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Nash Equilibrium of Hotel Pricing Strategies

Permanent Link: http://ufdc.ufl.edu/UFE0021755/00001

Material Information

Title: Nash Equilibrium of Hotel Pricing Strategies A Bertrand Model of Information Sharing
Physical Description: 1 online resource (126 p.)
Language: english
Creator: Kim, Sungsoo
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: Tourism, Recreation, and Sport Management -- Dissertations, Academic -- UF
Genre: Health and Human Performance thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The lodging industry uses diverse pricing strategies to maximize revenue, while maintaining customer satisfaction. Given the uncertain nature of decision-parameters, such as price or demand conditions, sharing information among competitors can dramatically impact a hotel?s behavior. Information sharing among competitors can enhance the quality of strategies because it reduces the uncertainty of market environments, and enables correlation of price strategies. Game-theoretic models can assist hotel managers to characterize the incentive for firms to share or not to share private information with competitors in order to establish an optimal pricing strategy. Game theory is the study of multi-person decision problems, which examines strategic interactions between decision-makers (e.g. hotel managers). The optimal strategy is achieved by finding Nash equilibrium (Nash strategies), which is the most commonly used solution concept in game theory. This study examined decisions of hotels to share or not share private information with competitors to maximize profits via game-theoretic model. In particular, a two-stage model was developed where hotels made sharing decisions in the first stage and then, in the second state, competed with each other in setting prices along the lines of a standard price competition model. More specifically, first, information sharing decisions were only made after each hotel learnt its own market demand (low versus high), and not before. Second, both symmetric and asymmetric situations about cost and demand in the price competition model were analyzed. The asymmetric situations about different costs and/or demands were employed to create various scenarios about the types of competitions among hotels. Data were collected in three market segments (upscale, midscale, and economy) among five hotels in Marion County, FL. This study identified market competition, marginal cost, market demand, size of hotel, and fluctuation of demand (seasonality) as significant indicators in resolving or establishing an optimal pricing strategy with respect to information-sharing behaviors in the lodging industry. Some of key results are summarized. First, regardless of the competitive nature of the market, similar sizes and types of hotels generally share their demand information with each other when low demand signal is identified, while they conceal demand information with high demand signal. Second, if there is a medium or high level of competition, hotels that are similar in type, but differ in size share their demand information with each other when they face low demand signal. However, as market competition increases, the relatively smaller sized hotels conceal demand information from larger hotels when they face low demand signal during high-level of competition. These hotels conceal demand information when high demand signal is identified, regardless of the extent of competition. Third, hotels, which are similar in type, but differ in size, face a fluctuation of demand (seasonality). They conceal their demand information with high demand signal when there is low-level of competition. But, the relatively larger hotels, which also have a higher fluctuation share demand information when they face low demand signal during low-level competition. Results of this study have contributed to theoretical and managerial implications with regards to information-sharing behaviors among hotels and optimal pricing strategy.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sungsoo Kim.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Thapa, Brijesh.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-08-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0021755:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021755/00001

Material Information

Title: Nash Equilibrium of Hotel Pricing Strategies A Bertrand Model of Information Sharing
Physical Description: 1 online resource (126 p.)
Language: english
Creator: Kim, Sungsoo
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: Tourism, Recreation, and Sport Management -- Dissertations, Academic -- UF
Genre: Health and Human Performance thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The lodging industry uses diverse pricing strategies to maximize revenue, while maintaining customer satisfaction. Given the uncertain nature of decision-parameters, such as price or demand conditions, sharing information among competitors can dramatically impact a hotel?s behavior. Information sharing among competitors can enhance the quality of strategies because it reduces the uncertainty of market environments, and enables correlation of price strategies. Game-theoretic models can assist hotel managers to characterize the incentive for firms to share or not to share private information with competitors in order to establish an optimal pricing strategy. Game theory is the study of multi-person decision problems, which examines strategic interactions between decision-makers (e.g. hotel managers). The optimal strategy is achieved by finding Nash equilibrium (Nash strategies), which is the most commonly used solution concept in game theory. This study examined decisions of hotels to share or not share private information with competitors to maximize profits via game-theoretic model. In particular, a two-stage model was developed where hotels made sharing decisions in the first stage and then, in the second state, competed with each other in setting prices along the lines of a standard price competition model. More specifically, first, information sharing decisions were only made after each hotel learnt its own market demand (low versus high), and not before. Second, both symmetric and asymmetric situations about cost and demand in the price competition model were analyzed. The asymmetric situations about different costs and/or demands were employed to create various scenarios about the types of competitions among hotels. Data were collected in three market segments (upscale, midscale, and economy) among five hotels in Marion County, FL. This study identified market competition, marginal cost, market demand, size of hotel, and fluctuation of demand (seasonality) as significant indicators in resolving or establishing an optimal pricing strategy with respect to information-sharing behaviors in the lodging industry. Some of key results are summarized. First, regardless of the competitive nature of the market, similar sizes and types of hotels generally share their demand information with each other when low demand signal is identified, while they conceal demand information with high demand signal. Second, if there is a medium or high level of competition, hotels that are similar in type, but differ in size share their demand information with each other when they face low demand signal. However, as market competition increases, the relatively smaller sized hotels conceal demand information from larger hotels when they face low demand signal during high-level of competition. These hotels conceal demand information when high demand signal is identified, regardless of the extent of competition. Third, hotels, which are similar in type, but differ in size, face a fluctuation of demand (seasonality). They conceal their demand information with high demand signal when there is low-level of competition. But, the relatively larger hotels, which also have a higher fluctuation share demand information when they face low demand signal during low-level competition. Results of this study have contributed to theoretical and managerial implications with regards to information-sharing behaviors among hotels and optimal pricing strategy.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sungsoo Kim.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Thapa, Brijesh.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-08-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0021755:00001


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1 NASH EQUILIBRIUM OF HO TEL PRICING STRATEGIES: A BERTRAND MODEL OF INFORMATION SHARING By SUNGSOO KIM A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008

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2 2008 Sungsoo Kim

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3 ACKNOWLEDGMENTS First of all, Id like to th ank the eternal God, for relentle ss blessings, the inspiration, and heart to pursue this research project. I am also i ndebted to my family, such as my father, mother, and two sisters for their unyielding support and en couragement during my research project. I want to thank my committee members at Un iversity of Florida for providing me the inspiration, heart to pursue this project, and lett ing me conduct this resear ch project. First and foremost, I thank Dr. Brijesh Th apa, for chairing my committee, and for investing much time, effort and interest in this rese arch project. I am also apprecia tive of the invaluable insights and contributions of doctors Lori Pennington-Gray and Holland Stephan. Furthermore, my sincere appreciation goes to Dr. Steven Slutsky. Without his efforts, I could not finish this project. Also, my life has been filled with contributi ons and supports from ma ny great individuals. Thanking them all is an almost impossible task.

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4 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................3 LIST OF TABLES................................................................................................................. ..........6 LIST OF FIGURES.........................................................................................................................7 LIST OF DEFINITIONS.................................................................................................................8 ABSTRACT...................................................................................................................................10 CHAP TER 1 INTRODUCTION..................................................................................................................12 Statement of Problem........................................................................................................... ..16 Purpose of Study.....................................................................................................................18 Delimitation................................................................................................................... .........19 2 LITERATURE REVIEW.......................................................................................................20 Hotels Pricing Strategies.......................................................................................................20 Competitions Versus Information Sharing in Hotel Business es..................................... 20 Pricing Strategies.............................................................................................................22 Economics Perspectives........................................................................................... 24 Marketing Perspectives............................................................................................26 Yield Management..........................................................................................................29 Theoretical Background of Hotels Price Competition Model............................................... 33 Development of Game Theory........................................................................................33 Game Theoretic Model.................................................................................................... 35 Static Games of Incomplete Information........................................................................ 38 Information Sharing Behavior......................................................................................... 39 Information Acquisition........................................................................................... 40 Cost or Demand Uncertainty in Monopolistic Competition............................................ 41 Cost or Demand Uncertainty in Oligopoly Market Environment...................................41 Bertrand Competition...................................................................................................... 44 Summary of Literature Review.............................................................................................. 46 3 METHODOLOGY................................................................................................................. 49 Phase 1....................................................................................................................................49 Model Building................................................................................................................49 Costs and Demands.........................................................................................................49 Timing and Information.................................................................................................. 50 Model Analysis................................................................................................................ 51

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5 Formalization.................................................................................................................. .51 Phase 2....................................................................................................................................54 Site Description...............................................................................................................55 Data Collection................................................................................................................56 Phone Interviews.............................................................................................................56 Secondary Data................................................................................................................ 57 Data Analysis...................................................................................................................57 4 RESULTS...............................................................................................................................62 Results of Phase 1...................................................................................................................62 Second Stage of the Model Equilibrium Prices............................................................ 62 Complete Information Subgames.................................................................................... 62 One-Side Private Information Subgames........................................................................ 64 Two-Side Private Information Subgame......................................................................... 71 First Stage of the Model In form ation Sharing Equilibrium......................................... 75 Results of Phase 2...................................................................................................................84 Results of Phone Interviews............................................................................................84 Empirical Validation of Pr icing Competition Model ......................................................86 Competition between Similar Type, but Different Size of Hotels.................................. 87 Competition between Similar Type and Size of Hotels.................................................. 88 Competition between an Upscale and a Mid-scale Hotel................................................ 89 Competition between an Upscale Hotel and an Econom y Hotel.................................... 90 5 DISCUSSION.......................................................................................................................101 Conclusions and Implications...............................................................................................111 Limitations.................................................................................................................... ........115 Recommendations for Future Study..................................................................................... 116 Cournot Competition..................................................................................................... 116 Cost Uncertainty............................................................................................................ 117 Demand Segments......................................................................................................... 117 Independent Hotel vs. Hotel by Chain.......................................................................... 117 LIST OF REFERENCES.............................................................................................................119 BIOGRAPHICAL SKETCH.......................................................................................................126

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6 LIST OF TABLES Table page 3-1 Probability distribution................................................................................................... ...59 3-2 Profiles of selected hotels in Marion County, FL .............................................................. 59 4-1 81 different cases......................................................................................................... ......91 4-2 Sensitivity analysis for proposition 1: 02 1H H and 1 L2 L 1........................ 93 4-3 Sensitivity analysis for proposition 2: 122 11H L H L.................................. 94 4-4 Sensitivity analysis for proposition 2: 1 H2 H 0 and 1 L2 L 1.......................... 95 4-5 Sensitivity analysis for proposition 3: 1 L1 H2 L2 H 1..................................... 96 4-6 Sensitivity analysis for proposition 3: 1 H2 H 0 and 1 L2 L 1.......................... 96 4-7 Sensitivity analysis for proposition 4: 1 H2 H2 L 0 and 1 L 1.......................... 97 4-8 Sensitivity analysis for proposition 5: 1 H2 L 0 and 1 L2 H 1.......................... 97 4-9 Sensitivity analysis for proposition 6: 1 H2 H2 L 0 and 1 L 1.......................... 98 4-10 Sensitivity analysis for proposition 7: 1 H2 H2 L 0 and 1 L 1.......................... 98 4-11 Sensitivity analysis for proposition 8: 1 H2 H1 L2 L 0.................................... 99 4-12 Actual information sharing behaviors of five hotels in M arion County, FL (20062007)..................................................................................................................................99 4-13 Monthly trend of prices a nd dem and in Marion County, FL........................................... 100

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7 LIST OF FIGURES Figure page 2-1 Different pricing index [S ource: Han ks et al. 1992, p17].................................................. 48 3-1 Game tree.................................................................................................................. .........60 3-2 Map of Florida with Marion County identified.................................................................61

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8 LIST OF DEFINITIONS Bayesian Nash equilibriu m Nash equi librium at the interim stage where each player selects a best resp onse against the average of the best responses of competing players (Gibbons, 1992; Osborne, 2004). Bertrand model Model of price competition in which each firm sets its own price and treats its ri val's price as fixed at its current level (Kuhn &Vives, 1995). Complete information When each player knows all the rules and strategies of the games (Gibbons, 1992; Osborne, 2004). Dynamic game Described when each player can move sequentially so that no player can observer the other players action (Gibbons, 1992). Incomplete information Assumed that ea ch player did not know the payoffs of the other players (Fink et al., 1998, p18). Nash Equilibrium or equilibrium An action profile a* with the property that no player i can do better by choosing an action different from ai*, given that every player j adheres to aj* (Nash, 1950b). Oligopoly Market Market condition in which sellers are so few that the actions of any one of them will materially affect price and have a measurable impact on competitors (Stigler, 1964). Perfect Bayesian Nash equilibrium Profile of complete strategies and a profile of complete beliefs, such that given the beliefs, the strategies are unilaterally not improvable at each potential decision node that might be reached. Also, the beliefs are cons istent with the actual evolution of play as pres cribed by the equilibrium strategies (Gibbons, 1992; Osborne, 2004). Player Identified as a list of everyone involved in the game (Gibbons, 1992; Osborne, 2004). Rational choice Defined as the action chosen by a decision-maker is at least as good, accordi ng to her preferences, as every other available action (Osborne, 2004, p6). Strategic setting Defined as situ ations of interdependence in which

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9 one person decides the be st behavior (Gibbons, 1992; Osborne, 2004). Subgame-perfect Nash equilibrium Equilibri um in which the strategies are a Nash equilibrium, and within each subgames, the parts of the strategies relevant to the subgame make a Nash equilibrium of the subgame (Gibbons, 1992; Osborne, 2004).

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10 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy NASH EQUILIBRIUM OF HO TEL PRICING STRATEGIES: A BERTRAND MODEL OF INFORMATION SHARING By Sungsoo Kim May 2008 Chair: Brijesh Thapa Major: Health and Human Performance The lodging industry uses di verse pricing strategies to maximize revenue, while maintaining customer satisfaction. Given the un certain nature of decisi on-parameters, such as price or demand conditions, shar ing information among competitor s can dramatically impact a hotels behavior. Information sharing among comp etitors can enhance the quality of strategies because it reduces the uncertainty of market environments, and enables correlation of price strategies. Game-theoretic models can assist hotel managers to characterize the incentive for firms to share or not to share private informa tion with competitors in order to establish an optimal pricing strategy. Game theory is the study of multi-person decision problems, which examines strategic interactions between decisi on-makers (e.g. hotel managers). The optimal strategy is achieved by finding Na sh equilibrium (Nash strategies ), which is the most commonly used solution concept in game theory. This study examined decisions of hotels to sh are or not share priv ate information with competitors to maximize profits via game-theoretic model. In particular, a two-stage model was developed where hotels made shari ng decisions in the first stage and then, in the second state, competed with each other in setting prices along the lines of a standard price competition model. More specifically, first, informa tion sharing decisions were only made after each hotel learnt its

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11 own market demand (low versus high), and not before. Second, both symmetric and asymmetric situations about cost and demand in the price competition model were analyzed. The asymmetric situations about different costs and/or demands were employed to create various scenarios about the types of competitions among hotels. Data were collected in three market segm ents (upscale, midscale, and economy) among five hotels in Marion County, FL. This study identified market competition, marginal cost, market demand, size of hotel, a nd fluctuation of demand (seasonali ty) as significant indicators in resolving or establishing an op timal pricing strategy with respect to information-sharing behaviors in the lodging industry. Some of key results are summarized. First, regardless of the competitive nature of the market, similar sizes and types of hotels generally share their demand information with each other when low demand signal is identified, while they conceal demand information with high demand signal. Second, if there is a medium or high level of competition, hotels that are simila r in type, but differ in size share their demand information with each other when they face low demand signal. However, as market competition increases, the relatively smaller sized hotels c onceal demand information from larger hotels when they face low demand signal during high-lev el of competition. These hotels conceal demand information when high demand signal is identified, regardless of the extent of competition. Third, hotels, which are similar in type, but differ in size, face a fluctuation of demand (seasonality). They conceal their dema nd information with high demand signal when there is low-level of competition. But, the re latively larger hotels, wh ich also have a higher fluctuation share demand information when they face low demand signal during low-level competition. Results of this study have contributed to theoretical and managerial implications with regards to information-sharing behavior s among hotels and optimal pricing strategy.

