisfaction (Model 6)
i
AGENTS SATISFACTION
2
3
3
5
5
E[ALL]
SD[ALL]
2
+
3
-
3
+
5
-
5
+
E[ALL]
-
SD[ALL]
+
1 This column denotes Agents Factors
2 Standard Deviation of Factor/Satisfaction of Agents who Quit
3 Mean Factor/Satisfaction of Agents who were Fired
4 Standard Deviation of Factor/Satisfaction of Agents who were Fired
5 Mean Factor/Satisfaction of Agents who remained Active (Normal)
6 Standard Deviation of Factor/Satisfaction of Agents who remained Active (Normal)

185
TABLE 10.47: Correlation of Principals Satisfaction with Agents Factors and
Agents Satisfaction (Model 6)
PRINCIPALS
SATISFACTION
AGENTS FACTORS
AGENTS SATISFACTION
E[QUIT]
SD[NORMAL]
E[QUIT]
E[ALL]
E[SATISFACTION]
+
-
-
SD[SATISFACTION]
+
4-
+
TABLE 10.48: Correlation of Principals Factor with Agents Factor (Model 6)
E[FIRED]
SD[FIRED]
SD[NORMAL]
PRINCIPALS
FACTOR
-
-
+
TABLE 10.49: Correlation of LP and CP with Simulation Statistics (Model 7)
AVEFIT
MAXFIT
VARIANCE
ENTROPY
LP
-
+
CP
-
+
+
-
TABLE 10.50: Correlation of LP and CP with Compensation Offered to Agents
(Model 7)
E1
SD1
E2
SD2
E3
SD3
SD4
SD5
E6
SD6
E7
SD7
LP
-
-
-
-
-
-
-
-
-
-
+
CP
-
+
+
+
+
1 BASIC PAY; 2 SHARE OF OUTPUT; 3 BONUS PAYMENTS; 4 TERMINAL
PAY;
5 BENEFITS; 6 STOCK PARTICIPATION; 7 TOTAL CONTRACT

186
TABLE 10.51: Correlation of LP and CP with Compensation in the Principals
Final Knowledge Base (Model 7)
SD1
E2
SD2
SD3
SD4
SD5
E6
SD6
E7
SD7
LP
-
-
-
-
-
-
-
CP
+
+
+
1 BASIC PAY; 2 SHARE OF OUTPUT; 3 BONUS PAYMENTS; 4 TERMINAL
PAY;
5 BENEFITS; 6 STOCK PARTICIPATION; 7 TOTAL CONTRACT
TABLE 10.52: Correlation of LP and CP with the Movement of Agents (Model 7)
QUIT
E[QUIT]
SD[QUIT]
FIRED
E[FIRED]
SD[FIRED]
LP
+
+
+
+
CP
+
-
+
-
-
TABLE 10.53: Correlation of LP with Agent Factors (Model 7)
SD[QUIT]
SD[NORMAL]
SD[ALL]
LP
-
-
-
TABLE 10.54: Correlation of LP and CP with Agents Satisfaction (Model 7)
E[QUIT]
SD[QUIT]
SD[FIRED]
SD[ALL]
LP
+
+
CP
+
+

187
TABLE 10.55: Correlation of LP and CP with Agents Satisfaction at Termination
(Model 7)
SD[QUIT]
SD [FIRED]
E[ALL]
LP
+
+
CP
+
TABLE 10.56: Correlation of LP and CP with Agency Interactions (Model 7)
E[QUIT]
SD[QUIT]
SD[FIRED]
E[NORMAL]
E[ALL]
SD[ALL]
LP
-
-
+
-
-
-
CP
+
+
+
TABLE 10.57: Correlation of LP and CP with Rule Activation (Model 7)
E[QUIT]
SD[QUIT]
E[FIRED]
SD [FIRED]
E[ALL]
SD[ALL]
LP
-
-
-
-
-
-
CP
-
TABLE 10.58: Correlation of LP with Rule Activation in the Final Iteration
(Model 7)
E[QUIT]
SD[QUIT]
SD[FIRED]
E[ALL]
SD[ALL]
LP
-
-
+
-
-

188
TABLE 10.59: Correlation of LP and CP with Payoffs from Agents (Model 7)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E1
SD1
E[ALL]
SD[ALL]
LP
+
-
-
+
-
+
-
CP
-
+
-
-
+
1 NORMAL (Active) Agents
TABLE 10.60: Correlation of LP and CP with Principals Satisfaction (Model 7)
E[SATP']
SD[SATP]
LASTS ATP2
LP
-
+
-
1 SATP: Principals Satisfaction
2 Principals Satisfction at Termination
TABLE 10.61: Correlation of Agent Factors with Agent Satisfaction (Model 7)
AGENTS
FACTOR
AGENTS SATISFACTION
SD[QUIT]
E[FIRED]
SD[FIRED]
SD[NORMAL]
SD[ALL]
SD[QUIT]
+
E[FIRED]
-
SD[FIRED]
+
SD[NORMAL]
+
SD[ALL]
+
TABLE 10.62: Correlation of Principals Satisfaction with Agent Factors (Model 7)
PRINCIPALS
SATISFACTION
AGENTS FACTORS
E[FIRED]
SD[FIRED]
SD[NORMAL]
SD[ALL]
E[SATISFACTION]
-
-
+
+
SD[SATISFACTION]
-

189
TABLE 10.63: Correlation of Principals Satisfaction with Agents Satisfaction
(Model 7)
PRINCIPALS
SATISFACTION
AGENTS SATISFACTION
E[QUIT]
SD[FIRED]
E[ALL]
E[SATISFACTION]
-
-
-
SD[SATISFACTION]
+
+
+
TABLE 10.64: Correlation of Principals Last Satisfaction with Agents Last
Satisfaction (Model 7)
AGENTS LAST SATISFACTION
E[QUIT]
E[NORMAL]
SD[NORMAL]
E[ALL]
SD[ALL]
PRINCIPALS
LAST
SATISFACTION
-
-
+
-
+
TABLE 10.65: Correlation of Principals Satisfaction with Outcomes from Agents
(Model 7)
PS1
OUTCOMES FROM AGENTS
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
3
5
E[ALL]
SD[ALL]
" 7
-
+
+
-
+
-
+
3
+
-
+
-
+
-
+
-
1 PS: This column contains the mean and standard deviation of the Principals
Satisfaction
2 Mean Principals Satisfaction
3 Standard Deviation of Principals Satisfaction
4 E[NORMAL] : Mean Outcome from Normal (non-terminated) Agents
5 SD[NORMAL]
TABLE 10.66: Correlation of Principals Factor with Agents Factor (Model 7)
E[FIRED]
PRINCIPALS FACTOR
+