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12 CHAPTER 1 INTRODUCTION The lodging industry h as expanded immensely in recent decades. There are approximately 14 million hotel rooms globally with more than 4 million rooms (about 28.6%) located in the U.S. In 2006, the U.S. lodging industry employed 1.25 million people and yielded $22.6 billion in pretax profits. Also, revenues grossed at $122.7 billion (Lodging Indu stry Profile, 2007). The lodging industry faces highly competitiv e markets since the number of rooms continues to increase with new hotels, resorts, and other lodging facilities (Angelo & Vladimir, 2004). Overall, the average occupancy rate has sli ghtly decreased in the last few decades. For example, the national average occupancy rate in 2 000 was at 62% with $97 billion in sales. In the 1990s average occupancy rate wa s at 64% ($60.7 billion in sales), and 70% in the 1980s ($25.9 billion in sales) (History of Lodging, 2007). In contrast, the national average daily room rate (ADR) of the lodging industry gradually increased: $75.31 in 1996, $82.52 in 2003, $86.23 in 2004, and $90.88 in 2005. Given the competit ive nature of the industry in demand and supply, it is critical for deci sion-makers (e.g., hotel managers) to understand the dynamics of ADR and occupancy rate in order to generate profits and secure fi nancial stability and growth in the lodging business. Hence, the ability to manage an effective pricing strategy with respect to ADR and occupancy rate is monumental in competing successfully in the industry. The lodging industry has establis hed diverse pricing strategies in order to maximize or optimize revenue and profitability, while ma intaining customer satisfaction (Lewis & Shoemaker, 1997). In particular, the ADR rule of thumb is pervasive in the lodging industry in which hotels should generate $1 in ADR per $1,000 in value per guest room (DeVeau, 1996; ONeill, 2003). Moreover, Nagle and Holden (1995) noted that room s prices should be established above and beyond all co sts associated with the production of the room. However,

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13 this cost-based pricing posits a problem of over-pricing during off-season and under-pricing in the high season as unit cost always fluctuates with sales volumes. Another pricing strategy widely adopted in the lodging i ndustry is fencing, which is de signed to allow customers to segment themselves into appropriate pricing cat egories based on their wi llingness to pay (Hanks, Cross & Noland, 1992). This strategy is particularly useful when a hotel wants to sell discounted rooms to one segment of customers without the sacrifice of the higher-rate customer segment (Carroll, 1991). Fenced pricing separates business travelers from leisure travelers, and attracts customers that otherwise would not have stayed in the respective hotels (Hanks et al., 1992). The industry has also adopted the most common method of pr icing (i.e., yield management), which is the process of allocating th e right type of capacity to the right type of customers at the right price in order to establis h effective pricing strategies (Kimes, 1989; 1994; Orkin, 1989). Yield management assists hotel managers to maximize revenues by adjusting guest-rooms rates. For example, hotels would increase average room rates when demand exceeds supply, and maximize occupancy by decr easing rates when s upply surpasses demand (Jones & Hamilton, 1992). However, current yiel d management tends to neglect analysis and choice for future demand (Orkin, 1988), market conditions, and uncertain price and demand conditions (Jauncey, Mitchell & Slamet, 1995). Thus, yield management may not correlate output or pricing decisions to ac tual market conditions as the parameters (e.g., cost, demand, price) are uncertain durin g most times. To this end, a thoughtfu l and integrated pl an to establish pricing strategies is necessary in yield management in the front -desk, reservations, and sales departments as they play a consequential role in yield-related deci sions (Kimes, 1994). Given the uncertain nature of decision-para meters, such as price and demand conditions, sharing information among competitors can drama tically impact firms behavior (Gal-Or, 1986;

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14 Kuhn & Vives, 1995). In general, hotels use mediated communication mechanisms via trade associations to whom the firms submit private information, which then makes that information available to other firms (Krishna, 2007). Trade associations period ically gather and accrue sales information from participating firms in the i ndustry and then the aggregate information is disseminated (Kirby, 1988). The American Hotel & Lodging Association (AH&LA), an industry trade associat ion, produces a Lodging Report on a re gular basis that disseminates information from participating hotels about occu pancy and average daily room rate. Similarly, Smith Travel Research periodically reports in formation about hotel operations (Lodging Market Data Book, 2007). Information includes, ADR, RevPar, demand, supply, and revenue by each respective hotel based on regions or cities. Hotels that participat e in Smith Travel Research are both senders and receivers of such confidential information. In addition, hoteliers often check prices of their competitors via hotel sites or independent travel websites, such as Expedia, Orbitz, a nd Travelocity (Best Hotel for Any Budget, July 2007). Although the room prices of most hotels are easily identif ied, however, in most cases hotels list only limited pr ice information (e.g., discounted pr ice). Also, to p-line financial indicators (e.g., ADR, occupancy rate) that often explain a hotels bottom line are difficult to obtain from the respective websites (ONeill & Mattila, 2006). Moreover, of significant relevance to the lodging industry are direct indicators in which executives place the most importance to hotel management, such as occupa ncy rate, average room rate, gross operating profit, marginal cost, and room sales (Geller, 1985). This information is fostered through information systems in a hotel, whereby managers have access to historical information used for budgeting and financial decisions (e.g., room price). Unfortunately, Geller (1985) found that hotel information systems fail to provide timely and predictive data for hotel operations due to

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15 the lack of the correct informa tion from competitors. Although hotel mangers can obtain broad pricing information from websites (e.g., hotel site s; independent travel s ites), the most accurate way to establish pricing strategies is to inves tigate current market rates offered by competitors (Badinelli & Olsen, 1990). Therefor e, in order to establish eff ective pricing st rategies, hotel managers need to interact with their compe titors and build relationships to further share confidential information. In a situation where decision-makers interact with each other, game-theoretic models can assist hotel managers to comprehend timely and prognostic information. Game theory examines strategic interactions between decision-makers (Gibbons, 1992). In strategic games, a decisionmaker selects strategies, which maximize profits along the line of the stra tegies the other agent chooses. In particular, inform ation sharing can enhance the qu ality of their strategies to competitors in a situation where a competitive ac tivity (price or demand competition) prevails in a market environment (Osborne, 2004). The rationa le is that game-theoretic models help to characterize incentives for firms to share or not to share private information with competitors (Cason, 1991). This can be achieved by seeking Na sh equilibrium, which is the core base of game-theoretic models (Osborne & Rubinste in, 1994). This notion captures a steady state (optimal strategy) of the play behavior in a ga me-theoretic model in which each firm holds the correct expectation about the other playe rs behavior and ac ts rationally. Nash equilibrium (optimal pric ing strategy) should be develo ped to associate their private information with the decision of hotels to share or not to share information with their competitors, so that hotel executives can determin e or predict their revenue and profitability. Furthermore, this approach can enhance the deci sion of hotel managers on hotel-rooms pricing

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16 strategy in addition to yield ma nagement. Thus, a hotel manage rs behavior can be explained and predicted by information sharing based on a game-theoretic model (Kuhn & Vives, 1995). Statement of Problem Game-theoretic models have been examined in social and behavioral sc iences (Fink, Gates, & Humes, 1998; Brewer & He nsher, 2000; Murphy, 2002; Cox & Deck, 2005; Fedenberg & Maskin, 2005; Wen, 2005; Engle-Warnick & Slonim, 2006). In particular, game-theoretic models have been applied to information shar ing behaviors in order to maximize profits. Furthermore, the decision of firms to share or not to share information with other companies (e.g., competitors) has been examined with various topics such as price competition (Cason, 1992; Gal-Or, 1985; Moorthy, 1988; Sakai, 1990, 1991; Shaked & Sutton, 1982; Vandenbosch & Weinberg, 1995; Vives, 1984), demand compe tition (Cason, 1992; Gal-Or, 1985; Sakai, 1990, 1991;), information exchange (information shar ing) (Clarke, 1983a; 1983 b; Doyle & Snyder, 1999; Jimenez-Martinez, 2006; Li, 1985; Kir by, 1988; Krishna, 2007; Kuhn & Vives, 1995; Novshek & Sonnenschein, 1982; Shapiro, 1986) or transmission (Gal-Or, 1986), and cheap talk or false information (Farrell, 1987; Farrell & Rabin, 1996). Previous studies about incentiv es in oligopoly markets whethe r to share or not to share information have been classified in terms of th e type of information sh aring arrangement (Kirby, 1988). Numerous researchers have examined situ ations where firms inde pendently select the amount of private information to be shared (Gal-Or, 1985; Li, 1985; Novshek & Sonnenschein, 1982; Vives, 1984). Others have investigated quid pro quo information shar ing arrangement, which means the condition that the trade associa tion provides the aggregate private information to any firm willing to pay. Nevertheless, the results for the two types of sharing arrangement are identical because each firm regards information sh aring as beneficial in the market place. Along

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17 the same line, Novshek and Sonnenschein (1982) indicated that under Cournot competition (demand competition), firms are never strictly better off by sharing information. Under price competition, Vives (1984) noted that firms might raise profits when they share their demand information with competitors. Likewise, Shapiro (1986) mentioned that when firms share their private cost information, their expected profits increase. In contrast, Gal-Or (1985) suggested that firms do not share their private cost inform ation in price competition. Cason (1991) further expanded the argument that a firm conceals cost information if the goods are substitutes, while firms share cost informa tion if the goods are complements. Collectively, the results suggest that firms optimal strategy to maximize profits varies w ith the type of competition. The nature of goods also creates variations in the firms information sh aring strategies. In the tourism and hospitality industry, the nature of the pr oduct sold is quite diffe rent from that of traditional products, such as automobiles and comput ers. Much of the product in the tourism and hospitality industry is intangible, and after tourists consumption of products, ther e is no tangible rate of return (Moutinho, 1987). The nature of product in the hotel busin ess is perishable, so hotels should sell more rooms each day even though the prices may be discounted (Kimes, 1994). The rationale is that hotels empty rooms repres ents an opportunity lost that can generate profits (Taylor, 1998). Therefore, competitive conditions (price or demand competition) and the nature of products create further combinations of different scenarios. For each scenario, as an applicable solution exists based on theoretica l reasoning and mathematical modeling. To this end, a model based on game-theoretical reasoning (i.e., game th eory) can offer an opport unity to investigate information sharing behavior under price competiti on in the tourism and hospitality discipline.

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18 The rationale is that the equilibrium for firms in the tourism and hospitality industry with respect to sharing of private information with competitors may differ compared to traditional firms. Since game-theoretic models have not been tested in the context of information sharing in the tourism and hospitality business, the potential implication to the discipline and business could be enormous. Purpose of Study The purpose of this study was threefold. Fi rst, a price competition model was developed based on the most significant indicators for hotel managers, which included hotels average daily room rate, occupancy rate (ADR), marginal cost, and market dema nd. In particular, a two-stage model was developed where hotels shared decisions in the first stage and then, in the second stage, competed with each other based on the sta ndard Bertrand model. S econd, all the strategies in the two-stage model were examined to fu rther determine either subgame-perfect Nash equilibrium or Bayesian perfect Nash equilibrium, which in sured that the predominated outcomes were based on rational behavior by hotels managers. Third, to examine the applicability of a two-stage game-theoretical mode l in the tourism and hospitality industry. This exploratory research examined hot el-pricing strategies at Nash equilibrium using game theoretic modeling. In this research, an optimal strategy(s) (i.e. Nash equilibrium) for hotels to share or not to share their private information with thei r competitors in order to maximize profitability was undertaken. More specifically, this res earch was conducted to answer the following question: What are Nash equilibria (Nas h strategies) of hotel pricing strategies in a Bertrand model with respect to information sharing behaviors among hotels?

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19 Delimitation Game theoretic models can be examined with four classes of games: static games of complete information, dynamic games of complete information, static games of incomplete information, and dynamic games of incomple te information (Gibbons, 1992; Osborne, 2004; Zagare, 1984). In a static game, players move simultaneously, while players sequentially move in a dynamic game. Players with complete inform ation recognize not only the rules of the game, but also the preferences of th e other players over the set of outcomes (Zagare, 1984). For example, in a static game of complete information, players know all the rules of the game and each others preference, and move simultaneously. Furthermore, four notions of Nash equilibrium in game theoretic models are recognized within the above four classes of games. These include Nash e quilibrium, subgame-perfect Nash equilibrium, Bayesian Nash equilibrium, and perfect Bayesian Nash equilibrium (Gibbons, 1992). However, the scope of this current study was largely limite d in a static game situation with incomplete information in order to develop Bertrand model (i.e., price competition model). The Bertrand model was further examined th rough price competition between oligopoly firms (hotels) which resulted in each to charge a price that would be charged under perfect competition, known as marginal cost pricing. Finally, a subgame-perfect Nash equilibrium and perfect Bayesian Nash equilibrium were primar ily sought in order to determine optimal price strategies in the lodg ing industry.

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20 CHAPTER 2 LITERATURE REVIEW Hotels Pricing Strategies The lodging industry usually esta blishes a variety of strategi c prices to maximize revenue and profitability while maintain ing consumers satisfaction (Lewis & Shoemaker, 1997). The ability of managing effective pr icing strategies affects a companys growth and profitability more quickly and directly than any other strate gic decision in business. The lodging industry has adapted yield management into their decision-making process to assist managers to set up an effective pricing strategy. To examine pricing strategies that have b een used in the lodg ing industry, hotels competition and their information-sharing behavior are examined. Also, yield management is reviewed with respect to hot els pricing in the context of decision making-process. Competitions Versus Informatio n Sharing in Hotel Businesses Hotel managers often check prices of competitors on their Websites or independent travel websites, such as Expedia, Orbitz, and Travelocit y to determine their own prices ("Best Hotels for Any Budget," July 2007). Although websites provide limited price information of competitors, such as cooperated rates or discounted rates, the room prices of most hotels are easily identified. However, hotel managers may not be aware of topline financial indicators through websites, which explain a large amount of the variation in a hotels bottom line (ONeill & Mattila, 2006). These include, occupancy rate ADR, revenue per available room (RevPAR). Furthermore, the age of the hotel, the type of hotel, and its brand affiliation are additionally important factors to affect the ov erall pricing strategy. To this end, the information of room prices via websites is not enough to establish pric ing strategies, but merely used as references (ONeill and Mattila, 2006).

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21 Firms often use a mediated communication m echanism in trade associations (Krishna, 2007). In general, this mechanism has a neutral third party to whom the firms submit private information, which then makes that information available to other firm s. In Kirbys (1988) survey on firms information exchange behavior trade associations periodically gather and accrue sales information from participating fi rms in the industry, and then the aggregate information is disseminated. Similarly, hotels have a mechanism by which they can share certain information. The trade asso ciation, the American Hotel & Lodging Association (AH&LA), produces a report called AH&LA's newsletter (e-newsletter) and lodging report in which information from participating hotels about o ccupancy and average daily room rate (ADR) are disseminated. Smith Travel Research is also an other agency that provide s occupancy percentage and ADR for registered firms. Additional inform ation about hotels scale, location type, region, and number of rooms can also be obtained (ONeill & Mattila, 2006). According to lodging market data book (2007), Smith Trav el Research periodically provi des lodging marketing data in their confidential report This data includes information about ADR, RevPar, demand, supply, and revenue by each hotel based on regions or cities based on mont hly and yearly basis. The information is largely referenced to establish pricing strategies. Part icipating hotels are both senders and receivers of this confidential information. Furthermore, of significant relevance to the lodging industry, Geller (1985) identified direct indicators in which executives place the most importance to their hotel management. These include, occupancy rate, average room ra te, gross operating profit, marginal cost, and room sales. The information is fostered through information systems in each hotel, whereby managers have access to historical information used for budgeting and financial decisions (e.g., room price). Additionally, a hotel and thei r competitors virtually face the same market

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22 conditions, and as a result, the information (e.g., ADR; marginal cost; occupancy rate) collected among competitors is useful (I ngram & Roberts, 2000). For ex ample, in Sydney, Australia competing managers in hotels exchanged price and occupancy information on a daily basis. This helped managers to analyze the competitors performance, industry trends, and establish pricing strategies accordingly (Ingr am & Roberts, 2000). Information sharing between hotel s is largely affected by pers onal friendship. Friendships among competing managers can yield legitimate benefits by improving collaboration (Ingram & Roberts, 2000). In particular, the expected benefits of friendships with competitors can be categorized by collaboration, mitigation of compet ition, and information exchange. Uzzi (1996) found that competitors used to collaborate in order to add value for customers, and share information to solve several cri tical issues or joint problems. For instance, when a hotel is overbooked, they usually send customers to a comp eting hotel because hotel managers can trust that the referred customers would be well treated based on their personal re lationship. In terms of information sharing among hotel s, higher levels of trust and empathy, as well as norms of reciprocity are necessary (Uzzi, 1996 ). To this end, hotels can improve the depth and quality of information exchange. Therefore, hotel managers need to share critical information (e.g., ADR, occupancy rate) with competitors in order to bette r establish an overall effective pricing strategy. Pricing Strategies Hotels use the common price method that th ey should generate $1 in ADR per $1,000 in value per guest room (DeVeau, 1996; ONeill, 2003). According to this technique (ADR rule of thumb), a 100-room hotel developed for $15,000, 000 would be valued at $150,000 per guest room, so that this property should generate a $150 ADR, which can be offered to potential customers. Hotel managers make use of the ADR rule of thumb in order to assist in decisionmaking in terms of a new hotel development to es tablish room rates and value existing hotels.