190
TABLE 10.67: Comparison of Models
(Standard Deviation in Parenthesis)
MODEL #
4
5
6
7
DESCRIPTION
Non-
Discriminatory
Discriminatory
Non-
Discriminatory
Discriminatory
COMPENSATION
ELEMENTS
2
2
6
6
VARIABLES
78
86
94
102
SIMULATION STATISTICS
Average Fitness
10401
(8194)
10342
(7432)
10255
(6637)
9263
(5113)
Maximum Fitness
46089
(15960)
44161
(16331)
36123
(16528)
35330
(16221)
Variance of Fitness
0.9803
(0.000049)
0.9803
(0.000041)
0.9803
(0.000040)
0.9803
(0.000039)
Entropy of Fitness
4.4687
(0.1303)
4.4830
(0.1201)
4.5032
(0.1256)
4.4833
(0.1390)
Contract Offered to
Agents
5.7835
(0.8466)
5.3706
(1.0095)
17.0137
(1.8618)
16.9674
(1.1063)
Contract Offered to
Agents (Normalized)
2.8918
2.6853
2.8356
2.8279
MOVEMENT OF AGENTS
Total Agents Who
Quit
444
996
234
232
Total Agents Fired
5
16
4
7

191
TABLE 10.67 -- continued
MODEL #
4
5
6
7
DESCRIPTION
Non-
Discriminatory
Discriminatory
Non-
Discri minatory
Discriminatory
COMPENSATION
ELEMENTS
2
2
6
6
VARIABLES
78
86
94
102
MEAN AGENT FAC
:tors
Agents who Quit
221
128
102
-60
Fired Agents
3380
1320
904
570
Normal Agents
38
2620
572
65
All Agents
584
436
185
-20
MEAN SATISFACTION OF AGENTS
Agents who Quit
-223
-221
-66
-65
Fired Agents
-240
-300
-57
-66
Normal Agents
-189
-166
-50
-64
All Agents
-228
-215
-63
-65
MEAN NUMBER OF INTERACTIONS (NORMALIZED)
Agents who Quit
2.3597
2.0180
3.9383
3.8724
Fired Agents
5.5558
3.5605
7.5252
5.8540
Normal Agents
2.8700
1.9850
5.7950
5.5150

192
TABLE 10.67 -- continued
MODEL if
4
5
6
7
DESCRIPTION
Non-
Discriminatory
Discriminatory
Non-
Discriminatory
Discriminatory
COMPENSATION
ELEMENTS
2
2
6
6
VARIABLES
78
86
94
102
All Agents
2.5100
2.0958
4.2363
4.1423
Principals
Satisfaction
-332.2
(129.7)
-406.2
(161.1)
-227.7
(105.5)
-234.6
(121.9)
Principals Factor
2.8789
(7.6635)
1.8123
(5.5003)
-0.1291
(5.9218)
0.2479
(5.8992)

193
TABLE 10.68: Probability Distributions for Models 4, 5, 6, and 7
VARIABLE
NOMINAL VALUES (Code Mappings)
1
2
3
4
5
AGE, A
< 20
(20,25]
(25,35]
(35,55]
> 55
Prob(A)
0.10
0.15
0.30
0.35
0.10
EDUCATION, D
none
high school
vocational
undergrad
graduate
Prob(DjA)
1
2
3
4
5
A
1
0.10
0.30
0.40
0.20
0.00
2
0.10
0.20
0.40
0.20
0.10
3
0.05
0.10
0.30
0.50
0.05
4
0.05
0.05
0.30
0.30
0.30
5
0.00
0.10
0.10
0.30
0.50
EXPERIENCE, X
none
< 2 years
< 5 years
< 20 years
> 20
years
Prob(X ¡ A)
1
2
3
4
5
A
1
0.70
0.20
0.10
0.00
0.00
2
0.60
0.30
0.10
0.00
0.00
3
0.20
0.40
0.30
0.10
0.00
4
0.00
0.10
0.30
0.60
0.00
5
0.00
0.00
0.00
0.20
0.80
GENERAL SOCIAL
SKILLS, GSS
Prob(GSSjA)
1
2
3
4
5
A
1
0.20
0.30
0.30
0.15
0.05
2
0.10
0.40
0.30
0.10
0.10
3
0.10
0.20
0.40
0.20
0.10
4
0.05
0.10
0.20
0.40
0.25
5
0.05
0.10
0.20
0.30
0.35
OFFICE AND
MANAGERIAL
SKILLS, OMS
Prob(OMS ¡ D)
1
2
3
4
5
D
1
0.60
0.25
0.05
0.05
0.05
2
0.50
0.20
0.15
0.10
0.05
3
0.30
0.30
0.20
0.10
0.10
4
0.10
0.10
0.20
0.40
0.20
5
0.05
0.05
0.30
0.40
0.20

CHAPTER 11
CONCLUSION
The basic model for the study of agency theory includes knowledge bases,
behavior and motivation theory, contracts contingent on the behavioral characteristics of
the agent, and learning with genetic algorithms.
The initial experiments were aimed at an exploration of the new methodology.
The goal was to deal with any technical issues in learning, such as length of simulation,
convergence behavior of solutions, choice of values for the genetic operators. The initial
studies were motivated by questions of the following nature:
* Can this new framework be used to tailor contracts to the behavioral
characteristics of the agents?
* Is it worthwhile to include in the contract elements of compensation other than
fixed pay and share of output?
* How can good contracts be characterized and understood?
Model 3 of agency described in detail in Chapter 9, includes and incorporates
theories of behavior and motivation, dynamic learning, and complex compensation plans
was examined from the viewpoint of different informational assumptions. The results
from Model 3 show that the traditional agency models are inadequate for identifying
194

195
important elements of compensation plans. The reasons that the traditional models fail
are their strong methodological assumptions and lack of a framework which deals with
complex behavioral and motivational factors, and their influence in inducing effort
selection in the agent. Model 3 attempts to remove this inadequacy.
The results of this research are dependent on the informational assumptions of the
principal and the agent. It is not suggested that the traditional theory is always wrong.
In some cases (i.e. for the informational assumptions of some principal), both theories
may agree on their recommendations for optimal compensation plans. However, this
research does present several significant counter-examples to traditional agency wisdom.
Sec. 9.5 contains the details.
Models 4 through 7 have comparatively more realism. These models simulate a
multi-agent, multi-period, and dynamic agency models which include contracts contingent
on the characteristics of the agents. The antecedents are not point estimates as in the
earlier studies, but interval estimates. This made it possible to use specialization and
generalization operators as learning mechanisms in addition to genetic operators.
Further, while these models followed the basic LEN model (as did the previous models),
the agents who enter the agency all have different risk aversions and reservation
welfares.
Models 4 and 5 have only two elements of compensation each, while Models 6
and 7 have six each. This enables one to study the effect of complex contracts as
opposed to simple contracts. Moreover, in Models 5 and 7, the principal evaluates the
agents individually. Performance of an agent is not compared to that of the others. As

196
a consequence, the firing policy is individualized to the agents. This is described as a
"discriminatory" policy. In Models 4 and 6, the evaluation of the performance of an
agent is relative to the performance of the other agents. Hence, there is one common
firing policy for all agents. This policy is described as a "non-discriminatory" policy.
This design of the experiments enables one to study the effect of the two policies on
agency performance.
Models 4 through 7 reveal several interesting results. The practice of
discriminatory evaluation of performance is beneficial to some agents (those who work
hard and are well motivated), while it is detrimental to others (shirkers). Discrimination
is not a desirable policy for the principal, since the mean satisfaction obtained by the
principal in the discriminatory models is comparatively less. However, a discriminatory
evaluation may serve to bootstrap an organization having low morale (by firing the
shirkers), and ensuring the highest rate of increase of satisfaction for the principal.
Increasing the complexity of contracts ensures low agent turnover (because of
increased flexibility) and increased overall satisfaction. This finding takes on added
significance when the cost of human resource management (such as hiring, terminating,
and training) is taken into account. This is suggested as future research in Chapter 12.
Complexity of contracts and the selective practice of relative evaluation of agent
performance are powerful tools which can be used by the principal to achieve the goals
of the agency. Their interaction and the trade-offs involved are, however, far from
straight-forward. Section 10.4 through 10.8 provide the details. Further research is

197
necessary to explore these agency mechanisms more fully. Suggestions are given in
Chapter 12.
On the one hand, each of the Models 4 through 7 seem to act as templates for
organizations with different goals. On the other, a model which accurately reflects an
existing organization may be chosen for simulation of the agency environment.

CHAPTER 12
FUTURE RESEARCH
A number of directions for future research are possible. These directions are
related to the nature of the agency, behavior and motivation theory, additional learning
capabilities, and the role of maximum entropy.
12.1 Nature of the Agency
The following enhancements to the agency attempt to include greater realism.
This would enable the study of existing agencies, and would ensure applicability of
research results.
1. The principal warns an agent whenever his performance triggers a firing decision.
The number of warnings could be a control variable to study agency models.
2. The role of the private information of the agent could be control variable -
number of elements of private information, and changing their values in different
periods of the agency.
3. Agents modify their behavior with time. This is an extremely realistic situation.
This would imply that the agents also employ learning mechanisms. The effort
selection mechanism of the agents and their acceptance/rejection criteria would
198

199
be specified by knowledge bases. This makes it possible to apply learning to
these knowledge bases, the same as was done for the principal.
4. Inclusion of the cost of human resource management for the principal. This cost
might be included either in the computation of rule fitnesses, or in the firing rules
of the principal. Coupled with a learning mechanism, this would ensure that the
principal learns the correct criteria, and to change the criteria in response to the
exogenous environment.
5. The type of simulation involved in the study of the models is discrete-event. The
time from the acceptance of a contract to the sharing of the output is one
indestructible time slice. In reality, there is a small probability for an agent to
resign, or for the principal to fire an agent, before the completion of the contract
period. This may be a desirable extension to the models above, and would be a
step towards achieving continuous simulation.
12,2 Behavior and Motivation Theory
As was pointed out in Chapter 9, further research is necessary in order to unveil
the cause-effect relationships among the elements of the behavioral models, and their
influence in unearthing good contracts in the learning process. This might shed insight
into the correlations observed among the various elements of compensation in Model 3.
Further research varying the "functional" assumptions must be carried out if any clear
pattern is to emerge. This would also help estimate the robustness of the model (the
change in the degree and direction of the correlations when the functional specifications

200
are changed). However, a correlational study of the compensation variables in the final
knowledge base is a starting point for characterizing good contracts. The acceptance or
rejection of contracts by the agents, or the effort-inducing influence of different
contracts, may be better predicted by forming correlational links between the different
compensation elements.
One potential benefit in investigating the role of behavior and motivation theory
is that compensation rules may be modified according to correlations. For example, if,
for a particular class of agents, benefits and share of output are strongly positively
correlated, then all rules that do not reflect this property may be discarded. Normal
genetic operators may then be applied. The mutation operator would ensure exploration
of new rules in the search space, while the correlation-modified rules would fix the rule
population in a desirable sector of the search space. This procedure may not be
defensible if, upon further research, it was found that the correlations are purely random.
This research indicates that this is unlikely to happen.
12,3 Machine Learning
PAC-leaming may be applied to the set of final contracts in order to determine
their closeness to optimality. Genetic algorithms do not guarantee optimality, even
though in practice they perform well. However, some measure of goodness of solutions
is necessary. PAC-leaming, described in Chapter 2, provides such a measure along with
the confidence level. PAC theory is statistical and non-parametric in nature.

201
The learning mechanisms may also be expanded. For example, as pointed out in
Section 12.2 above, learning could be modified by correlational findings if a significant
causal relationship could be found between motivation theory and the identification of
good contracts.
The genetic operators may be varied in future research. For example, only one-
point uniform crossover was used. The number of crossover points could be increased.
Similarly, the mutation operator may be made dependent on time (or the number of
learning periods). The knowledge base may also be coded as a binary string, instead of
being a string of multi-valued nominal and ordinal attributes. Instead of randomly trying
all combinations of genetic operators and codings, the structure of the knowledge base
should be studied in order to see if there are any clues that point to the superiority of one
scheme over the other.
Another interesting, and quite important, research is the study of deceptiveness
of the knowledge base. A particular coding of the strings (which are the rules) might
yield a population that deceives the genetic algorithm. This implies that the population
of strings wanders away from the global optimum. An examination of the learning
statistics of Chapter 10 suggest that such deception might be happening in Models 4
through 7. Deceptiveness is characterized as the tendency of hyperplanes in the space
of building blocks to direct search in non-optimal directions. The domain of the theory
of genetic algorithms is the n-dimensional euclidean space, or its subspaces (such as the
n-dimensional binary space). The main problem in the study of deceptiveness in the
models used in this research is that the relevant search spaces are n-dimensional nominal

202
and ordinal valued spaces. It remains to be seen how to adapt the theory of genetic
algorithms as dynamical systems to such models. It is encouraging to note that the
deterioration in average fitness with increasing learning periods (as in Models 4 through
7) is minor, suggesting that the model might be GA-deceptive instead of GA-hard (GA-
hard problems are those that seriously mislead the genetic algorithm). Further
encouragement derives from Whitleys theorem which states that the only challenging
problems are GA-deceptive (Whitley, L.D., 1991). Hence, one is at least assured, while
studying the more realistic models of agency, that these models are in fact sufficiently
challenging.
It is fairly straight-forward to include learning mechanisms wherever knowledge
bases are employed. In addition to having knowledge bases for selection of appropriate
compensation schemes and firing of agents, one may also have knowledge bases for the
agent(s) for effort selection, acceptance or rejection of contracts, and resigning from the
agency. The rules for calculation of satisfaction or welfare in the agency may be made
as extensive and detailed as one pleases. This highlights the flexibility of the new
framework it is possible to extend the model by adding knowledge bases in a modular
manner without increasing the complexity of the simulation beyond that caused by the
size and number of knowledge bases. In contrast, models in mathematical optimization
quickly become intractable by the addition of additional variables.