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23 The ADR approach to establish guest room rates ca n be a reliable predictor of a hotels sale price (ONeill, 2003). However, Collins and Parsa (2006) argued that pricing decisions of a guest room should be based on additional factors, such as demand relative to the available supply of a product or service, as well as the quality of their compe titors product, the cost of a substitute product, value, and brand. The overall pricing strategy of a hotel needs managers judgment and future demands based on precise calculation using the f actors noted earlier (N agle & Holden, 1995). More importantly, Collins and Parsa (2006) noted that the overall pricing strategy is facilitated by proper communication with cust omer groups targeted by the hotel in order to maximize revenue and profitability. Nagle and Holden (1995) also indicated three different pric ing approaches which hotel mangers can consider in overall pr icing strategy of hotel rooms. First, cost-based pricing is a financially driven approach in which products are priced to yiel d an equitable profit above and beyond all costs associated with the production of the product. But, this approach may not appropriately determine the unit cost associated with the product since unit costs fluctuate with sales volumes. Hence, this drives over-pricing in weak markets, and under-pricing in strong markets, which is not an effective strategy. Second, customer-driven pricing is a market-driven approach where prices are determined by the amount that customers are willing to pay for a product. However, customers are not motivated to be candid relativ e to the price that they are willing to pay for a product. Moreover, firms al ways try to increase customers willingness to pay a price than that reflected in the products true value. Lastly a market-driven approach such as, competition-driven pricing is determined by the pricing level at which a target market-share level is attained by firms. This strategy often lead s to inappropriate price cutting as firms seek to

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24 gain more market share (Collins & Parsa, 2006). This is due to the fact that any business, including a hotel always faces a trade off between losing a customer because of a high price and losing a customers surplus due to a low price (Bitran & Susana, 1997). In hotel pricing, there are two different perspectives of comprehending hotel-pricing strategies: economics and marketing perspectives (Chung, 1998). Each pers pective is reviewed in the following section. Economics Perspectives Meek (1938) developed a theory of hotel room rates based on the fundamental principles of supply and demand in the market. The rationa le is that the classi cal economic analysis revealed that price is determined in terms of supply and demand. He further noted that the lodging industry was characterized by imperfect competitive market structures, and an action of a hotel influenced other hotels by offering a similar rooms prices for sale. He further indicated that the potential for rooms rate difference is due to an imperfect knowledge of competitors prices. Hence, hoteliers should establish price strategies under the assumptions of short-term analysis, rational economic decisi ons, complete knowledge of occupancy, homogeneity of dates, and similar types of hotel rooms (Meek, 1938). Ho wever, Meeks research neglected that total costs did not sufficiently explain the hotel room pr ices, as well as he did not consider the demand prediction, although it was the first research that addressed hotel room ra te pricing strategies (Shaw, 1984). Shaw (1984) insisted that economic theory pr ovides sound theoretical pricing models (e.g., Bertrand Model; Cournot Model; Peak Load Prici ng Theory). For example, peak load pricing theory considers product non-storab ility, fluctuating demand, and high fixed cost to establish hotels pricing strategies (Aranoff, 1995). Th is theory explains why high prices should be

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25 charged during periods of full capacity and low pr ices during periods of idle capacity (Aranoff, 1995). In addition, lag effects of price can increase hotel room rates, and price elasticity of demand strongly affects the prici ng strategies (Cournoyer, 1972). In the lodging industry where fixed costs are high and variable co sts are low, costs play a secondary role to demand in pricing. Rather, the critical factors that influence pric ing is based on the type of customers, local competition, trends in room sales, time of year (seasonality), and so forth. Conversely, Kraus (2000) argued that internal cost is of compara tive high importance relative to other factors. The rationale is the fact that in th e lodging industry profitability hinge s substantially on the ability to fill room capacity. Therefore, hotels sell hotel ro oms at deeply discounted rates when revenue is greater than the cost of opening the room (Relihan, 1989). In othe r words, the marginal cost of selling another inventory is far less than th e marginal revenue (Kimes, 1994). Thus, hotel managers should identify an appropriate discoun t level to increase sales while securing enough inventories to sell to latebooking rack-rates customers. The Hubbart Formula is one of the widely ad apted approaches to determine hotels room rates (Coltman, 1994). This formula is based on the desired profit for in vestors, and costs are directly or indirectly related to rooms operation. In particular, this approach includes six distinct steps. First, the desi red profit has to be determined, and then converted into pre-tax earnings. Second, fixed charges, such as propert y taxes, depreciation, interests, and rent are added to the desired pre-tax earnings. Thir d, undistributed operat ing expenses, including administrative and general, human resources, mark eting, and maintenance are estimated. Fourth, estimated department income or losses of othe r revenue centers are added or subtracted to determine required income. Fifth, rooms departments direct cost s, such as payroll and related

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26 expenses and other direct expenses have to be added to determine required rooms department revenue. Lastly, the average room rate can be determined by dividing th e required room revenue by rooms expected to sell (Coltman, 1994). Gu (1997) applied optimization th eory in the lodging industry in order to establish pricing strategic model (i.e., a quadratic room pricing model) under the assumption of a negative relationship between the demand fo r hotel rooms and its rates. This model explained that optimal hotels room rate is a function of variab le costs and two features of the demand for hotel rooms: potential demand for rooms and the price sensitivity of the demand. However, this model has several shortcomings. As Gu (1997) noted, the demand for a hotel is affected by not only room rates, but also other factors such as, seas onality, disposable inco me, service quality and competition. Hence, considering these factors it was recommended to establish pricing strategies under price competition. Marketing Perspectives In the marketing perspective, hotel mana gers establish hotel room rates based on customers viewpoint (Lewis, 1986; Kimes, 1994). In general, customers in the service industry pay differential prices depending on when they make their reservations (Kimes, 1994). For example, customers are charged different rates fo r the same flight. They also receive specific benefits (e.g., low-price ticket) in accepting certain restrictions (e.g., nonrefundable fare). Similarly, all guests staying during the same night in hotels w ith comparable amenities and rooms receive different rates. The rationale is that hotels use multiple prices on their guest rooms to optimize their revenue. These prices include premium, rack, corporate, and discount prices. As noted from Figure 2-1, if a hotel sells 80 r ooms with four different prices, it generates $4,000 of realized revenue. However, the hotel could generate more profits if they sell the rooms at a premium price or rack rate (Hank et al., 1992).

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27 Hank et al. (1992) further men tioned three strategic approaches to rate guest rooms that include a single rate, rates by room type, and fenced pricing. A single rate is easy to administer and explain to customers. More over, that rate could change ba sed on season or the day of the week. However, this approach does not meet daily demand swings, accommodate customers price sensitivity, and more importantly will not maximize revenues. Secondly, hoteliers can establish room rates according to differential room characteristics (e.g., size, view floor level). Many hotels currently use this approach because customers notice the room differences offered at different rates. Thus, it ameliorates the si ngle rate approach by allowing a hotel to offer different rates on a daily basis in order to ma ximize revenues. However, this approach to segmentation may not be feasible in markets wh ere customers are unwilling to pay for upgraded rooms. Further, it may be difficult for front-des k attendants and reservations sales agents to manage different prices in operation. The last approach is to erect fe nces (logical, rational rules or restrictions) that are designed to allow customers to segment th emselves into appropriate rate categories based on their needs, behavior, or willingness to pay. These fences include advance reservations and non-refundable advance purchases (Hank et al., 1992). This appro ach is useful because it allows a hotel to sell discount rooms to one segment of customers without allowing the higher-rate customers to trade down. For example, opening up discounts when demand is weak and closing off discounts during strong demand periods, so that hotels must have regular rates that are correctly positioned for the marketplace. Fenced pricing is the a ppropriate direction for at least a portion of its discounted rates (Carroll, 1991). Furthermore, Ha nk et al. (1992) noted that the fences serve

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28 their purpose as follows: 1) to sepa rate business travelers from leisur e travelers, and 2) to attract customers who otherwise would not have stayed in hotels. Similarly, Lewis and Shoemaker (1997) noted that hotel mangers can use reference prices to establish guest rooms rate. The reference pr ice of any service or good is the price that a customer perceives as an appropria te price for that item. The refe rence price is composed of the price last paid, or the average of all prices cust omers have paid for similar services (Zeithaml & Bitner, 1996). However, reference prices for se rvices are generally fuzzier in the customers mind than for manufactured goods because service products, such as hotels rooms vary widely in size, features, location, and attendant se rvices (Lewis & Shoemaker, 1997). Moreover, customers consider a price range instead of the exact price to be an appropriate price. To this end, Zeithaml and Bitner (1996) stated that the service industry faces at least three complicating factors in pricing. First, customers often have inaccurate or lim ited reference prices for services. Second, customers use price as a key signa l for quality. Third, monetary price is not the only relevant cost for service customers. As a result, pricing of service firms must be based on the customers view of the relationship between price and value; and not based on cost-driven prices (Lewis & Shoemaker, 1997). For example, Gabor and Gr anger (1966) indicated that customers are determined to set the highest and lowest prices fo r selected items that they would purchase. This allows firms to determine the upper and lower lim its for products. A price that is above the upper limit can cause the item to be judged as bei ng too expensive, which suggests quality levels and attributes that exceed those desired by customers, and vice versa. The concept of a price range whereby a customer enters the market with two-price limit in mind is a far more realistic

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29 approach than reference pricing. The rationale is that a price range does not assume that the customer has a perfect knowledge of current market prices (Lewis & Shoemaker, 1997). According to Kraus (2000), internal cost cons iderations are of rela tively high importance, especially in the lodgi ng industry whereby fixed co sts are high, and profitability heavily depends on the ability to turn-over hotel rooms daily. Although economic models ar e useful in analyzing pricing strategies in these cont exts, however in establishing shor t-term prices hotel managers often need yield-management to change pricing strategies in response to current or potential demand changes with available supply. Yield ma nagement is a proven technique for maximizing hotel room revenues (Relihan, 1989) and is further reviewed in the following section. Yield Management Yield management was first introduced a nd used by the airlin e industry. Yield management is the process of allocating the right t ype of capacity to the ri ght kind of customer at the right price so as to maximize revenue or yield (Jones & Hamilton, 1992; Kimes, 1989; 1994; Orkin, 1989). Prior to yield management, hot els had front office practices based around maximizing occupancy with discounts from rack rate to get business (Jones, 1999). Discounts are usually applied to specific categories of custom ers, such as those with a loyalty card, working for key account business clients, and tour operators More specifically, in chain hotels, there are myriad types of discounts as more than 80% of the business are at below rack rate (Jones & Hamilton, 1992). Yield management tries to maximize guest-r oom rates when demand exceeds supply, and maximize occupancy at the expense of aver age rate, when supply exceeds demand (Jones & Hamilton, 1992). Kimes (1989) further explaine d that yield management consists of two separate, but related parts: room-inventory management and prici ng. The inventory management process deals with how different types of rooms are to be allocated to demand. The pricing

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30 procedure is concerned with the be st prices to charge in different situations. In addition, the yield statistic, a basic element for yield manageme nt is defined as the occupancy rate multiplied by the rate efficiency which is the average room rate divided by the maximum room rate (rack rate) (Orkin, 1988). Furthermore, Orkin (1988) suggested that a hotel s effectiveness in improving yield should be based on its infrastructure in the following four critical factors. These included forecasting, systems and procedures, strategi c and tactical plans, a nd feedback systems. For yield management, good forecasts of daily rooms demand with a system for continuous updates are necessary. Due to season ality, hotel managers need diffe rent strategies that generate higher yields (Kimes, 1994). When demand is high, a hotel can restrict or close availability of low-rate categories and packages to transients, a nd further require minimum lengths of stay. On the other hand, during the low demand season, a hotel can provide rese rvation agents with special promotional rates to offer transients who balk at standard rates, and solicit group business from organizations and segments that are charac teristically price sensitive. However, many critical decisions in hotel busin esses are made by a casual continua tion of past practices, rather than analysis and choice for future dema nd (Orkin, 1988). Additionally, high competitive market environments surround hotel businesse s (Kimes, 1994). Thus, the importance of thoughtful and integrated plans is fundamental in yield management for front-desk, reservations and sales departments, as collectively they play a consequential role in yield-related decisions. Kimes (1994) noted that there are two key success factors in yield management, which are maintaining the balance between the reference transaction and educating customers about the practice of yield management. Since the airlines have been using yield management longer than any other industry, customers are conditioned to u nderstand that they are charged different fares for the same flight, and will receive specific be nefits (e.g., low-fare) if they accept certain

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31 restrictions (e.g., non-refundable fares) (Kimes, 1989). In othe r words, customers that buy a similar seat seem to buy a different product because of the associated restri ctions. However, in the lodging industry, restricti ons are not in place although custom ers pay differentiated prices depending on when they reserve a hotel room. The rationale is th at a customer who pays more for an analogous room with a si milar service may not perceive a difference in the service, and hence may view the situation as unfair (Relihan, 1989). Moreover, owing to the perishable nature of products in the l odging industry, a hotel should sell more rooms each day because a hotel s empty room represents an lost opportunity (Kimes, 1994; Taylor, 1998). Thus, a hotel must decide to discount prices to sell more hotel rooms while maintaining enough inventory to sell to late-booking full-price customers. In other words, marginal cost of selling another inventory is far less th an the marginal revenue (Kimes, 1994). For example, hotels sell a certain number of rooms at deep ly discounted rates so long as the revenue is greater th an the cost of opening the room (Relihan, 1989). With the use of yield management, hotels can adjust prices in seve ral ways. One method of pricing a hotel room is to a dd more services or products (e.g., meal or drink discounts) to the services sold at the increased pr ices (Thaler, 1985). Another method includes the service as part of a package, obscuring the price of the service. For example, customers may not know the price of a room when it includes wine and meals. The final method is to attach restrictions to discounted prices such as, 1) booking a certain length ahead of time, 2) staying for a minimum length of time, 3) staying over a particular night, 4) assessing a change or cancellation penalties, or 5) imposing a nonrefundable reservation. Therefore, to maximize revenue through yield management, hotels can advertise the various rates available and the restrictions or benefits associated with the ra te (Thaler, 1985).

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32 Relihan (1989) stated that yield manage ment should begin with an understanding of customers purchase behavior and a comparison of current demand with forecasts of future occupancy. Thus by identifying sales opportuni ties, a balance between supply and demand can be controlled through yield management because of the price where hotel rooms are affected by demand for those rooms. Relihan (1989) furt her noted that hotel guests are commonly grouped into roughly two segments; business and leisure, and each share distinct price-elasticity and timesensitivity characteristics. For example, leisure traffic nor mally books early, as holidays are planned well ahead in advance. Also, leisure tr avelers may be time sensitive to some degree, but price is the overriding factor in their decision. On the other hand, business bookings tend to be concentrated in the days immedi ately prior to a trip. Therefor e, hotel mangers should develop different pricing strategies in order to meet the differential needs for each customer segment (Relihan, 1989). Since hotels within a vicinity are closer subs titutes for each other, some hotels can reduce prices to attract more customers, otherwise, rooms would remain vacant (Kimes, 1994). In yield management, the actual booking level for a day shoul d be compared to a de sired or ideal pattern that is usually derived from sta tistical analysis of the hotels booking history (Relihan, 1989). The rationale is that a hotel can provide its full value to yield management system only with a foundation of accurate and specific information. Moreover, the most accurate way to establish prices is by researching the current market rate s offered by competitors, since this is how most customers determine their expected prices of st aying at a hotel (Badinelli & Olsen, 1990). Overall, yield management is concerned w ith the maximization of room revenues through the manipulation of room rates in a structured manner, consideri ng forecasted patterns of demand based on the predetermined market segments (Jauncey et al., 1995). Jones (1999) identified that

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33 managing yield tends to use price element (e.g., occupancy rate and rate charged) to achieve revenue maximization. However, rooms price can be differentiated on a number of criteria other than price, such as th eir in-room facilities, and locat ion within the property. The complexity of the decision-making processes in balancing differential demand from market segments with room availability at different pric es requires strategic pricing methods in order to maximize revenues and profits. Moreover, in or der to truly maximize revenue, space should be designated to market segments on the basis of to tal spending and room rate. However, current yield management theory and practice tends to ignore the non-rooms generating incomes by guests (e.g., restaurant and bar), which may vary widely between market segments (Jauncey et al., 1995). There are two non-traditional attempts of developing pricing models. A thresholdprices model is developed in the line with marg inal revenue, allocating one unit of capacity to a higher-yield customer (B adinelli & Olsen, 1990). In additio n, the process of determining a conventions room rates should consider hotels ro om rate and the number of rooms allocated at each price level (Schwartz, 1996). Theoretical Background of Hotels Price Competition Model Development of Game Theory The development of game theory began in the 1920s by Emile Borel and John von Neumann who created the base for game theory (uti lity theory). The basic ideas of game theory originated from the problems of maximum a nd minimum offered by Borel (1953a; 1953b) and von Neumann (1959) (Zhang & Zhang, 2003). La ter, researchers have applied more mathematical methods to study game theory to ma ke it more robust. Finally, Nash (1950a), a mathematician, developed a key concept of game theory (i.e., Nash Equilibrium) to be widely employed as an economic theory. Since then, game -theoretic models (i.e., game theory) have

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34 been broadly used in economics, and also in other social and behavioral sciences (Osborne, 2004). The development of game theory began from finite to infinite; from two players to many players; from certainty problem s to random problems (Zhang & Zhang, 2003). For example, a two-persons game refers to the game in which th e strategic space of participants is two persons. A finite game is a game where the strategic space of participants is finite. More importantly, game theory is built on two major assumptions: 1) maximization, which means that every player in the game is a rational decision maker with a clear understanding of the ga me structures, and 2) consistency, which implies that the players expe ctations of other player s behavior is correct (Gibbons, 1992; Mailath, 1998; Osborne, 2004; Zagare, 1984). Nonetheless, Mailath (1998) noted that a major complaint of other social sc ientists about game theory is the maximization hypothesis. The core of this argument is t hat any player not optim izing any firm not maximizing their profits will be driven out by market forces (Mailath, 1998, p1347), not from whether each player in the game is a rational decision maker or not. Players are not rational decision makers as they interact with other play ers over time, and with their behavior adjusting in response to their profits (payoffs), various choices or strategies have hist orically been received (Elster, 1989; Mailath, 1998; Skyrms, 1996; Young, 1996). T hus, players are not rational decision makers, but they can optimize their prof its through interactions with other players. Basically, each player can choose the best stra tegy (Nash equilibrium) through interactions over time. Elster (1989) also mentioned that successful behavior (e.g., Nash strategy) is more prevalent in the game not only because market forces select against unsuccessful behavior (e.g., a dominated strategy), but also because players imitate and learn successful behavior (Nash

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35 equilibrium). Therefore, each player in a game -theoretic model can choose the best strategy (Nash equilibrium) based on historical informa tion which conveys the information about how opponents are expected to play and the observati on of success or failure of various choices, which assists players to determine good stra tegies in the future (Mailath, 1998). Moreover, evolutionary dynamic game-theor etic models are developed without any assumptions on rational behavior or learning (Aoyagi, 1996; Sonsi no, 1997). Rather, the models posit a basic principle of differen tial selection in the game (Mailath, 1998). For example, players usually cannot determine any cycles (common knowledge) generated by the dynamics in a game, but apparently identify successful behavior in the game. Therefor e, without the two assumptions (maximization and consistency), ga me-theoretic models enable pl ayers (e.g., hotel managers) to find the best strategy (Nash equilibrium), whic h other firms will imitate and learn through the interactions. Along the same line, game theory was ini tially developed with games of complete information. von Neumann and Morgenstern (1944) noted that each player in games of complete information attempts to maximize individual benefits (or results), such as firms profits. Zagare (1984) argued that a game of co mplete information rarely exists in the real world. Although it provides a useful starting point for a players in vestigation of game situations, unrealistically, each game player knows all the information of the games and players preferences (Schmidt, 2003). Thus, the focus on game theory has shifte d into games of incomplete information. Furthermore, strategic behavior al interactions between players in games of incomplete information should be emphasized instead of individual maximization (Schmidt, 2003). Game Theoretic Model A game is an example of situations, such as a competitive activity (e.g., price competition) in which players contend with each other based on a set of rules in a game. In general, a game

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36 consists of a set of players, strategies, a nd payoff functions (von Ne umann and Morgenstern, 1944; Nash, 1950a; Gibbons, 1992; Osborne and Rubinste in, 1994; Osborne, 2004). Set of players, I the set of players (e.g. 1, 2, N) Set of strategies, S the set of all possible strategies (e.g. S1, S2, Sn) Specific strategies the strategies for player i Opponents strategies the strategies played by player is opponent Utility function, U the set of payoff profiles (e.g. U1, U2, Un) Payoff functions the function within the domain of action profiles and whose range is a real number (e.g. U: S R) and written as Ui (S1, S2, Sn) or Ui (si, s~i). Osborne (2004) noted that for tw o players with a finite number of strategies, the strategies of player i can be listed by rows, and the other players strategies by column creating a matrix in which the cells contain payoffs for each player. In this sense, Nash Equilibrium, which is the cornerstone of game theory can be characterized as the action profile s* in a strategic game with ordinal preferences in which every player i and every action (or strategy) si of player i, s* is at least as good according to player is preferences as the action profile (si,, s~j) in which player i choose si while every other player j choose sj*. For every player i, ui (s*) ui (s*,s*~i) for every action si of player i, where ui is a payoff function that represents player is preferences (Gibbons, 1992; Osborne, 2004). Osborne and Rubinstein (1994, p14) stated that the most commonly used solution concept in game theory is that of Nash Equilibrium, b ecause this notion captures a steady state of play in a strategic game whereby each player holds the correct expectation about the other players behavior and acts rationally. Eliza (2003) also noted the equ ilibrium strategy of a player

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37 represents not only the action plan a player act ually takes, but also the plan of action as envisioned by the other players. Similarly, rational choice by play ers (i.e., the theory of rational choice) is assumed in game theory (Gibbons, 1992; Osborne, 2004). According to this theory, Gibbons ( 1992) explained that a decision-maker must choose the best action (choice) based on his/he r preference from all available actions or choices. Mo re importantly, Eliza (2003) noted that players strategies in Nash Equilibrium must meet two requirements: the players must be responsive to ea ch other, and they must also represent what the other players expect each player to do. Thus, if for some reason player is actual strategy does not coincide with player js expectations, then Nash Equilibrium might not exist in the game (Eliaz, 2003; Osborne, 2004). Game theory is the study of multi-pe rson decision problems (Gibbons, 1992). Such problems arise frequently in economics, and social and behavioral scienc es (Osborne, 2004). For example, oligopolies present multi-person problems where each firm must consider what the others will do. Furthermore, the essence of an oligopolistic competition is interdependence, which means that the consequences to a busine ss (e.g. hotel) to employ of a specific pricing strategy also depend on the competitors pricing strategies (Chung, 2000). At the micro level, models of trading processes (e .g. bargaining and auction models ) involve game theory (Gibbons, 1992; Nash, 1950b). At an intermediate level, aggregation, labor a nd financial economics include game-theoretic models of firms behavior (Kagel & Ro th, 1995). At the macro level, international economics includes models in whic h countries compete or collude in choosing tariffs and other trade polices (Kagel & Roth, 1995). Gibbons (1992) further stated that there also are multi-person problems within a firm. For instance, many workers may vie for one promotion or several divisions may compete for the corporations investment capital. In the

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38 following section, static games of incomplete in formation are discussed, followed by information sharing behaviors. Static Games of Incomplete Information In static games of incomplete information, two important concepts are warranted: static games and incomplete information. Kagel and Ro th (1995) noted that in instances of two-person games, static games mean players i and player j move simultaneously, while during the game of incomplete information, players do not know a bout the game situations (Gibbons, 1992; Osborne, 2004; Zagare, 1984). In other word s, players partially know the st ructures of the games (e.g., who are the players; what are the sets of strategies, played by both players; what are the payoffs) (Gibbons, 1992). Osborne (2004) further stated that games of incomplete information are solved by rational players who do not play stri ctly dominated strate gies, which are common strategies for all game situations. The rationale is that players are never better off when they choose strictly dominated strategies But in other game situations, this approach may generate an inaccurate prediction about the play of the game. As such, it is very important to motivate and define Nash equilibrium (i.e., a solution concept) that can produce better predictions in a broad class of games. One simple way to define Nash equilibriu m (i.e., subgame perfect Nash equilibrium or perfect Bayesian Nash equilibrium) in the context of static games of incomplete information is that, if game theory is to provide a solution to a game theoretic problem, then the solution must be Nash equilibrium (Gibbons, 1992). In addition, each players predicted strategy must be that players best response to the other players st rategy (Gibbons, 1992; Osborne & Rubinstein, 1994; Osborne, 2004). This approach has been noted to be strategically stab le or self-enforcing because no single player likes to deviate from th eir predicted strategy (Gibbons, 1992). It can be mathematically defined as follows (Gibbons, 1992 p. 8):

PAGE 39

39 In the n-player normal-form game G = {S1, Sn; U1, ,Un}, the strategies (S* 1,, S* n) are a Nash equilibrium if, for each player i, S* I, is (at least tied for) player is best response to the strategies specified for the n-1 other players, (S* 1,, S* i-1, S* i+1,, S* n): ui (S* 1,, S* i-1, S* i+1,, S* n) ui (S* 1,, S* i-1, S* i+1,, S* n) for every feasible strategy si in Si; S* i, solves max ui (S* 1,, S* i-1, S* i+1,, S* n), where si Si Information Sharing Behavior Firms face a decision to share or conceal thei r private information with their competitors in order to maximize profits (Cason, 1992; Gal-Or, 1985; Gal-Or, 1986; Kuhn & Vives, 1995; Novshek & Sonnenschein, 1982; Shapiro, 1986; Vives, 1984). Cason (1992) indicated that firms have an incentive to share or not to share informa tion with their competitors. For example, when a firm shares its private information with compe titors, the firm has an opportunity to increase the market information, such as the cost of th e rivals product (Gal-Or, 1986), and to reduce uncertain cost or demand conditions (Cason, 1991). Thus, it helps the firm to generate profits in the competitive marketplace (Kuhn & Vives, 1995). However, when firms share or conceal informa tion, their expected profits hinge not only on market characteristics, such as monopolistic competition and oligopoly, but also on the type of competition (Bertrand competition vs. Cour not competition) (Cason, 1992; Gal-Or, 1986; Kuhn & Vives, 1995). Kuhn and Vives (1995) furt her noted that firms information sharing behavior varies according to the strategic variables (price vs. quant ity) used by a firm, as well as the type of uncertainty (cost uncertainty vs demand uncertainty) in Bertrand or Cournot competition. In other words, the outcome of information sharing behaviors allows firms to better maximize their profits (Raith, 1996). Furthermore, explanation of information sharing behavior about cost and demand under Bertrand or Cournot co mpetition is reviewed in the next section.

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40 More specifically, a focus on monopolistic competition markets and oligopoly market environments. First, the concept of information acquisition is explor ed to better understand information sharing behavior. Information Acquisition Information sharing is considered as a particul ar type of information acquisition. There are two main effects in any type of information acquisition (Kuhn & Vi ves, 1995). First, firms can make more precise and effec tive decisions with acquisition of information about market environments (Gal-Or, 1986). For example, if hotels receive rigorous information about their competitors ADR, occupancy rate, and marginal co st, it allows hotels executives to swiftly determine a pricing strategy that corresponds to the market competition environment (Geller, 1985). Second, information acquisition critically affects other firms (e.g., competitors) within the same market environment (Kuhn & Vives, 19 85). Doyle and Snyder (1999) mentioned that firms share information with their competitors because they are faced with demand or cost uncertainty, so that they can better correlate th eir output or pricing deci sions to actual market conditions (Cason, 1991; 1992). In other words, firms share their private information to acquire the right information about prevailing market co nditions, which helps to generate profits (Raith, 1996; Vives, 1984). Furthermore, if firms recogni ze that competitors have the information about the market conditions, including their competitors private information, these firms will adjust their strategies in the market place (Kuhn & Vive s, 1985). The rationale is that information sharing improves the information of a firm and th e market (Gal-Or, 1996). Through information sharing, firms can enhance the quality of their strategies to their co mpetitors (Kuhn & Vives, 1995), while the homogeneity of information among fi rms leads to a change in the correlation of their strategies (Raith, 1996) Kuhn and Vives (1995) furthe r emphasized that information

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41 acquisition from other firms has an effect only if it has some information about unknown or uncertain parameters, such as cost or demand. Cost or Demand Uncertainty in Monopolistic Competition As in the case of monopolistic competition, firms try to diminish the variance of the demand information, and their results from information sharing among competitors (Kuhn and Vives, 1995). Also, acquisition of additional inform ation from other firms increases the benefits, which enables maximization of profits (Gal-Or, 1 996). However, there is a trade-off between the benefits of precise information about uncertain cost or demand through information sharing, and the losses incurred from offering other firms more accurate information (Kuhn & Vives, 1995). For example, Gal-Or (1985) revealed that in th e case of monopolistic co mpetition with perfect substitutes information sharing, it reduces the pr ofits for firms. Furthermore, if goods are poor substitutes, firms gain an incentive to share their private in formation (Vives, 1984). Cost or Demand Uncertainty in Oligopoly Market Environment Kirby (1988) noted that firms sh are their private information with their competitors based on two conditions: first, when firms margin al costs increase in the oligopoly market environment, they will share their private informa tion with competitors. S econd, if the effect of increased precision in the information about unc ertain market conditions dominates in the oligopoly market, firms will share private information. Similarl y, firms precisely increase the information about other firms under oligopoly an d demand uncertainty. Also, competitor firms can increase information, which may benefit or negatively impact the firm that relies on the residual demand information in an oligopoly ma rket environment (Kuhn & Vives, 1995). The rationale is the fact that information acquisiti on from other firms not only improves the accuracy of information, but also influences the variab ility of the residual demand information in an oligopoly market (Kuhn & Vives, 19 95; Vives, 1984). In contrast under price competition in an

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42 oligopoly market, the residual demand informati on of a firm becomes more volatile when competitors improve the quality of information ac quisition. Interestingly, the degree of market competition does not significantly influen ce this phenomenon (Kuhn & Vives, 1995). Similarly, Cason (1992) examined the impact of decision-making on information sharing about uncertain demand and cost conditions in the noncooperative oligopoly market environments. He revealed that firms pric ing behavior may be influenced by information sharing decisions. For example, each firm has in centives in order to share information to reduce uncertainty and correlate their pr icing strategies. Moreover, he identified that information sharing is a form of non-market in teraction that firms may be able to use to alter the competitive environment where they operate. Clarke (1983b) also investigated incentives th at firms use to share or not to share private information about a stochastic market. He found that there is no mutual incentive for all firms within an industry to share pr ivate information unless they cooperate on strategies when information is shared in the market place. In other words, firms share their private information to maximize the social welfare, not their own profits although they act competitively in the market place. Furthermore, a universal in formation sharing proce ss does not exist in a competitive market if firms are not perfectly informed or are comp letely ignorant and indifferent towards information shar ing (Clarke, 1983b). Jimenez-Martinez (2006) furt her analyzed a two-person game-theoretic model to investigate information sharing de cisions with incomplete informa tion in an oligopoly market. He identified that information sh aring decision has a collective ac tion structure. Further, the incentive of firms not to share their private info rmation decreased with respect to the amount of information disclosed by other firms.