203
12,4 Maximum Entropy
Maximum entropy (MaxEnt) distributions seek to capture all the information about
a random variable without introducing unwarranted bias in the distribution. This is
called "maximal non-commitalness". The information of the agents and of the principal
is specified by using probability distributions. The role of MaxEnt distributions was not
attempted in this thesis. It is worthwhile to pursue the question of whether using a
maximum entropy distribution having the same mean and variance as the original
distribution makes any difference. In other words, an interesting future study might be
examination of the "MaxEnt robustness" of agency models. The results might have
interesting implications. If the results show that agency models coupled with learning
(as in this thesis) are MaxEnt robust, then it is not necessary to insist on using MaxEnt
distributions (which are computationally difficult to find). Similarly, if the models are
not MaxEnt robust, then deviation from MaxEnt behavior might yield a clue about the
tradeoffs involved in seeking a MaxEnt distribution.

APPENDIX
FACTOR ANALYSIS
We use the SAS procedures (PROC FACTOR) which uses Principal Components
Method to extract factors from the final rule population (Guertin and Bailey, 1970). We
also subject the data to Kaisers Varimax rotation, which is employed to avoid skewed
distribution of variance explained by the factors. In the initial "direct" solution, the first
factor accounts for most of the variance, followed in decreasing order by the rest of the
factors. In the "derived" solution (i.e. after rotation), variables load either maximum or
close to zero. This enables the factors to stand out more sharply. By the Kaiser
criterion, factors whose eigenvalues are greater than one are retained since they are
deemed to be significant. The size of a sample (or the size of the population)
approximates the degrees of freedom for testing significance of factor loadings. Using
500 degrees of freedom (the population size) and a relatively stringent 1 % significance
level, the critical value of correlation is 0.115. The critical value of a factor loading,
fc, is given by the Burt-Banks formula (Child, 1990):
f
C
N
n
n+l-r'
204

205
where rc is the critical correlation value, n is the number of variables, and r is the
position number of the factor being considered.
The Burt-Banks formula ensures that the acceptable level of factor loadings
increases for later factors, so that the criteria for significance become more stringent as
one progresses from the first factor to higher factors. This is essential, because specific
variance plays an increasing role in later factors at the expense of common variance.
The Burt-Banks formula, in addition to adjusting the significance, also accounts for the
sample size and the number of variables.

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BIOGRAPHICAL SKETCH
Kiran K. Garimella holds a Master of Computer Applications (M.C.A.) degree
from the University of Hyderabad, India (1983-1986) and a Bachelor of Science (with
Honors) degree from New Science College, Osmania University, Hyderabad, India
(1980-1983). His undergraduate major was chemistry with specialization in
biochemistry. His M.C.A. concentration was artificial intelligence and machine learning.
He worked as a software engineer for two years (1986-1988) at Frontier
Information Technologies Pvt. Ltd. in Hyderabad, India. His work involved design and
development of application software and systems analysis and design studies. He has
also consulted with several small businesses in Hyderabad, helping them with
computerizing their operations and in the selection of appropriate hardware and
applications software. During this time, he was also a part-time doctoral student at the
University of Hyderabad, engaged in machine learning research in the Department of
Mathematics and Computer Science. He was a guest lecturer at the Institute of Hotel
Management, Catering Technology, and Applied Nutrition of the Advanced Training
Institute and at the Indian Institute of Computer Science, both in Hyderabad, India. He
taught discrete-event system simulation (QMB 4703 Managerial Operations Analysis
III) at the University of Florida, Gainesville, in the Summer A terms of 1990 and 1993
219

220
and has been a teaching assistant for information systems, operations research and
statistics at the University of Florida.
He secured distinction and First place in the undergraduate class (1982-1983), a
University Merit Fellowship (1984), distinction in graduate studies (1985-1986), and the
Junior Doctoral Fellowship of the University Grants Commission, India (1987). He
holds honorary membership in the Alpha Chapter of Beta Gamma Sigma (1993), and in
Alpha Iota Delta (1993).
He has three conference publications (including one book reprint) and is a
member of the Association for Computing Machinery, the Decision Sciences Institute,
and the Institute of Management Sciences.

I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
/^\
Gary J. jt^ehler, Chairman
Professor of Decision and
Information Sciences
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Dvid E. M. Sappington
Lanzilotti-McKethan Professor
of Economics
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
1
I *-
tbii'C ^ t \ I L
Richard A. Elnicki
Professor of Decision and
Information Sciences
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Anthal Majthay
Associate Professor of
Decision and Information
Sciences

This dissertation was submitted to the Graduate Faculty of the Department of
Decision and Information Sciences in the College of Business Administration and to the
Graduate School and was accepted as partial fulfillment of the requirements for the degree
of Doctor of Philosophy.
August 1993
Dean, Graduate School



33
lim
N-* oo
N'1 log W = -Y 7 log
^ N
N
= H.
Distributions of higher entropy therefore have higher multiplicity. In other words,
Nature is likely to realize them in more ways. If W, and W2 are two distributions, with
corresponding entropies of H, and H2, then the ratio W2/W[ is the relative preference of
W2 over Wj. Since W2/W, ~ exp[N(H2 H,)], when N becomes large (such as the
Avogadro number), the relative preference "becomes so overwhelming that exceptions
to it are never seen; and we call it the Second Law of Thermodynamics." (Jaynes, 1982).
The problem may now be expressed in terms of constrained optimization as
follows:
/ AT \
V
Maximize log W = -N Y
[Nk] * 1 ^ N/
M4
subject to
S
E Nk Ek = E> and
k = 1
s
E N* = N-
k 1
The solution yields surprisingly rich results which would not be attainable even
if the individual trajectories of all the molecules in the closed spaces were calculated.
The efficiency of the method reveals that in fact, such voluminous calculations would
have canceled each other out, and were actually irrelevant to the problem. A similar
idea is seen in the chapter on genetic algorithms, where ignorance can be seemingly