PAGE 43

43 Similarly, Raith (1996) dissected a two-stage model of inform ation sharing in an oligopoly market environment. In the first stage, each firm received a private signal with information about the true state of nature. In other words, firms may receive noisy signals about the intercept of a common demand function; while they may know their own costs precisely, but not the costs of their competitors (Clarke, 1983b; Novshek & Sonnenschein, 1982; Vives, 1984). In addition, Raith (1996) noted that private information is exchanged with two conditions; firms revealed their private information to other firms, or they conceal it before receipt of any private information. In the second stage, to maximize their expected profit conditi ons based on available private and revealed information, firms non-cooper atively determine prices or quantities in an oligopoly market. Similarly, Gal-Or (1985) examined information sharing in oligopoly market where firms are faced with an uncertain demand fo r their products. Interestingly, Gal-Or (1985) found that lack of information sh aring is the unique aspect of Nash equilibrium of the game, irrespective of the degree of correlation among the private signals in oligopoly market environments. More importantly, Raith (1996) identified that a pooling of complete information helps firms to find the efficient equilibrium of the tw o-stage game, regardless of all other parameters, such as common and private value, and perfect si gnals. Vives (1984) further mentioned that the pooling of complete information has effects. Fo r example, firms have better information about prevailing market conditions. T hus, the strategies to acquire private information from other firms are perfectly correlated. In Raiths (1996) st udy, firms faced either a stochastic intercept of a linear demand function or a stochastic marginal cost. Doyle and Snyder (1999) also i nvestigated the information exchange of production plans in an oligopoly market. In particular, they examined actual auto production from pre1965 to

PAGE 44

44 1999 from a trade journal, Wards Automotive Repor ts. Doyle and Snyder (1999) revealed that a firms auto production plan announcement affect ed competitors later revisions of their own plans and eventual production. This result was consistent with the fi ndings of Shapiro (1986) and Vives (1984). However, Doyle and Snyde r (1999) mentioned that firms may ignore competitors production plans if the market is characterized by perfect competition with no uncertainty. In contrast, Shapiro (1986) investigated the social welfare effects of information sharing between firms in oligopoly market environments. In particular, he analyzed the firms decision to share or not to share their private cost data through a trade associati on with the condition that firms would decide on an informational regime be fore they received private information from their competitors (Li, 1985; Millon & Thakor, 1985; Pagano & Jappelli, 1993). Shapiro (1986) found that under a linear demand condition with C ournot behavior, the exchange of cost data increased firms expected profits and welfare, while it reduced expected consumer surplus. In general, Bertrand competition (price comp etition) is more competitive than Cournot competition (demand competition) (Kuhn & Vives, 1995; Vives, 1985). Moreover, firms are more likely to use price in demand comparison as the strategic variable (Kuhn & Vives, 1995). Bertrand competition along the lines of information sharing behavior and price as the strategic variable is further examined in the next section. Bertrand Competition Cason (1992) noted that most Bertrand models assume that behavior in the output market is non-cooperative, regardless of the firms information sharing decisions. Shapiro (1984) demonstrated that two firms are better off if bot h reveal than conceal in formation about costs. Among firms competing in price, Gal-Or ( 1986) stated that colle cting and publicizing information about a parameter of the model are routine, such as a common demand intercept.

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45 However, with an uncertain common demand intercept and price competition, a firms dominant strategy is to reveal demand inform ation if the goods are substitutes (Vives, 1984). Similarly, under the condition th at costs are uncertain, but are conditionally independent across firms, the dominant strategy is to conceal co st information under price competition (Gal-Or, 1985). With price competition and perfectly correl ated but uncertain costs, a firms dominant strategy is to conceal their private information about cost if the goods are substitutes (Cason, 1991). Moreover, to make a price prediction, fi rms conceal cost information and share demand information, if the goods are substitutes (Cason, 1994). With unknown common demand under Bertrand competition, sharing is a dominant stra tegy. In addition, under Bertrand competition with unknown private costs, concealing is a domin ant strategy (Gal-Or, 1986; Vives, 1984). More importantly, Clarke (1983b) mentioned that there is a very strong incen tive to share information in the oligopoly market because firm s profits may be higher than if each firm acts independently. As Clarke (1983a) indicated, co llusion among firms might occur when each firm has incentives for information sh aring only if they cooperatively determine an optimal strategy based on the homogenized beliefs about the market. However, a stochastic market environment restricts collusion (C larke 1983b; Green & Porter, 1981; Posner, 1976; Spence, 1978). The rationale is that firms are not sure of precise market conditio ns as long as information is imperfect. Therefore, it is difficult to detect cheating in a collusive agreement among firms (Stigler, 1964). In addition, when information is private (not shared), firms may hold divergent views about market conditions. In other word s, without mutual agreements, firms have difficulties in agreeing on a cooperative strategy. Thus, if firms share their private information with other firms in the oligopoly market, there is an incentive to coope rative without collusion (Clarke 1983a).

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46 Summary of Literature Review The ability to manage effective pricing strate gies greatly influences a hotels growth and profitability. In addition to demand and supply, other variables such as hotels size, features, location, services, and customers segment are al so employed to establish pricing strategies and decisions. Generally, hotels use various pricing strategi es to maximize revenues and profitability, while optimizing cu stomer satisfaction (Lewis & S hoemaker, 1997). There are two distinct perspectiv es (economics and marketing) within hotel pricing strate gies (Chung, 2000). From the economics perspective, hotel-pricing st rategies should be based on fixed costs and fluctuating demand (Shaw, 1984). Gu (1997) notes th at an optimal price in a hotel should be a function of costs and demand. However, cost-bas ed pricing generates a problem of over-pricing during off-seasons and under-pricing in high se asons, as unit costs fluctuate with demand and sales volume. In the marketing perspective, the attention is focused on th e customers viewpoint (Bitran & Susana, 1997), as pricing strategies are based on customers perception of the relationship between prices and values (Lewis & Shoemaker, 1997) The practice of fencing is also used to segment customers into appropriate rate categories (premium; rack rate; cooperate; discounted prices) based on need s, behavior, or willingness to pay (Hanks, Cross & Noland, 1992). Collectively, hotels pricing strategies are fo cused on top-line financial factors, such as demand, marginal costs, average daily rate, and occupancy rate (ON eil & Mattila, 2006). However, hotels face decisions whether to share or not to share private information with competitors in order to maximize revenues and profitability (Gal-Or, 1986; Shapiro, 1986; Vives, 1984). Information sharing among comp etitors reduces uncertain cost or demand conditions and can generate profits in the co mpetitive marketplace. Since the lodging industry faces highly competitive markets as new hotels, re sorts, and other lodging facilities open each

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47 year, information sharing among competitors can enhance the quality of strategies because it reduces uncertainty of market e nvironments, and enables correlation of price strategies (Cason, 1992; Kuhn & Vives, 1995). Game-theoretic models can assist hotel manage rs to characterize the incentive for firms to share or not to share private information with comp etitors in order to establish an optimal pricing strategy (Cason, 1991). Game theory is the study of multi-person decision problems, which examines strategic interactions between decisi on-makers (e.g. hotel managers). The optimal strategy is achieved by finding Na sh equilibrium (Nash strategies ), which is the most commonly used solution concept in game theory (Gibbons 1992; Osborne, 2004). Howe ver, firms optimal strategy to maximize profits vari es based on different conditions. For example, in formulating optimal pricing strategies, firms conceal cost information and share demand information if goods are substitutes (Cason, 1 991). Moreover, with unknown common demand under Bertrand competition (price competition), informa tion sharing is a dominant strategy.

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48 Figure 2-1. Different pricing index [Source: Hanks et al. 1992, p17] Rooms Requested Premium RackCorporateDiscount 0 20 40 60 80 100 Rate $100 $80 $60 $40 $20 Unrealized potential revenue $4,000 realized revenue

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49 CHAPTER 3 METHODOLOGY Phase 1 The objective of phase 1 was to develop a two-stage Bertrand model based on the most significant indicators for hotels business, which includes hot els average daily room rate, occupancy rate, marginal cost, and market demand. Model Building The model considered competition in price between two hotels (Bertrand competition) using a form of differentiated products when th ere was uncertainty about demand. The demand uncertainty model was developed and analyzed using a version advanced by Vives (1984). In this model, hotels knew their own demand, but were imperfectly informed about the demand of their competitors. In the presence of this uncertainty, hotels had to decide whether to share or conceal their private information in order to maximize expected profits (Vives, 1984). For the purpose of this study, three majo r modifications were made to the model. First, the random structure was simplified. The ra ndom variable experienced by a hot el, typically the level of the demand intercept, was discrete instead of continuous Given that it was either of a high or low value, the demand intercept was a discrete random variable. Second, hotels were allowed to be asymmetric with differential costs or demands, which enabled competition between different types of hotels. Third, hotels made their sh aring decisions only afte r learning their private information, not before. Costs and Demands Similar to Gus room pricing model (1997) hotels were assumed to have constant marginal costs (operating costs) for each unit sold. Different types of hotels would have different costs. An upscale hotel would have higher marginal cost s than a mid-scale hotel, which

PAGE 50

50 would subsequently have higher costs than an ec onomy hotel. These hotels also differed in their fixed costs, but such fixed costs were not separately considered si nce they did not directly affect pricing or information sharing. In this duopoly model, each hotel faced a linear demand curve where the quantity (occupancy rates) equaled an amount (the demand intercept), which decrea sed with increases in its own price, and respectively increased with increases in its competitors price. The demand intercept can be of a high or low value. Base d on large, medium, and small-scale hotels, they differed in size (the number of rooms). Togeth er, the demand and cost differences vary among different types of hotels. For example, conventio n hotels are likely to be large in size with high costs, while budget hotels are usua lly small with comparatively lo w costs. Also, boutique hotels are generally small in size with high costs. Hote ls were assumed to be mo re responsive to their own price than their competitors. Basically, wh en hotels own price-eff ect was closer to the cross-effect, the market was more competitive. Ho wever, the more they differed, the market was less competitive. The difference between these effects is dependent on whether hotels are similar or different, with respect to cost or demand. Similar hotels would be highly competitive whereas different types of hotels woul d be significantly less competitive. Timing and Information As noted from Figure 3.1, nature1 first chooses the demand in tercept, and then hotels decide simultaneously whether to share or conceal demand informa tion based on their own respective demands. Hotels simultaneously set pr ices following an assessment of their demand and based on any particular information about their competitors. This game is based on incomplete information since hotels may not know their competitors type. Given the structure 1 Nature is a term used in game theory for any ran domly determined variables such as demand intercepts.

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51 of the game, the basic solution concept used was subgame perfect Nash equilibrium. To apply in this context, the game was solved backwards. For example, equilbrium prices were found conditional on the hotels inform ation and on sharing decisions in the final stage. These equilibrium prices implied the le vel of expected profits for the two hotels. Using these, hotels made decisions on whether or not to share inform ation. The equilibrium sharing decisions were found in the first stage of the game. Model Analysis In solving the model, the fi nal stage was conducted analytic ally using mathematica 5.2, which yielded expressions for the equilibrium prices that were dependent on the parameter values in the model. The first stage equilibrium was too complex to be solved analytically. The best reply correspondences betw een unknown parameters in equatio ns were found analytically, but their intersections were identified numeri cally using mathematica 5.2 for a variety of parameter values. When multiple equilibria existe d during this first stage, equilibrium that had weakly dominated strategies was discarded. Formalization The formal specification of the model was as follows. The two hotels had constant marginal costs which differed, and denoted as c1 and c2. Each firm had an inverse demand function denoted as: p1 = a1 bq1 dq2 (3-1) p2 = a2 bq2 dq1 (3-2) where a1 and a2 were the demand intercepts, q1 and q2 were the quantities (occupancy rate), and b and d were constants (coefficients) related to the own and cross-price effects. Solving the equation 3-1 and 3-2 for q1 and q2 yielded the ordina ry demand functions:

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52 q1= a1ba2d b2d2 bp1dp2b2d2 (3-3) q2= a2ba1d b2d2 bp2dp1b2d2 (3-4) The demand intercepts a1 and a2 could each take on one of two values, high or low, denoted as a1 H and a1 Lfor hotel 1 and a2 H and a2 Lfor hotel 2. Nature randomly chose the value of these demand intercepts. The probability distri bution over different pairs of the intercepts for the two hotels was illustrated in Table 3.1. This general specification cont ained different special cases. One polar case with only common uncertainty would arise if e j 0. Then, each hotel woul d know exactly the other hotels demand when it learned its own. On the other hand, if kk e jjf which was also implied kkj eef then each hotels uncertainty was purely private. When a hotel learned its demand intercept, this conveyed no information a bout the intercept of the other hotel. Inbetween situations with kke jjf 0 and kkj eef 0 would involve a mixture of common and private uncertain ty. Hotels partially learned about the other hotels demand based on their own demand. The timing of actions and the strategies at each stage were presented in the game tree in Figure 3.1. In the final stage, based upon what the hotel s learned about their own demand and their competitors demand from information sharing, th ere were nine subgames, divided into three

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53 types: complete information, one-sided private in formation, and two-sided private information. The four complete information subgames occurred for the four states of nature L L L H H L and H H when both hotels shared information. The four subgames of one-sided private information arose when one shared inform ation and the other did not. If hotel 1 shared, then hotel 2 was completely informed, but hotel 1 did not know the demand of hotel 2. Thus, one of four subgames was that nature selected hotel 1 as L with probability k e, that hotel 2 knew whether nature selected L,L or L,H but hotel 1 di d not, viewing L,L arising with probability 1 2 Lk 1 2 Lk 1 2 He and L,H with probability 1 2 He 1 2 Lk 1 2 He The terms a2 H and a2 L were the equilibrium probabilities with which hotel 2 decided to share or conceal information gi ven knowledge of its own type. These entered the equations because the belief by hotel 1 of whether hotel 2 is L or H depended on natures actions and on hotel 2 s sharing actions. Similarly, na ture could select hotel 1 as H with probability jf. Then, hotel 1 would be in a subgame where H,L arose with probability 1 2 Lj 1 2 Lj 1 2 Hf and H,H arose with probability 1 2 Hf 1 2 Lj 1 2 Hf while hotel 2 knew whether nature selected H,L or H,H. Two similar subgames existed if hotel 2 shared information and hotel 1 did not. Finally, one subgame of two-si ded incomplete information existed when neither hotel chose to share. Then, neither hotel knew the othe r hotels demand. Thus, in this subgame nature selected L for hotel 1 with probability k e. Hotel 1 knew this outcome, but did not know hotel 2s type. Hotel 1 did know that hotel 2 chose not to share information. Thus, hotel 1

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54 believed that L,L arose with probability 1 2 L k 1 2 L k 1 2 H e and that L,H arose with probability 1 2 He 1 2 Lk 1 2 H e If, nature selected hotel 1 as H with probability jf, that hotel 1 considered H,L arose with probability 1 2 Lj 1 2 Lj 1 2 Hf and H,H arose with probability 1 2 Hf 1 2 Lj 1 2 Hf Similarly, if hotel 2 were L which arose with probability kj, it did not know whether hotel 1 was L or H viewing L,L with probability 1 1 Lk 1 1 Lk 1 1 Hj and L,H with probability 1 1 He 1 1 Lk 1 1 He If hotel 2 were H it believed that H,L arose with probability 1 1 Lj 1 1 Lj 1 1 Hf and H,H arose with probability 1 1 Hf 1 1 Lj 1 1 Hf In each subgame, the equilibrium prices and expected profits were examined. Using the equilibrium prices, the expected pr ofits to the hotels from sharing or not sharing were calculated. Then, in the first stage, hotels simultaneously ch ose to share or not to share information. The game was converted to the mixed extension where hotels, given their private information, chose the probabilities with which they shared or concealed. As described above, these are a1 H and a1 Lfor hotel 1 and a2 H and a2 Lfor hotel 2. The equilibrium valu es of these probabilities were then determined for a variety of different parameter values. Phase 2 The objective of phase 2 was to examine the third objective of this study; to confirm the applicability of Bertrand model within the tourism and hospitality industry.

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55 Site Description Marion County, located in Central Florida was the site for this exploratory study. There are 316,183 people in Marion County, which in cludes 106,755 households and 74,621 families (U.S. Census, 2006). As noted in Figure 3-2, the county has a total area of 1,663 square miles, and is about a two-hours drive fr om Florida's major cities. Fo r example, Orlando and Tampa are about ninety minutes to the sout heast and the southwest, respectively. Jacksonville is about a two-hour drive northeast and Daytona Beach is an hour and a half to the east. The incorporated cities and towns encompass Ocala, Belleview Dunnellon, McIntosh and Reddick, whilst unincorporated communities include Fort McCoy, Marion Oaks, Silver Springs Shores and Salt Springs. Marion County has a variety of attractions fo r visitors, such as th e Ocala National Forest, lakes, festivals, and historic sites (e.g., art ga llery; museum). The county also has the highest number of horses and ponies in residence in U.S. There are many famous farms, such as Petty Quarter Horses, Rohara Arabians and Youngs Paso Finos that attract visito rs (Horse Capital of the World, 2007). There are seventy-three hote ls, including two upscale hotels, ten mid-scale hotels, eleven economy hotels, and fifty budget motels. Most visitors are day-trippers who visit fri ends and relatives, and are mostly Florida residents. Visitors to Marion County engage in outdoor recreation, special events and festivals, and business. In particular, participation in outdoor recreation activities and nature-based tourism has grown significantly over the past decade. Base d on a recent study, 38% were overnight visitors who were more likely to stay in hotels/motels (54.9%), followed by campgrounds (23%), and friends/relatives homes (7.2%) (Pennington-Gray & Huang, 2007).

PAGE 56

56 Data Collection Data for this study were collected as part of a project entitled: Marion County Occupancy Study. For the purpose of phase 2 of this study, tw o separate methods were used to collect data: phone interviews and secondary data. The pr imary purpose of the phone interview was to investigate hotels actual information sharing be haviors in Marion County, Florida. The purpose of obtaining secondary data was to examine thei r actual ADR (average daily rate), occupancy rate, and market shares. Phone Interviews General managers of five hotel s in Marion County within different market segments (i.e., economy, mid-scale, upscale) we re interviewed by phone during th e periods of: November 20 to 27, 2006 & January 28 to February 2, 2007. T ypically, great expense is involved in building and operating upscale hotels, while economy hotel s are relatively inexpensive to build and simple to operate. Also, mid-scale hotels offer the amenities they want at prices that are below those offered by upscale hotels (N inemeier & Perdue, 2005). Th e interviews were conducted within 5-10 minutes. Table 3-2 illustrates profiles of the respec tive hotels in Marion County. Each participant was asked fo r their actual information shar ing behaviors during the past three months. In particular, four questions we re asked to examine their information sharing behavior about their average daily rate (ADR) and occupancy rate. Interview question 1: If hot els in Marion County have a choice of participating in sharing average daily rate and o ccupancy rate, why would they decide to or not to participate? Interview question 2: If they participate, what do they perceive th e benefits to be? Interview question 3: If they do not participate, what do they perceive the benefits of not

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57 participating to be? Interview question 4: If hotel s in Marion County decide to or not to participate in sharing ADR and occupancy, what information would they want to share or not want to share about demand? Secondary Data Data for three different types of hotels ( economy, mid-scale, and upscale) were obtained from Marion County, Marion County Occupancy Study, Marion County Website, and results of phone interviews. Data included average daily rate occupancy rate, the number of rooms in the property, and market shares. Five hotels were selected in the anal ysis. Of the five hotels, there was one upscale, one economy, and three mid-scale properties (Table 3-2). Data Analysis Two separate approaches were utilized to analyze the data. First, the raw data from phone interviews were transcribed and organized into descriptive notes. Python version 2.1 and cross-case analysis were used for the interview analysis. Specifically, the data were used to compare information sharing equilibrium with a hotels current information sharing behaviors. The information sharing equilibrium was found from the results of Phase 1, while hotels current information sharing behaviors we re revealed through analyses of the phone interviews. This procedure further examined whether or not hotels in Marion County use effective pricing strategies aligned with inform ation sharing equilibrium. Second, through secondary data, the level of market competition in Marion County, FL was defined. More specifically, ADR and occupa ncy rate of hotels in Marion County, FL were compared with those of U.S. national averages. This procedure ensured th at information sharing equilibria revealed from the results of Phase 1 were compared with actual information sharing behaviors of hotels in the County, and its mark et competition. Therefore, by confirming Nash

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58 equilibrium, this study examined whether or not Bertrand model (price competition model) was applicable in the l odging industry.

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59 Table 3-1. Probabil ity distribution a2 L a2 H a1 L k e a1 H j f k e j f 1 k e j f 0 Table 3-2. Profiles of select ed hotels in Marion County, FL Hotels # of Rooms Market Segment A Hotel 81 Upscale B Hotel 152 Mid-scale C Hotel 152 Mid-scale D Hotel 86 Mid-scale E Hotel 80 Economy (Sources: the Marion County Website ( http://www.ocalamarion.com/ ))

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60 Figure 3-1. Game tree

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61 Figure 3-2. Map of Florida with Marion County identified Marion County

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62 CHAPTER 4 RESULTS Results of Phase 1 The two-stage competition model was solved by backward induction. First, equilibrium prices were determined in the second stage based on hotels demand in formation and sharing decisions. Second, based on the findings, the equ ilibrium sharing decisions were determined in the first stage of the game. As such, the sec ond stage of the model was first examined, followed by the first stage. Second Stage of the Model Equilibrium Prices Following information sharing decisions in the first stage, nine pricing subgames existed, which were divided into three t ypes: 1) four complete informa tion subgames, 2) four one-sided private information subgames, and 3) one two-side d private information subgame. Each of these subgames was solved and described below. In each subgame, hotels simultaneously determined their prices. Complete Information Subgames When both hotels shared their demand information, four complete information subgames were identified for the four states of nature L,L L,H H,L and H,H For example, L,L occurred when nature chose L for hotel 1 and hotel 2, and both hotels shared this information. The two hotels knew both demand in tercepts. The profit functions for each hotel were: 1 11112,LLLLL=P-Cq(P,P) (4-1) 2 22212,LL LLL=P-Cq(P,P) (4-2)

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63 where q1(P1 L,P2 L) and q2(P1 L,P2 L) were given in the equati ons 3-3 and 3-4. From maximizing the profit functions 4-1 and 4-2 with respect to P1 L and P2 L respectively; best reply functions of hotel 1 and hotel 2 were cal culated using the first order conditions: 1 P1 L 0 and 2 P2 L 0 These gave one hotels optimal price as a function of the other hotels price. Finding the intersection of these best reply functions yielded the e quilibrium prices for the two hotels in this subgame: P1 L 2 b2c1 a1 L d2a1 L bdc2 a2 L 4 b2 d2 (4-3) P2 L 2 b2c2 a2 L d2a2 L bdc1 a1 L 4 b2 d2 (4-4) Next, these equilibrium prices were substituted into the pr ofit functions 4-1 and 4-2 to identify expected profits as functions of the demand and cost parameters: L L1 b 2 b2c1 a1 L d2 c1 a1 L bd c2 a2 L 2b2 d2 4 b2 d22 (4-5) L L2 b 2 b2c2 a2 L d2 c2 a2 L bd c1 a1 L 2b2 d2 4 b2 d22 (4-6) Similar prices and profits were found fo r the other complete information subgames L H H L and H H had exactly the same form replacing a1 L and a2 L as appropriate with a1 H and a2 H. The complete information subgames L L L H H L and H H were denoted as subgames 1, 2, 3, and 4, respectively.

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64 One-Side Private Information Subgames When one hotel shared demand information and the other did not, four subgames of onesided private information arose. One such subga me, called subgame 5 existed when nature chose L for hotel 1 with probability k e and hotel 1 shared their inform ation with hotel 2. Hotel 2 knew its own type, then knew whether nature selected L L or L H but hotel 1 did not know which of these existed, viewing L L as arising with probability 12 Lk 12 Lk12 He and L H with probability 12 He 12 Lk12 He With kk 1 2 Lk 1 2 Lk 1 2 He denoted as kk, the expected profit function that hotel 1 maximized was: 1L L^Cor H + 1 kkP1 L-c1q1(P1 L,P2 H) kkP1 L-c1q1(P1 L,P2 L) (4-7) Hotel 2 solved two optimization proble ms depending upon whether it was type L or H : 2L LCP2 L-c2q2(P1 L,P2 L) (4-8) 2L HCP2 H-c2q2(P1 L,P2 H) (4-9) The best reply functions for three types were found from the first order conditions to the following optimizations, 1 P1 L 0, 2 L, L P2 L 0 and 2 L, H P2 H 0. Upon solving these functions simultaneously yielded the equilibrium prices for the two hotels in this subgame.

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65 P1 L d2a1 L 2 b2c1 a1 L bdc2 1 kk a2 H kka2 L 4 b2 d2 (4-10) P2 L 2 bdc1 a1 L 4 b2c2 a2 L d2 1 kk a2 H 1 kk a2 L 8 b2 2 d2 (4-11) P2 H 2 bdc1 a1 L 4 b2c2 a2 H d2 2 kk a2 H kka2 L 8 b2 2 d2 (4-12) Next, these equilibrium prices we re substituted into the profit f unctions 4-7, 4-8, and 4-9 in order to find expected profits as functions of the parameters: 1L L or HCb d2 c1 a1 L 2 b2c1 a1 L bd c2 a2 H kka2 H kka2 L 2b2 d2 4 b2 d22 (4-13) L L2 b 2 bd c1 a1 L 4 b2c2 a2 L d2 2 c2 a2 H kka2 H a2 L kka2 L 24 b2 d2 4 b2 d22 (4-14) L H2 b 2 bd c1 a1 L 4 b2c2 a2 H d2 2 c2 2 a2 H kka2 H kka2 L 24 b2 d2 4 b2 d22 (4-15) A second subgame of one sided private inform ation called subgame 6 existed when nature chose H for hotel 1 with probability j f and hotel 1 shared its inform ation with hotel 2. Hotel 2 knew its own type, and then had knowledge whether nature selected H L or H H, but hotel 1 did not know, viewing H L as arising with probability

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66 1 2 Lj 1 2 Lj 1 2 Hf and H H with probability 1 2 Hf 1 2 Lj 1 2 Hf Denoting 1 2 Lj 1 2 Lj 1 2 Hf by jj, the expected profit function that hotel 1 maximized was: 1H LC or H + 1 jjP1 H-c1q1(P1 H,P2 H) jjP1 H-c1q1(P1 H,P2 L) (4-16) Hotel 2 solved two optimization problems th at were dependent upon whether it was type L or H : 2H LC P2 L-c2q2(P1 H,P2 L) (4-17) 2H HC P2 H-c2q2(P1 H,P2 H) (4-18) The best reply functions for three types were found from the first order conditions to the following optimizations, 1 P1 H 0 2 H L P2 L 0 and 2 H H P2 H 0. Upon solving these functions simultaneously yielded the equilibrium prices for the two hotels in this subgame: P1 H d2a1 H 2 b2c1 a1 H bdc2 1 jj a2 H jja2 L 4 b2 d2 (4-19) P2 L 2 bdc1 a1 H 4 b2c2 a2 L d2 1 jj a2 H 1 jj a2 L 8 b2 2 d2 (4-20)

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67 P2 H 2 bdc1 a1 H 4 b2c2 a2 H d2 2 jj a2 H jja2 L 8 b2 2 d2 (4-21) Next, these equilibrium prices were substituted into the prof it functions 4-16, 4-17, and 418 in order to find expected profits: 1H L or HCb d2 c1 a1 H 2 b2c1 a1 H bd c2 a2 H jja2 H jja2 L 2b2 d2 4 b2 d22 (4-22) H L2 b 2 bd c1 a1 H 4 b2c2 a2 L d2 2 c2 a2 H jja2 H a2 L jja2 L 24 b2 d2 4 b2 d22 (4-23) H H2 b 2 bd c1 a1 H 4 b2c2 a2 H d2 2 c2 2 a2 H jja2 H jja2 L 24 b2 d2 4 b2 d22 (4-24) A third subgame of this type called subgame 7 existed when nature chose L for hotel 2 with probability k j and hotel 2 shared their informati on with hotel 1. Hotel 1 knowing its own type, then knew whether nature selected L L or H L but hotel 2 did not know, viewing L L as arising with probability 1 1 L k 1 1 L k 1 1 H j and H L with probability 1 1 Hj 1 1 Lk 1 1 Hj Denoting 1 1 Lk 1 1 Lk 1 1 Hj by ff, the expected profit function that hotel 2 maximized was:

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68 2LC or H L + 1 ffP2 L-c2q2(P1 H,P2 L) ffP2 L-c2q2(P1 L,P2 L) (4-25) Hotel 1 solved two optimization problems that were dependent on whether it was type L or H : 1L LC P1 L-c1q1(P1 L,P2 L) (4-26) 1H LC P1 H-c1q1(P1 H,P2 L) (4-27) The best reply functions for three types were found from the first order conditions to the follwoing optimizations, 2 P2 L 0, 1 L L P1 L 0 and 2 H L P1 H 0. Solving these functions simultaneously yielded the equilibrium prices for the two hotels in this subgame: P2 L d2a2 L 2 b2c2 a2 L bdc1 1 ff a1 H ffa1 L 4 b2 d2 (4-28) P1 L 2 bdc2 a2 L 4 b2c1 a1 L d2 1 ff a1 H 1 ff a1 L 8 b2 2 d2 (4-29) P1 H 2 bdc2 a2 L 4 b2c1 a1 H d2 2 ff a1 H ffa1 L 8 b2 2 d2 (4-30) Next, these equilibrium prices were substituted into the prof it functions 4-25, 4-26, and 427 in order to find expected profit s as functions of the parameters:

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69 2L or H LCb d2 c2 a2 L 2 b2c2 a2 L bd c1 a1 H ffa1 H ffa1 L 2b2 d2 4 b2 d22 (4-31) L L1 b 2 bd c2 a2 L 4 b2c1 a1 L d2 2 c1 a1 H ffa1 H a1 L ffa1 L 24 b2 d2 4 b2 d22 (4-32) 1H L b 2 bd c2 a2 L 4 b2c1 a1 H d22 c1 2 a1 H ffa1 H a1 L 24 b2 d2 4 b2 d22 (4-33) The last of the subgames called subgame 8 existed when nature chose H for hotel 2 with probability e f and hotel 2 shared its information with hotel 1. Hotel 1 knowing its own type, then knew whether nature selected L H or H H but hotel 2 did not know, viewing L H as arising with probability 1 1 Le 1 1 L e 1 1 H f and H H with probability 1 1 Hf 1 1 Le 1 1 Hf Denoting 1 1 Le 1 1 Le 1 1 Hf by ee, the expected profit function that hotel 2 maximized was: 2LC or H H + 1 eeP2 H-c2q2(P1 H,P2 H) eeP2 H-c2q2(P1 L,P2 H) (4-34) Hotel 1 solved two optimization prob lems depending upon whether it was type L or H : 1L HC P1 L-c1q1(P1 L,P2 H) (4-35)

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70 1H HC P1 H-c1q1(P1 H,P2 H) (4-36) The best reply functions for three types were found from the first order conditions to the following optimizations, 1 P2 H 0, 2 L H P1 L 0 and 2 H H P1 H 0. Solving these functions simultaneously yielded the equilibrium prices for the two hotels in this subgame: P2 H d2a2 H 2 b2c2 a2 H bdc1 1 ee a1 H eea1 L 4 b2 d2 (4-37) P1 L 2 bdc2 a2 H 4 b2c1 a1 L d2 1 ee a1 H 1 ee a1 L 8 b2 2 d2 (4-38) P1 H 2 bdc2 a2 H 4 b2c1 a1 H d2 2 ee a1 H eea1 L 8 b2 2 d2 (4-39) Next, these equilibrium prices were substituted into the prof it functions 4-34, 4-35, and 436 in order to find expected profits: 2L or H HCb d2 c2 a2 H 2 b2c2 a2 H bd c1 a1 H eea1 H eea1 L 2b2 d2 4 b2 d22 (4-40) L H1 b 2 bd c2 a2 H 4 b2c1 a1 H d2 2 c1 a1 H eea1 H a1 L eea1 L 24 b2 d2 4 b2 d22 (4-41)

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71 H H1 b 2 bd c2 a2 H 4 b2c1 a1 H d2 2 c1 2 a1 H eea1 H eea1 L 24 b2 d2 4 b2 d22 (4-42) Two-Side Private Information Subgame When neither hotel shared its demand info rmation, one subgame of two-sided private information existed, which was called subgame 9. Nature randomly selected L L L H H L and H H. Nature could select hotel 1 as L with probability k e and hotel 2 as L with probability kj, but neither hotels knew what nature chose for the other hotels since the hotels concealed demand information. Accordingly, hotel 1 considered L L with probability 1 2 Lk 1 2 Lk 1 2 He and L H with probability 1 2 He 1 2 Lk 1 2 He Hotel 2 considered L L with probability 1 1 Lk 1 1 Lk 1 1 Hj and H L with probability 1 1 Hj 1 1 Lk 1 1 Hj Similarly, nature could select hotel 1 as H with probability jf and hotel 2 as H with probability e f, but neither hotels knew if nature chose L or H for the other hotels demand. Thus, hotel 1 considered H L with probability 1 2 Lj 1 2 Lj 1 2 Hf and H H with probability 1 2 Hf 1 2 Lj 1 2 Hf Hotel 2 also considered L H with probability 1 1 Le 1 1 Le 1 1 Hf and H H with probability 1 1 Hf 1 1 Le 1 1 Hf