7
themselves suffer (i.e., human mental processes). While the full simulation of the human
brain is a distant dream, limited application of this idea has already produced favorable
results.
Speech-understanding problems were investigated with the help of the HEARSAY
system (Erman et al., 1980, 1981; and Hayes-Roth and Lesser, 1977). The faculty of
vision relates to pattern recognition and classification and analysis of scenes. These
problems are especially encountered in robotics (Paul, 1981). Speech recognition
coupled with natural language understanding as in the limited system SHRDLU
(Winograd, 1973) can find immediate uses in intelligent secretary systems that can help
in data management and correspondence associated with business.
An area that is commercially viable in large business environments that involve
manufacturing and any other physical treatment of objects is robotics. This is a proven
area of artificial intelligence application, but is not yet cost effective for small business.
Several robot manufacturers have a good order book position. For a detailed survey see
for example, Engelberger, 1980.
An interesting viewpoint to the application of artificial intelligence to industry and
business is that presented by decision analysis theory. Decision analysis helps managers
to decide between alternative options and assess risk and uncertainty in a better way than
before, and to carry out conflict management when there are conflicts among objectives.
Certain operations research techniques are also incorporated, as for example, fair
allocation of resources that optimize returns. Decision analysis is treated in Fishbum
(1981), Lindley (1971), Keeney (1984) and Keeney and Raiffa (1976). In most


56
3. We assumed U is public knowledge. If this were not so, then the agent has to
test all offers to see it they are at least as high as the utility of his reservation
welfare. The two problems then become:
(M1.P2) Maxc 6 c maxq 6 Q UP[q c]
and
(M1.A4) Maxe6EUA[c*-d(e)]
such that
c* ^ UA[U], (IRC)
c* E argmax M1.P2.
In this case, there is a distinct possibility of the agent rejecting an offer of the
principal.
4. Note that in most realistic situations, a distinction must be made between the
reservation welfare and the agents utility of the reservation welfare. Otherwise,
merely using IRC with the reservation welfare in Ml.PI may not satisfy the
agents constraint. On the other hand, = UA() implies knowledge of UA by
the principal, a complication which yields a completely different model.
When U ^ UA(U), the following two problems occur:
(M1.P3) Maxc 6 c maxq 6 Q UP(q c)
such that
c > .
(M1.A5) Maxe e E UA(c* d(e))


10
Collins, 1977). For a more exhaustive treatment, see, for example Stefik et al. (1982),
Barr and Feigenbaum (1981, 1982), Cohen and Feigenbaum (1982), and Barr et al.
(1989).
2,3 Machine Learning
2.3.1 Introduction
One of the key limitations of computers as envisaged by early researchers is the
fact that they must be told in explicit detail how to solve every problem. In other words,
they lack the capacity to learn from experience and improve their performance with time.
Even in most expert systems today, there is only some weak form of implicit learning,
such as learning by being told, rote memorizing, and checking for logical consistency.
The task of machine learning research is to make up for this inadequacy by incorporating
learning techniques into computers.
The abstract goals of machine learning research are broadly
1. To construct learning algorithms that enable computers to learn.
2. To construct learning algorithms that enable computers to learn in the same way
as humans learn.
In both cases, the functional goals of machine learning research are as follows:
1. To use the learning algorithms in application domains to solve nontrivial
problems.
To gain a better understanding of how humans learn, and the details of human
cognitive processes.
2.


136
TABLE 9.20: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 3 Eigenvalues of the Correlation Matrix
Factor
1
2
3
4
5
6
Eigenvalue
2.051970
1.485699
1.393947
1.302750
1.019307
0.766105
Difference
0.566272
0.091752
0.091196
0.283444
0.253202
0.134694
Proportion
0.2052
0.1486
0.1394
0.1303
0.1019
0.0766
Cumulative
TT252
0.3538
0.4932
0.6234
0.7254
0.8020
Factor
7
8
9
10
11
12
Eigenvalue
0.631411
0.529438
0.495105
0.324267
0.0000
0.0000
Difference
0.101973
0.034334
0.170837
0.324267
0.0000
0.0000
Proportion
0.0631
0.0529
0.0495
0.0324
0.0000
0.0000
Cumulative
0.8651
0.9181
0.9676
1.0000
1.0000
1.0000
Factor
13
14
15
16
Eigenvalue
0.0000
0.0000
0.0000
0.0000
Difference
0.0000
0.0000
0.0000
Proportion
0.0000
0.0000
0.0000
0.0000
Cumulative
1.0000
1.0000
1.0000
1.0000


161
Several correlations among the dependent variables, in addition to the thirteen
groups listed above, will be presented for each model. The correlations are indicated as
" + for positive correlations and as for negative correlations. All correlations are
at the 0.1 significance level. After all the models are summarized, they will be
compared and the implications will be discussed. Tables 10.1 through 10.16 cover
Model 4. Tables 10.17 through 10.34 cover Model 5, Tables 10.35 through 10.48 cover
Model 6, and Tables 10.49 through 10.66 cover Model 7. Table 10.67 compares the
four models. Sections 10.4 through 10.7 discuss the results for the four models.
10,4 Model 4: Discussion of Results
Model 4 has two elements of compensation, and the principal does not practice
discrimination in evaluating the agents. Increasing the number of learning periods tends
to result in a lower contract (by individual contract element and also by total contract)
offered to agents. Increasing the number of data collection periods during which no
evaluation of the agents occurs, results in a higher contract being offered to the agents.
In both cases, the variance of the total contract increases (Table 10.2). Interestingly
enough, in both cases, the contracts that make up the final knowledge base of the
principal show positive correlation (Table 10.3). Tables 10.2 and 10.3 together imply
that while the final knowledge base favors comparatively high contracts, the principal is
able to select only the low contracts. This affects the agents factors (which determine
if the agents are better off at termination in this agency model) adversely. In fact,
increasing the number of learning periods leaves all the agents worse off (Table 10.5).


43
T3. The agent chooses an action or effort level from a set of possible actions or effort
levels.
T4. The outcome occurs as a function of the agents actions and exogenous factors
which are unknown or known only with uncertainty.
Another example of timing is when a communication structure with signals and
messages is involved (Christensen, 1981):
Tl. The principal designs a compensation scheme.
T2. Formation of the agency contract.
T3. The agent observes a signal.
T4. The agent chooses an act and sends a message to the principal.
T5. The output occurs from the agents act and exogenous factors.
Variations in the principal-agent problems are caused by changes in one or more
of these components. For example, some principal-agent problems are characterized by
the fact that the agent may not be able to enforce the payment commitments of the
principal. This situation occurs in some of the relationships in the context of regulation.
Another is the possibility of renegotiation or review of the contract at some future date.
Agency theory, dealing with the above market structure, gives rise to a variety
of problems caused by the presence of factors such as the influence of externalities,
limited observability, asymmetric information, and uncertainty (Gjesdal, 1982).