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72 The expected profit functions for hotel 1 and hotel 2 were: 1L LC or H + 1 kkP1 L-c1q1(P1 L,P2 H) kkP1 L-c1q1(P1 L,P2 L) (4-43) 1H LC or H + 1 jjP1 H-c1q1(P1 H,P2 H) jjP1 H-c1q1(P1 H,P2 L) (4-44) 2LC or H L + 1 ffP2 L-c2q2(P1 H,P2 L) ffP2 L-c2q2(P1 L,P2 L) (4-45) 2LC or H H + 1 eeP2 H-c2q2(P1 H,P2 H) eeP2 H-c2q2(P1 L,P2 H) (4-46) The best reply functions for four types were found from the first order conditions to the following optimizations, 1 P1 L 0, 1 P1 H 0, 2 P2 L 0 and 2 P2 H 0. Solving these functions simultaneously yielded the equilibrium prices for the two hotels in this subgame: P1 L 8 b4c1 a1 L d4ee ffjj kk a1 L 2 b2d2a1 H a1 L ffc1jj kk kka1 H 2 a1 L jja1 L eec1jj kk 1 kka1 H 1 jj 2 kka1 L 4 b3dc2 1 kka2 H kka2 L bd3jj kkc2ff ee 1 ffa2 H a2 L eea2 L4 b2 d24 b2 d2ee ffjj kk (4-47)

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73 P1 H 8 b4c1 a1 H d4ee ffjj kk a1 H 2 b2d22 a1 H ffc1 jj kk kka1 H jja1 L 2 a1 H eec1jj kk 1 2 jj kka1 H 1 jja1 L 4 b3dc2 1 jja2 H jja2 L bd3jj kkc2ee ff ffa2 H eea2 L4 b2 d24 b2 d2ee ffjj kk (4-48) P2 L 8 b4c1 a1 L d4ee ffjj kk a1 L 2 b2d2a1 H a1 L ffc1jj kk kka1 H 2 a1 L jja1 L eec1jj kk 1 kka1 H 1 jj 2 kka1 L 4 b3dc1 1 ffa1 H ffa1 L bd3ee ffc1jj kk 1 kka1 H a1 L jja1 L4 b2 d24 b2 d2ee ffjj kk (4-49) P2 H 8 b4c2 a2 H d4ee ffjj kk a2 H 2 b2d22 a2 H kkc2ff ee ffa2 H eea2 L 2 a2 H jjc2ee ff 1 2 ee ffa2 H 1 eea2 L 4 b3dc1 1 eea1 H eea1 L bd3ee ffc1jj kk kka1 H jja1 L4 b2 d24 b2 d2ee ffjj kk (4-50) Next, these equilibrium prices were substituted into the prof it functions 4-43, 4-44, 4-45, and 4-46 to find expected profits as func tions of the demand and cost parameters:

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74 1L LC or H b 2 b2d2c12 ff jj eejj kk ffkk 1 ee 1 kk ff kka1 H 1 2 ff kk ff jj ee 1 jj 2 kka1 L d4ee ffjj kkc1 a1 L bd3jj kkc2ee ff 1 ffa2 H a2 L eea2 L 4 b3dc2 1 kka2 H kka2 L 8 b4c1 a1 L 2b2 d2 4 b2 d22 4 b2 d2ee ffjj kk2 (4-51) 1H LC or H b 2 b2d2c12 ff jj eejj kk ffkk 2 2 ff jj ff kk ee 1 kk 2 jja1 H ee 1 jj ff jja1 L d4ee ffjj kkc1 a1 H bd3jj kkc2ee ff ffa2 H eea2 L 4 b3dc2 1 jja2 H jja2 L 8 b4c1 a1 H 2b2 d2 4 b2 d22 4 b2 d2ee ffjj kk2 (4-52) 2LC or H L b 2 b2d2c22 ff jj eejj kk ffkk 1 jj 1 ff ff kka2 H 1 2 ff kk ee kk jj 1 ee 2 ffa2 L d4ee ffjj kkc2 a2 L bd3ee ffc1jj kk 1 kka1 H a1 L jja1 L 4 b3dc1 1 ffa1 H ffa1 L 8 b4c2 a2 L 2b2 d2 4 b2 d22 4 b2 d2ee ffjj kk2 (4-53)

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75 2LC or H H b 2 b2d2c22 ff jj eejj kk ffkk 2 2 ee kk ff kk jj 1 ff 2 eea2 H jj 1 ee ee kka2 L d4ee ffjj kkc2 a2 H bd3ee ffc1jj kk kka1 H jja1 L 4 b3dc1 1 eea1 H eea1 L 8 b4c2 a2 H 2b2 d2 4 b2 d22 4 b2 d2ee ffjj kk2 (4-54) First Stage of the Model Information Sharing Equilibrium In the first stage, each hotel knew its type a nd had to decide whether or not to share its private demand information with its competitor. To solve this, the game was converted to the mixed extension in which each type of hotel chose the probability with which it shared information. These probabilities were denoted as 1 L and 1 H for the decisions of the high and low demand types for hotel 1, and 2 L, and 2 H for the high and low demand types for hotel 2. The optimal mixed strategies of each hotel type can take on one of three types of values: a pure strategy of sharing with i j 1, a pure strategy of not sharing with i j 0, or a mixed strategy in which the hotel is indifferent between sharing and not sharing denoted by i j[ ]. The occurrence depends on the expected profits from sharing versus not shar ing information. If i j 1 then hotel i of type j must get higher profits from sh aring information; while if i j 0 the profits from not sharing must be greater. If the hotel is indi fferent, then expected profits are equal. Thus: 1 L0 1 as E1 L S E1 L NS > <= 0 (4-55) 1 H0 1 as E1 H S E1 H NS > <= 0 (4-56)

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76 2 L 0 1 as E2 L S E2 L NS > <= 0 (4-57) 2 H 0 1 as E2 H S E2 H NS > <= 0 (4-58) The expected profits from sharing or not sharing were dependent on which second stage subgames arose from the different options a hotel could embark upon. For example, if hotel 1 receives information that its demand is low, a nd subsequently shares information, then second stage subgame 1 or 2 might arise if firm 2 also shared or subgame 5 if firm 2 did not share. This yielded the following equation for E1 L S : E1 L S k k e 2 Ls 1 1L Le k e 2 Hs 2 1L H k k e 1 2 L e k e 1 2 H s 5 1L LorH (4-59) where s 1 1L,L, s 2 1L,H, and s 5 1L,LorH were given in the profit function for subgames 1 and 2 in 4-5, and the expected profit f unction 4-13 for subgame 5. The subscript of s in all the profit and the expected profit functions represents a subgame, such as s1 is subgame 1. If hotel 1 did not share then subgame 7 or 8 arose if hotel 2 shared information and subgame 9 if hotel 2 also did not share inform ation. This yielded the following equation for E1 L NS : E1 L NS k k e 2 Ls 7 1L Le k e 2 Hs 8 1L H k k e 1 2 L e k e 1 2 H s 9 1L LorH (4-60) where s 7 1L,L, s 8 1L,H, and s 9 1L,LorH were given in the equations 4-32, 441, and 4-51. Similarly, for hotel 1 with high demand:

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77 E1 H S j j f 2 Ls 3 1H Lf j f 2 Hs 4 1H H j j f 1 2 L f j f 1 2 H s 6 1H LorH (4-61) where s3 1H,L, s4 1H,H, and s6 1H,LorH were given in the profit function for subgames 3 and 4 in 4.5, and expected profit function 4-16 for subgame 6. E1 H NS j j f 2 Ls 7 1H Lf j f 2 Hs 8 1H H j j f 1 2 L f j f 1 2 H s 9 1H LorH (4-62) where s7 1H,L, s8 1H,H, and s9 1H,LorH were given in the equations 4-33, 442, and 4-52. For hotel 2 with low demand, the expected profits were: E2 L S k k j 1 Ls 1 2L Lj k j 1 Hs 3 2H L k k j 1 1 L j k j 1 1 H s 7 2LorH L (4-63) where s1 2L,L, s3 2H,L, and s7 2LorH,L were given in the profit function for subgames 1 and 3 in 4-6, and the expect ed profit function 4-31 for subgame 7. E2 L NS k k j 1 Ls 5 2L Lj k j 1 Hs 6 2H L k k j 1 1 L j k j 1 1 H s 9 2LorH L (4-64) where s5 2L,L, s6 2H,L, and s9 2LorH,L were given in the equations 4-14, 423, and 4-53. For hotel 2 with high demand:

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78 E2 H S e e f 1 Ls 2 2L Hf e f 1 Hs 4 2H H e e f 1 1 L f e f 1 1 H s 8 2LorH H (4-65) where s2 2L,H, s4 2H,H, and s8 2LorH,H were given in the profit function for subgames 2 and 4 in 4.6, and the exp ected profit function 4-40 for subgame 8. E2 H NS e e f 1 Ls 5 2L Hf e f 1 Hs 6 2H H e e f 1 1 L f e f 1 1 H s 9 2LorH H (4-66) where s5 2L,H, s6 2H,H, and s9 2LorH,H were given in the equations 4-15, 4-24, and 4-54. These four best reply correspondences in 445 to 4-58 were too complex to be solved analytically in order to determine information sh aring equilibrium. Instead they were solved numerically using mathematica 6.0 for a va riety of parameter values of costs (ci), demands (ai j), beliefs (ff, jj, kk, ee), and probabilities (f, j, k, e). To do this, note that 81 different types of equilibrium existed depending on the type of values each i j took. Each of 1L, 1H, 2L, and 2H could have 3 different values (0, [ ], 1), wh ich were chosen simultaneously of each other. Thus, 3481 different cases were possibly at equilibrium (Table 4-1). Each case was solved for different parameter values to see if it was at an equilibrium. For example, 1L 1, 1H 0, 2L 0, and 2H 1 was one of the 81 cases. For these values of the i j, the values of jj, kk, ee, and ff were determined to be j jkk 1 and ee f f 0 using the equations 4-7, 4-16, 4-25, and 4-34. The actions of the hotels were sufficient to determine their beliefs. These values were plugged in each of the best reply correspondences associated with a specif ic numerical value of

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79 costs (c1, c2), demands (a1 L, a1 H, a2 L, a2 H), and probabilities (f, j, k, e). Then, if E1 L S > E1 L NS E1 H S < E1 H NS E2 L S < E2 L NS and E2 H S > E2 H NS this case was a Nash equilibrium. If any of these ineq ualities failed, it was not a Nash equilibrium. However, for some cases, such as that with 1 L 1, 1 H 1, 2 L 1, and 2 H 1, the beliefs (jj, kk, ee, and ff) were not defined since their denomin ators were 0. As such, the four best reply correspondences in 4-45 to 4-58 were first sought analytically with beliefs (ff, jj, kk, ee). This arose because with thes e actions, a subgame with private information did not arise. If a hotel found itself in such a subgame, it would be because of an equilibrium, an action were not followed. The hotels beliefs as to why they were in the subgame were not defined by their actions, but were based on beliefs about the likel ihood of the different types of the competitive hotels making errors. Since such beliefs were arb itrary, they can be assu med to have any values consistent with being probabilities if the valu es led to the hotels al ways decided to share information. That is, this case was an equilibrium if some values of jj, kk, ee, and ff existed for which E1 L S > E1 L NS E1 H S > E1 H NS E2 L S > E2 L NS and E2 H S > E2 H NS This was possible under some parameters values. Among the parameters of the model, two parameters (d, c1) could be eliminated. First, d could be set equal to 1 without loss of generality since in all the subgame profit functions, d only entered in a ratio with b. Second, c1 could be factored out without loss of generality from all the subgame profit functions. Then, c1 only entered in a ratio with c2 and various demand intercepts. Considering these, the followi ng propositions were found from the numerical analysis for the equilibria at the different parameters values.

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80 Proposition 1: 1H 0, 1L 1, 2H 0, and 2L 1 in case 21 is a Nash equilibrium under the following parameter values: c1c2a1La2La1Ha2H, if ej1 4 or ej1 6 and b 1.1. First, note that 1H 0, 1L 1, 2H 0, and 2L 1 implied that ff, jj, kk, and ee were defined and equaled to 0. Substituting these values and the parameters into 4-55 to 4-58 yielded the results that E1H S E1H NS = 0, E1L S E1L NS > 0, E2H S -E2H NS = 0, and E2L S E2L NS > 0 consistent with equilibrium under the given parameter values. Proposition 2: 1L1H2L2H 1 in case 21 with ee f f j jkk 0 or 1H 0, 1L 1, 2H 0, and 2L 1 is a Nash equilibrium under the following parameter values: c2c1a1La2La1Ha2H, where a1La2L 30, if ej1 4 or ej1 6 and b 1.6. First, note that given actions 1L1H2L2H 1, the beliefs ff, jj, kk, and ee were not defined since their denominators were 0. S ubstituting these values and the parameters into 455 to 4-58, left four equations in the unknowns ff, jj, kk, and ee. The only solution for these equations found was for ff, jj, kk, and ee to equal 0. This yielded the results that E1H S E1H NS = 0, E1L S E1L NS > 0, E2H S -E2H NS = 0, and E2L S E2L NS > 0 consistent with equilibrium under the given parameter values

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81 Second, note that 1H 0, 1L 1, 2H 0, and 2L 1 implied that ff, jj, kk, and ee were defined and equaled to 0. Substituting these values and the parameters into 4-55 to 4-58 yielded results that E1H S E1H NS = 0, E1L S E1L NS > 0, E2H S -E2H NS = 0, and E2L S E2L NS > 0 consistent with equilibrium under the given parameter values. Proposition 3: 1L 1 H 2 L 2 H 1 in case 21 with ee ff j j k k 0 or 1 H 0, 1 L 1, 2 H 0, and 2 L 1 in case 61 is a Nash equili brium under the following parameter values: c2c1z, where z 30, if ej1 4 or ej1 6 and b 1.9. Specifically, a2 L z, a2 H wz, a1 L tz, a1 H wtz, w9 5 and t7 5 The first equilibrium followed as in proposition 2. Second, for 1 H 0, 1 L 1, 2 H 0, and 2 L 1, then ff, jj, kk, and ee were defined and equaled to 0. Substituting these values and the parameters into 4-55 to 4-58 yielded the results that E1 H S E1 H NS = 0, E1 L S E1 L NS > 0, E2 H S -E2 H NS = 0, and E2 L S E2 L NS > 0 consistent with equilibrium under the given parameter values.

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82 Proposition 4: 1 H 0, 1 L 1, 2 H 0, and 2 L 0 in case 24 is a Nash equilibrium under the following conditions: c2 c1 z, z 30 if ej1 4 or ej1 6 and b 1.9. Specifically, a2 L z, a2 H wz, a1 L tz, a1 H wtz, w9 5 and t7 5 For 1 H 0, 1 L 1, 2 H 0, and 2 L 0, then ff, jj, kk, and ee were defined with ee ff 0. Thus, for ej1 4 jj1 2 and kk1 2 while for ej1 6 jj1 3 and kk2 3 Substituting these values and the parameters into 4-55 to 4-58 yielded the results that E1 H S E1 H NS = 0, E1 L S E1 L NS > 0, E2 H S -E2 H NS = 0, and E2 L S E2 L NS < 0 consistent with equilibrium under the given parameter values. Proposition 5: 1 H 0, 1 L 1, 2 H 1, and 2 L 0 in case 25 is a Nash equilibrium under the following conditions: c2 c1 z, if ej1 4 or ej1 6 and b 2.3. Specifically, a2 L z, a2 H wz, a1 L tz, a1 H wtz, where z 30, w9 5 and t 5. For 1 H 0, 1 L 1, 2 H 1, and 2 L 0, ff, jj, kk, and ee were defined with ee f f 0 and j j k k 1. Substituting these values and the pa rameters into 4-55 to 4-58 yielded the results that E1 H S E1 H NS = 0, E1 L S E1 L NS > 0, E2 H S -E2 H NS > 0, and E2 L S E2 L NS = 0 consistent with equilibrium under the given parameter values.