178
TABLE 10.21: Correlation of LP with Agent Factors (Model 5)
SD[QUIT]
E[FIRED]
SD[NORMAL]
SD[ALL]
LP
-
-
-
-
CP
+
+
TABLE 10.22: Correlation of LP and CP with Agents Satisfaction (Model 5)
E[QUIT]
SD[QUIT]
EfFIRED]
SD[FIRED]
SD[NORMAL]
E[ALL]
SD[ALL]
LP
+
-
-
+
-
+
-
CP
-
+
+
-
+
TABLE 10.23: Correlation of LP and CP with Agents Satisfaction at Termination
(Model 5)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
SD [NORMAL]
E[ALL]
SD[ALL]
LP
+
-
-
+
-
+
-
CP
-
+
+
-
-
+
TABLE 10.24: Correlation of LP and CP with Agency Interactions (Model 5)
E[QUIT]
SD[QUIT]
E[FIRED
SD[FIRED]
E[NORMAL]
E[ALL]
SD[ALL]
LP
-
-
-
+
-
-
-
CP
+
+
+
+
+
TABLE 10.25: Correlation of LP with Rule Activation (Model 5)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
E[ALL]
SD[ALL]
LP
-
-
-
-
-
-


129
TABLE 9.9: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 1 Factor Pattern
Factor 1
Factor 2
Factor 3
Factor 4
Factor 5
Factor 6
X
-0.38741
-0.32701
-0.33959
0.31473
-0.02677
-0.10644
D
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
A
-0.00000
0.00000
0.00000
0.00000
0.00000
-0.00000
RISK
-0.39646"
-0.13369
0.50581
0.25216
-0.11529
0.46880
GSS
0.17684
0.23305
0.28615
-0.36547
-0.61216
0.30750
OMS
-0.00000
0.00000
0.00000
-0.00000
-0.00000
0.00000
M
0.45141
0.44846
-0.30819
0.01878
-0.02665
-0.04173
PQ
0.54728
-0.53206
0.16099
0.05279
0.21852
0.00511
L
-0.00000
-0.00000
0.00000
-0.00000
-0.00000
0.00000
OPC
0.00000
-0.00000
-0.00000
0.00000
0.00000
-0.00000
BP
0.24127
0.19271
0.26919
0.66974
0.26082
0.24682
S
0.15889
0.06246
-0.59932
0.06671
0.04408
0.52285
BO
0.55605
-0.44006
0.19261
0.03879
-0.21608
-0.29675
TP
0.28107
0.47123
0.27576
-0.15331
0.47397
0.01654
B
-0.31708
-0.16489
0.12134
-0.52885
0.51514
0.06433
SP
-0.28396
0.45292
0.16366
0.24367
-0.08786
-0.50860
Factor 7
Factor 8
Factor 9
Factor 10
Factor 11
X
0.53275
0.32110
0.18254
-0.24025
0.19642
D
0.00000
0.00000
0.00000
0.00000
0.00000
A
0.00000
-0.00000
-0.00000
0.00000
0.00000
RISK
0.15023
0.09305
0.00794
0.48441
0.08071
GSS
0.13197
0.30346
0.03435
-0.34316
-0.03492
OMS
-0.00000
0.00000
0.00000
-0.00000
0.00000
M
0.38181
0.20000
-0.44346
0.31541
0.12412
PQ
0.21527
0.25601
0.02163
0.04990
-0.47547
L
-0.00000
0.00000
0.00000
-0.00000
0.00000
OPC
0.00000
-0.00000
-0.00000
0.00000
-0.00000
BP
-0.17272
0.06504
-0.24630
-0.38664
0.10238
S
-0.38033
0.29019
0.29471
0.12585
-0.01855
BO
-0.26496
0.16193
0.12058
0.12813
0.44320
TP
0.28937
-0.02725
0.51720
0.01514
0.14920
B
-0.15392
0.41618
-0.28532
-0.07102
0.15815
SP
-0.25267
0.47536
0.12030
0.12243
-0.20590
Notes:
Final Communality Estimates total ll.C
and are as follows: 0.0 for D,
A, OMS, L, and OPC; 1.0 for the rest of the variables.


139
TABLE 9.23: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 4
COMPENSATION
VARIABLE
VALUES OF THE VARIABLE
1
2
3
4
5
BASIC PAY
8.0
10.8
6.8
20.3
54.1
SHARE
100.0
0.0
0.0
0.0
0.0
BONUS
W7
24.3
4.1
8.1
1.4
TERMINAL PAY
82.4
5.4
5.4
4.1
2.7
BENEFITS
78.4
12.2
6.8
1.4
1.4
STOCK
82.4
14.9
1.4
0.0
1.4
TABLE 9.24: Range, Mean and Standard Deviation of Values of Compensation
Variables in the Final Knowledge Base in Experiment 4
Variable
Minimum
Maximum
Mean
S.D.
BP
1.0000
5.0000
4.0135135
1.3395281
S
1.0000
1.0000
1.0000000
0~
BO
1.0000
5.0000
1.6216216
0.9890178
TP
1.0000
5.0000
1.3918919
0.9625532
B
1.0000
5.0000
1.3513514
0.7839561
SP
1.0000
5.0000
1.2297297
0.6092281
TABLE 9.25: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 4
(Spearman Correlation Coefficients in the first row for each variable,
Prob> ¡R¡ under Ho: Rho=0 in the second)
BP
S
BO
TP
B
SP
BP
1.00000

-0.07927
-0.12735
0.17890
0.09947
0.00000
0.5020
0.2796
0.1272
0.3991
S
.
1.00000
.
.
.

0.00000
BO
-0.07927
.
1.00000
0.04158
-0.05059
-0.05058
0.5020
0.00000
0.7250
0.6686
0.6687
TP
-0.12735
.
0.04158
1.00000
-0.15591
-0.03370
0.2796
0.7250
0.00000
0.1847
0.7756
B
0.17890
.
-0.05059
-0.15591
1.00000
-0.07384
0.1272
0.6686
0.1847
0.00000
0.5318
SP
0.09947
.
-0.05058
-0.03370
-0.07384
1.00000
0.3991
0.6687
0.7756
0.5318
0.0


213
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11
When the goal is to come up with paradigms that can be used to solve problems,
several subsidiary goals can be proposed:
1. To see if the learning algorithms do indeed perform better than humans do in
similar situations.
2. To see if the learning algorithms come up with solutions that are intuitively
meaningful for humans.
3. To see if the learning algorithms come up with solutions that are in some way
better or less expensive than some alternative methodology.
It is undeniable that humans possess cognitive skills that are superior not only to
other animals but also to most learning algorithms that are in existence today. It is true
that some of these algorithms perform better than humans in some limited and highly
formalized situations involving carefully modeled problems, just as the simplex method
consistently produces solutions superior to those possible by a human being. However,
and this is the crucial issue, humans are quick to adopt different strategies and solve
problems that are ill-structured, ill-defined, and not well understood, for which there
does not exist any extensive domain theory, and that are characterized by uncertainty,
noise, or randomness. Moreover, in many cases, it seems more important to humans to
find solutions to problems that satisfy some constraints rather than to optimize some
"function." At the present state of the art, we do not have a consistent, coherent and
systematic theory of what these constraints are. These constraints are usually understood
to be behavioral or motivational in nature.


This dissertation was submitted to the Graduate Faculty of the Department of
Decision and Information Sciences in the College of Business Administration and to the
Graduate School and was accepted as partial fulfillment of the requirements for the degree
of Doctor of Philosophy.
August 1993
Dean, Graduate School


(f) output is observed;
(g) principal keeps the residuum.
70
Special technological assumptions: Some of these assumptions are used in only some of
the results; other results are obtained by relaxing them.
(a) The joint probability distribution function on output, signals, and actions is
twice-differentiable in effort, and the marginal effects on this distribution of
the different components of effort are independent.
(b) The principals utility function UP is trice differentiable, increasing, and
concave.
(c) The agents utility function UA is separable, with the function on the
compensation scheme (or sharing rule as it is known) being increasing and
concave, and the function on the effort being concave.
Results:
Result 2.1: There exists a marginal incentive informativeness condition which is
essentially sufficient for marginal value given a signal information system Y. When
information about the output is replaced by signals about the output and/or the agents
effort, marginal incentive informativeness is no longer a necessary condition for marginal
value since an additional information system Z may be valuable as information about
both the output and the effort.


131
TABLE 9.11: Frequency (as Percentage) of Values of Compensation Variables in the
Final Knowledge Base in Experiment 2
Compensation
Variable
VALUES OF THE VARIABLE
1
2
3
4
5
Basic Pay
6.5
2.0
17.1
45.3
29.0
Share
95.7
1.8
0.8
1.3
0.5
Bonus
50.1
22.7
7.6
13.4
6.3
Terminal Pay
93.7
3.3
1.3
0.5
1.3
Benefits
85.1
8.6
3.5
2.0
0.8
Stock
87.9
6.8
2.0
1.8
1.5
TABLE 9.12: Range, Mean and Standard Deviation of Values of Compensation
Variables in the Final Knowledge Base in Experiment 2
Variable
Minimum
Maximum
Mean
S.D.
BP
1.00
5.00
3.8816121
1.0582000
S
1.00
5.00
1.0906801
0.4839221
BO
1.00
5.00
2.0302267
1.2964961
TP
1.00
5.00
1.1234257
0.5617257
B
1.00
5.00
1.2468514
0.6849916
SP
1.00
5.00
1.2216625
0.7079878
TABLE 9.13: Correlation Analysis of Values of Compensation Variables in the Final
Knowledge Base in Experiment 2
(Spearman Correlation Coefficients in the first row for each variable, Prob > ¡ R ¡
under Ho: Rho=0 in the second)
BP
S
BO
TP
B
SP
BP
1.00000
0.02951
-0.23955
0.05064
-0.11008
0.01298
0.0
0.5578
0.0001
0.3142
0.0283
0.7965
S
0.02951
1.00000
0.03275
-0.00414
0.06030
0.00038
0.5578
0.0
0.5153
0.9344
0.2307
0.9940
BO
-0.23955
0.03275
1.00000
0.01020
0.10281
-0.02808
0.0001
0.5153
0.0
0.8394
0.0406
0.5770
TP
0.05064
-0.00414
0.01020
1.00000
0.04402
-0.00848
0.3142
0.9344
0.8394
0.0
0.3817
0.8663
B
-0.11008
0.06030
0.10281
0.04402
1.00000
0.01402
0.0283
0.2307
0.0406
0.3817
0.0
0.7807
SP
0.01298
0.00038
-0.02808
-0.00848
0.01402
mwmmm
0.7965
0.9940
0.5770
0.8663
0.7807
0.0


174
TABLE 10.1: Correlation of LP and CP with Simulation Statistics (Model 4)
AVEFIT
MAXFIT
VARIANCE
ENTROPY
LP
-
-
+
CP
-
+
+
-
TABLE 10.2: Correlation of LP and CP with Compensation Offered to Agents
(Model 4)
E[BP]
SD[BP]
E[SH]
SD[SH]
E[COMP]
SD[COMP]
LP
-
-
-
-
+
CP
+
+
+
+
TABLE 10.3: Correlation of LP and CP with Compensation in the Principals Final
KB (Model 4)
E[BP]
SD[BP]
E[SH]
SD[SH]
E[COMP]
SD[COMP]
LP
-
+
-
+
-
CP
+
+
+
TABLE 10.4: Correlation of LP and CP with the Movement of Agents (Model 4)
QUIT
E[QUIT]
SD[QUIT]
FIRED
E[FIRED]
SD[FIRED]
LP
+
+
+
+
-
-
CP
+
-
+
-
-
TABLE 10.5: Correlation of LP with Agent Factors (Model 4)
E[QUIT]
SD[QUIT]
E[FIRED]
SD[FIRED]
SD[ALL]
LP
-
-
+
-


BIOGRAPHICAL SKETCH
Kiran K. Garimella holds a Master of Computer Applications (M.C.A.) degree
from the University of Hyderabad, India (1983-1986) and a Bachelor of Science (with
Honors) degree from New Science College, Osmania University, Hyderabad, India
(1980-1983). His undergraduate major was chemistry with specialization in
biochemistry. His M.C.A. concentration was artificial intelligence and machine learning.
He worked as a software engineer for two years (1986-1988) at Frontier
Information Technologies Pvt. Ltd. in Hyderabad, India. His work involved design and
development of application software and systems analysis and design studies. He has
also consulted with several small businesses in Hyderabad, helping them with
computerizing their operations and in the selection of appropriate hardware and
applications software. During this time, he was also a part-time doctoral student at the
University of Hyderabad, engaged in machine learning research in the Department of
Mathematics and Computer Science. He was a guest lecturer at the Institute of Hotel
Management, Catering Technology, and Applied Nutrition of the Advanced Training
Institute and at the Indian Institute of Computer Science, both in Hyderabad, India. He
taught discrete-event system simulation (QMB 4703 Managerial Operations Analysis
III) at the University of Florida, Gainesville, in the Summer A terms of 1990 and 1993
219


143
TABLE 9.28: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 4 Varimax Rotated Factor Pattern
FACTOR
1
2
3
4
5
X
0.03602
0.04669
0.14883
0.05089
0.00711
D
0.05774
0.09209
0.12082
0.09927
-0.08622
A
-0.10231
-0.24787
-0.14726
0.08419
0.91011
RISK
0.14759
-0.17610
0.06520
0.92643
0.07767
GSS
0.08372
0.00725
0.04552
0.01376
-0.03982
OMS
-0.16731
-0.06523
-0.08774
0.03698
-0.04746
M
-0.02422
-0.01799
-0.10685
0.02106
-0.08576
PQ
0.95101
-0.00952
0.10464
0.13279
-0.08740
L
0.00879
0.05939
-0.16568
0.07772
0.02935
OPC
0.04738
0.10469
0.13445
-0.01761
0.05144
BP
-0.03349
0.08663
0.04612
-0.21501
-0.13151
S
0.00000
0.00000
0.00000
0.00000
0.00000
BO
-0.06461
0.03125
-0.02082
0.04200
-0.04468
TP
0.05751
-0.07338
0.00566
-0.05950
0.03865
B
-0.01518
0.05088
0.03210
-0.02021
-0.11377
SP
0.07991
0.08161
0.04361
0.06382
0.03603
Notes: Final Communality Estimates total 15.0 and are as follows: 0.0 for S; 1.0
for the rest of the variables.


84
The set of all compensation schemes is in fact a set of knowledge bases consisting
of the following components (B.R. Ellig, 1982):
(1) Compensation policies/strategies of the principal;
(2) Knowledge of the structure of the compensation plans, which means specific rules
concerning short-term incentives linked to partial realization of expected output,
long-term incentives linked to full realization of expected output, bonus plans
linked to realizing more than the expected output, disutilities linked to
underachievement, and rules specifying injunctions to the agent to restrain from
activities that may result in disutilities to the principal (if any).
There are various elements in a compensation scheme, which can be classified as
financial and non-financial:
Financial elements of compensation
1. Base Pay (periodic).
2. Commission or Share of Output.
3. Bonus (annual or on special occasions).
4. Long Term Income (lump sum payments at termination).
5. Benefits (insurance, etc.).
6. Stock Participation.
7. Non-taxable or tax-sheltered values.
Nonfinancial elements of compensation
1. Company Environment.
2.
Work Environment.


190
TABLE 10.67: Comparison of Models
(Standard Deviation in Parenthesis)
MODEL #
4
5
6
7
DESCRIPTION
Non-
Discriminatory
Discriminatory
Non-
Discriminatory
Discriminatory
COMPENSATION
ELEMENTS
2
2
6
6
VARIABLES
78
86
94
102
SIMULATION STATISTICS
Average Fitness
10401
(8194)
10342
(7432)
10255
(6637)
9263
(5113)
Maximum Fitness
46089
(15960)
44161
(16331)
36123
(16528)
35330
(16221)
Variance of Fitness
0.9803
(0.000049)
0.9803
(0.000041)
0.9803
(0.000040)
0.9803
(0.000039)
Entropy of Fitness
4.4687
(0.1303)
4.4830
(0.1201)
4.5032
(0.1256)
4.4833
(0.1390)
Contract Offered to
Agents
5.7835
(0.8466)
5.3706
(1.0095)
17.0137
(1.8618)
16.9674
(1.1063)
Contract Offered to
Agents (Normalized)
2.8918
2.6853
2.8356
2.8279
MOVEMENT OF AGENTS
Total Agents Who
Quit
444
996
234
232
Total Agents Fired
5
16
4
7


A KNOWLEDGE-INTENSIVE MACHINE-LEARNING APPROACH
TO THE PRINCIPAL-AGENT PROBLEM
By
KIRAN K. GARIMELLA
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1993


89
Figure 1 shows the Porter & Lawler model of the instrumentality theory of motivation.
The model parts are described below.
Value of reward describes the attractiveness of various outcomes to the individual.
The instrumentality model agrees with the drive model that rewards acquire attractiveness
as a function of their ability to satisfy the individual.
Perceived effort-reward probability refers to the subjective estimate of the
individual that increased effort will lead to the acquisition of some valued reward. This
consists of two estimates: the first is the probability that improved performance will lead
to the value reward, and the second is the probability that effort will lead to improved
performance. These two probabilities have a multiplicative relationship. Instrumentality
model makes a distinction between Effort and Performance: effort is a measure of how
hard an individual works, while performance is a measure of how effective is his effort.
Abilities and traits are included as a source of variation in this model, while other
models implicitly assume some fixed levels of abilities and traits. Abilities and traits refer
to relatively stable characteristics of the individual such as intelligence, personality
characteristics, and psychomotor skills, which are considered as boundary conditions or
limitations on performance.
Role Perception denotes an individuals definition of successful performance in
work. An appropriate definition of success is essential in determining whether or not
effort is transformed into good performance, and also in perceiving equity in reward.
Distinction is made between intrinsic and extrinsic rewards. Intrinsic rewards
are rewards that satisfy higher-order Maslow needs (A.H. Maslow, 1943; A.H. Maslow,


140
TABLE 9.26: Factor Analysis (Principal Components Method) of the Final
Knowledge Base of Experiment 4 Eigenvalues of the Correlation Matrix
Total = 15 Average = 0.9375
Factor
1
2
3
4
5
6
Eigenvalue
2.266645
1.820044
1.740554
1.392479
1.222659
1.127880
Difference
0.446601
0.079490
0.348075
0.169820
0.094779
0.081301
Proportion
0.1511
0.1213
0.1160
0.0928
0.0815
0.0752
Cumulative
0.1511
0.2724
0.3885
0.4813
0.5628
0.6380
Factor
7
8
9
10
11
12
Eigenvalue
1.046579
0.911929
0.720692
0.673039
0.590800
0.540745
Difference
0.134650
0.191237
0.047653
0.082239
0.050055
0.139484
Proportion
0.0698
0.0608
0.0480
0.0449
0.0394
0.0360
Cumulative
0.7078
0.7686
0.8166
0.8615
0.9009
0.9369
Factor
13
14
15
16
Eigenvalue
0.401261
0.330169
0.214527
0.000000
Difference
0.071092
0.115642
0.214527
Proportion
0.0268
0.0220
0.0143
0.0000
Cumulative
0.9637
0.9857
1.0000
1.0000


158
The probability distributions are detailed in Table 10.68. The index of risk
aversion is unique to the agent and is drawn from the uniform (0,1) distribution. When
the principal offers a compensation scheme, the agent draws a reservation welfare from
the associated distribution, and compares the utility of the reservation compensation with
the utility of the compensation offered by the principal (in these models, the agent does
not take into account the expected utility from future contracts). The agent rejects the
contract if the latter utility does not exceed the former.
10.2 Learning with Specialization and Generalization.
The structure of the antecedents of the principals knowledge base have been
modified. In the previous models, each antecedent was a single number between 1 and
5 inclusive. However, it is felt that more realism is captured (and the application of
other learning operators is made possible) if each antecedent is expressed as an interval
bounded inclusively by 1 and 5. This would enable the principals knowledge base to
be as precise or as general as necessary. For example, if the agents who participated in
the agency in some learning period had a wide diversity of characteristics, then the
knowledge base would be appropriately generalized so that the principal would be able
to offer contracts to as many of them as possible. Similarly, if the agents had
characteristics which were close to the others, then the principals knowledge base could
be specialized or made more precise in order to distinguish between the agents and tailor
compensation schemes appropriately.