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83 Proposition 6: 1 H 0, 1 L 1, 2 H 0, and 2 L 0 in case 26 is a Nash equilibrium under the following conditions: c2 c1 z, if ej1 4 or ej1 6 and b 2.3. Specifically, a2 L z, a2 H wz, a1 L tz, a1 H wtz, where z 30, w9 5 and t5. For 1 H 0, 1 L 1, 2 H 0, and 2 L 0, ff, jj, kk, and ee were defined with ee ff 0. Thus, for ej1 4 jj1 2 and kk1 2 while for ej1 6 jj1 3 and kk2 3 Substituting these values and the parameters in to 4-55 to 4-58 yielded the results that E1 H S E1 H NS = 0, E1 L S E1 L NS > 0, E2 H S -E2 H NS < 0, and E2 L S E2 L NS = 0 consistent with equilibrium under the given parameter values. Proposition 7: 1 H 0, 1 L 1, 2 H 0, and 2 L 0 in case 23 is a Nash equilibrium under the following parameter values: c2 c1 z, if ej1 4 or ej1 6 and 1.5 b 2.4. Specifically, a2 L z, a2 H wz, a1 L tz, a1 H wtz, w 3, and t7 5 For 1 H 0, 1 L 1, 2 H 0, and 2 L 0, ff, jj, kk, and ee were defined with ee f f 0. Thus, for ej1 4 jj1 2 and kk1 2 while for ej1 6 jj1 3 and kk2 3 Substituting these values and the parameters in to 4-55 to 4-58 yielded the results that E1 H S E1 H NS = 0, E1 L S E1 L NS > 0, E2 H S -E2 H NS < 0, and E2 L S E2 L NS < 0 consistent with equilibrium under the given parameter values.

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84 Proposition 8: 1 H 0, 1 L 0, 2 H 0, and 2 L 0 in case 41 is a Nash equilibrium under the following parameter values: c2 c1 z, if ej1 4 or ej1 6 and 2.4 b 2.8. Specifically, a2 L z, a2 H wz, a1 L tz, a1 H wtz, w 3, and t7 5 For 1 H 0, 1 L 0, 2 H 0, and 2 L 0, then ff, jj, kk, and ee were defined as follows. For ej1 4 and fk1 4 jjkkeeff1 2 while for ej1 6 and fk1 3 jjee1 3 and kkff2 3 Substituting these values and the parameters into 4-55 to 4-58 yielded the results that E1 H S E1 H NS < 0, E1 L S E1 L NS < 0, E2 H S -E2 H NS < 0, and E2 L S E2 L NS < 0 consistent with equilibrium under the given parameter values. Results of Phase 2 The preliminary results for Phase 2 were composed of two parts: resu lts of phone interview and empirical validation of pricing competition model. The results of phone interview were interpreted to find actual information sharing be haviors in five hotels in Marion County, FL. Through secondary data, the actual informationsharing behaviors were compared with the information sharing equilibrium. Results of Phone Interviews The responses of phone interviews partic ipants showed similar patterns across respondents based on the four interview questions. Table 4-12 showed that the four out of five hotels shared their private information with competitors. The upscale hotel did not share the information. The rationale was de monstrated in the quote below:

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85 General Manager 1 (upscale hote l): Information is confiden tial since there are only few upscale hotels in Marion C ounty, it is not necessary somewhat risky to share information we can buy their ADR, occupanc y rate from Smith Travel Research why do we need to share private information with them On the other hand, the general managers of four hotels (three midscale hotels and one economy hotel) noted that shar ing information was beneficial. Information was exchanged through phone calls and personal fri endships. Interestingly, they did not identify primary and secondary competitors for their market segmen ts; rather they recognized competitors by a geographical location. Below were some of the comments: General Manager 2 (Mid-scale hotel): I am sure the benefits would be very helpful when planning in the future. General Manager 3 (Mid-scale hot el): it is a kind of a tool for you guys to know what people are willing to pay and what type of clientele is coming into the area General Manager 4 (Economy hotel): sh aring information is sometimes risky in terms of knowing market comp etition and the economy in this ar ea, we call several hotels near by

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86 Although most hotels in the C ounty participated in shari ng ADR and occupancy with competitors, they obtained prices and demand information from several different sources. These included, Smith Travel Research, phone calls, a nd third party websites (e.g., Expedia.com, and Travelocity.com). As a result, the actual information sharing be haviors of seven hotels in Marion County, FL were summarized. The one upscale hotel (hotel A) did not share their information with the other hotels. Thus, the upscale hotels actual inform ation sharing behavior was noted as concealing information. The four hotels, including three mid-scale hotels (hotel B, C, and D) and one economy hotel (hotel E) shared information with competitors. Hence, the mid-scale and economy hotels actual informati on sharing behaviors were shari ng information. Five hotels were selected for the empirical validation for pricing competition model within a different scale hotel in Marion County (Table 4-12). Th ese included hotel A, B, C, D, and E. Empirical Validation of Pricing Competition Model As indicated earlier, the lodging industry faces highly competitive markets as the number of rooms continues to increase with new developments of hotel s, resorts, and other lodging facilities. For example, despite the new develo pment of hotels in Las Vegas, NV, the average occupancy rate has reached over 85%, and the range of average ADR is between $127.47 to $268.13. Considering the national averages of ADR and occupancy rate was at 63.4% and $ 97.31, respectively (Lodging Industry Profile, 20 07), the market in Las Vegas, NV could be considered as a high-level competitive market. As noted in Table 4-13, the average occupa ncy rate and ADR in hotels in Marion County in 2006 was 64.2% and $ 71.91, respectively in co mparison to the national averages (63.4% and

PAGE 87

87 $ 97.31). This presupposed that the market in Marion County would be at a medium-level competitive market due to the similarity of th e average occupancy rate; although ADR was about $25.40 lower than the national average ($ 97.31). Accordingly, the actual information sharing behaviors of hotels in Marion County were compared with Bertrand equilibrium associated with information-sharing equilibrium in the medium-level competitive market. More specifically, four different competitions were examined: 1) Competition between similar type, but different size of hotels 2) Competition between similar type and size of hotels 3) Competition between an upscale and a mid-scale hotel 4) Competition between an upscale hotel and an economy Hotel Competition between Similar Type, but Different Size of Hotels Two mid-scale hotels of different sizes (number of rooms) in Marion County were selected and examined to test price competition model. These included hotels C and D. ADR and occupancy rate of hotel C were $80.69 a nd 86.14%, while hotel E were $79.08 and 82%, respectively. Their ADR and occupancy rate were similar, but relative demand for hotel C was about 1.8 times bigger than hotel E, which was supported by market share: hotel C (16.93%) and hotel E (9.12%). This condition aligned with proposition 3 with re spect to the size of hotels, and was transformed to c E cc, a E L z, a E H wz, a C L tz, and a C H wtz, where z 45, w9 5 and t7 5

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88 The mid-scale hotels actual information-sharing behavior was sharing information. However, the results of proposition 3 offered an insight for competition between two mid-scale hotels but differed in size, and indicated that E H C H C L 0 and E L 1 and E H C H E L C L 1 were Nash equilibria. As noted in the results of proposition 3, the first information sharing equilibrium strict ly dominated the sec ond information sharing equilibrium, which may be identical to th eir actual information-sharing behavior: E H C H 1 and E L C L 1, whereby both hotels always shared information with each other. Therefore, proposition 3 theoretically suggested that both ho tels concealed demand information if there was high demand signal in order to maximize their pr ofits. However, a relatively small number of rooms mid-scale hotels shared demand informa tion if there was low demand signal, while a relatively larger number of mid-scale hotels c oncealed demand information if there was low demand signal in the medium-level of competition. Competition between Similar Type and Size of Hotels Two mid-scale hotels of similar size in Marion County were selected and examined to test price competition model. These included hotels B and C. ADR and occupancy rate of hotel C were $80.69 and 86.14%, while hotel B were $74. 24 and 83.05%, respectively. Their ADR and occupancy rate were similar. The relative demand for both hotels were also similar, as supported by market share: hotel B (16. 32%) and hotel C (16.93%). Th is condition was aligned with proposition 1 with respect to types and si zes of hotels, and was transformed to cB c C aB L a C L aB H a C H, where aB L a C L aB H a C H 152. The mid-scale hotels actual information-sharing behavior was sharing information. However, the results of proposition 1 provided an insight for competition between two mid-scale and similar size of hotels that indi cated an unique Nash equilibrium: B H C H 0 and

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89 B L C L 1. To this end, propositio n 1 theoretically suggested that both hotels concealed demand information if there was high dema nd signal, while the hotels shared demand information if there was low demand si gnal in order to maximize profits. Competition between an Upscale and a Mid-scale Hotel One upscale hotel (hotel A) and one mid-scale hotel (hotel D) were selected to test the price competition model. ADR and occupancy rate of hotel A were $102.74 and 92.02%, while hotel D was $79.08 and 82%, respectively. The relative demands for hotel A and E were similar, which were supported by market share: hotel A (9.64%) and hotel D (9.12%). However, their actual ADR and occupancy rate were not similar, as the occupancy rate of hotel A was about 1.2 times larger than hotel D. Moreover, the cost (cA) of an upscale hotel (hot el A) could be higher than the mid-scale hotel (hotel D; c E ). Thus, this condition alig ned with proposition 2 with respect to the scale of hot els, and transformed to c E 15 c A a E L z, a E H wz, a A L tz, aA H wtz, where z 45, w = 9/5, and t = 7/5 The upscale hotels actual information-sh aring behavior was based on concealing information with the mid-scale hotel, while th e mid-scale hotel was sharing information. However, the results of proposition 2 offered an insight for a competition between an upscale hotel and a mid-scale hotel that were similar in size. Two Nash equilibria were found, and included A H E H 0 and A L E L 1 and A H E H A L E L 1. Similar to the results of proposition 3, the first information sh aring equilibrium strictly dominated the second information sharing equilibrium. Proposition 2 theoretically suggest ed that both hotels concealed demand information if there was high demand signal, while the hotels shared demand information if there was low demand signal in the medium-level of competition. In other words,

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90 an information sharing equilibrium was determined by a demand signal in the market in Marion County, and not by type of hotels. Competition between an Upscale Hotel and an Economy Hotel One upscale hotel (hot el A) and one economy hotel (hot el E) in Marion County were selected and examined. ADR and occupancy rate of hotel A were $102.74 and 92.02%, while hotel E were $52.22 and 66.99%, respectively. The occupancy rate of hotel A was about 1.4 times larger than hotel E, but relative demands for hotel A (9.6 4%) were about 2 times larger than hotel E (4.47%). However, this condi tion did not support any proposition in the price competition model. Theoretically, not a single information sharing equilibrium was found in this condition. However, the upscale hotels actual information sharing behavior was concealing information, while the economy hotel was sharing information.

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91 Table 4-1. 81 different cases Case 1 L 1 H 2 L 2 H 1 > > > > 2 > > > < 3 > > > 0 4 > > < > 5 > > < < 6 > > < 0 7 > > 0 > 8 > > 0 < 9 > > 0 0 10 > < > > 11 > < > < 12 > < > 0 13 > < < > 14 > < < < 15 > < < 0 16 > < 0 > 17 > < 0 < 18 > < 0 0 19 > 0 > > 20 > 0 > < 21 > 0 > 0 22 > 0 < > 23 > 0 < < 24 > 0 < 0 25 > 0 0 > 26 > 0 0 < 27 > 0 0 0 28 < > > > 29 < > > < 30 < > > 0 31 < > < > 32 < > < < 33 < > < 0 34 < > 0 > 35 < > 0 < 36 < > 0 0 37 < < > > 38 < < > < 39 < < > 0 40 < < < > 41 < < < < 42 < < < 0 43 < < 0 > 44 < < 0 <

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92 45 < < 0 0 46 < 0 > > 47 < 0 > < 48 < 0 > 0 49 < 0 < > 50 < 0 < < 51 < 0 < 0 52 < 0 0 > 53 < 0 0 < 54 < 0 0 0 55 0 > > > 56 0 > > < 57 0 > > 0 58 0 > < > 59 0 > < < 60 0 > < 0 61 0 > 0 > 62 0 > 0 < 63 0 > 0 0 64 0 < > > 65 0 < > < 66 0 < > 0 67 0 < < > 68 0 < < < 69 0 < < 0 70 0 < 0 > 71 0 < 0 < 72 0 < 0 0 73 0 0 > > 74 0 0 > < 75 0 0 > 0 76 0 0 < > 77 0 0 < < 78 0 0 < 0 79 0 0 0 > 80 0 0 0 < 81 0 0 0 0 1 H=E1 H S -E1 H NS 1 L=E1 L S -E1 L NS 2 H=E2 H S -E2 H NS and 2 L=E2 L S -E2 L NS

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93 Table 4-2. Sensitivity analysis for proposition 1: 1 H2 H 0 and 1 L2 L 1 a1L a1H a2L a2H 1 L 1 H 2 L 2 H 30 a1 L 120 30 a1 H 120 < 120 < 160 > 0 > 0 120 160 120 160 > 0 > 0 120 165 120 165 > 0 > 0 120 170 120 170 > 0 > 0 120 175 120 175 > 0 > 0 120 180 120 180 > 0 > 0 125 160 125 160 > 0 > 0 125 165 125 165 > 0 > 0 125 170 125 170 > 0 > 0 125 175 125 175 > 0 > 0 125 180 125 180 > 0 > 0 130 160 130 160 > 0 > 0 130 165 130 165 > 0 > 0 130 170 130 170 > 0 > 0 130 175 130 175 > 0 > 0 130 180 130 180 > 0 > 0 135 160 135 160 > 0 > 0 135 165 135 165 > 0 > 0 135 170 135 170 > 0 > 0 135 175 135 175 > 0 > 0 135 180 135 180 > 0 > 0 140 160 140 160 > 0 > 0 140 165 140 165 > 0 > 0 140 170 140 170 > 0 > 0 140 175 140 175 > 0 > 0 140 180 140 180 > 0 > 0 > 140 > 180 > 140 > 180 > 0 > 0 Other Parameters: c1 c2 a1 L a2 L a1 H a2 H, where c1 15, a1 L 30, if ej1 4 or ej1 6 and b 1.1. 1 H=E1 H S -E1 H NS 1 L=E1 L S -E1 L NS 2 H=E2 H S -E2 H NS and 2 L=E2 L S -E2 L NS

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94 Table 4-3. Sensitivity analysis for proposition 2: 1 L1 H2 L2 H 1 a1L a1H a2L a2H 1 L 1 H 2 L 2 H 30 a1 L 120 30 a1 H 120 < 120 < 160 > 0 > 0 120 160 120 160 > 0 > 0 120 165 120 165 > 0 > 0 120 170 120 170 > 0 > 0 120 175 120 175 > 0 > 0 120 180 120 180 > 0 > 0 125 160 125 160 > 0 > 0 125 165 125 165 > 0 > 0 125 170 125 170 > 0 > 0 125 175 125 175 > 0 > 0 125 180 125 180 > 0 > 0 130 160 130 160 > 0 > 0 130 165 130 165 > 0 > 0 130 170 130 170 > 0 > 0 130 175 130 175 > 0 > 0 130 180 130 180 > 0 > 0 135 160 135 160 > 0 > 0 135 165 135 165 > 0 > 0 135 170 135 170 > 0 > 0 135 175 135 175 > 0 > 0 135 180 135 180 > 0 > 0 140 160 140 160 > 0 > 0 140 165 140 165 > 0 > 0 140 170 140 170 > 0 > 0 140 175 140 175 > 0 > 0 140 180 140 180 > 0 > 0 > 140 > 180 > 140 > 180 > 0 > 0 Other Parameters: c2 c1 a1 L a2 L a1 H a2 H, where c2 15, a1 L a2 L 30, if ej1 4 or ej1 6 and b 1.6. 1 H=E1 H S -E1 H NS 1 L=E1 L S -E1 L NS 2 H=E2 H S -E2 H NS and 2 L=E2 L S -E2 L NS

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95 Table 4-4. Sensitivity analysis for proposition 2: 1 H2 H 0 and 1 L2 L 1 a1L a1H a2L a2H 1 L 1 H 2 L 2 H 30 a1 L 120 30 a1 H 120 < 120 < 160 > 0 > 0 120 160 120 160 > 0 > 0 120 165 120 165 > 0 > 0 120 170 120 170 > 0 > 0 120 175 120 175 > 0 > 0 120 180 120 180 > 0 > 0 125 160 125 160 > 0 > 0 125 165 125 165 > 0 > 0 125 170 125 170 > 0 > 0 125 175 125 175 > 0 > 0 125 180 125 180 > 0 > 0 130 160 130 160 > 0 > 0 130 165 130 165 > 0 > 0 130 170 130 170 > 0 > 0 130 175 130 175 > 0 > 0 130 180 130 180 > 0 > 0 135 160 135 160 > 0 > 0 135 165 135 165 > 0 > 0 135 170 135 170 > 0 > 0 135 175 135 175 > 0 > 0 135 180 135 180 > 0 > 0 140 160 140 160 > 0 > 0 140 165 140 165 > 0 > 0 140 170 140 170 > 0 > 0 140 175 140 175 > 0 > 0 140 180 140 180 > 0 > 0 > 140 > 180 > 140 > 180 > 0 > 0 Other Parameters: c2 c1 a1 L a2 L a1 H a2 H, where c2 15, a1 L a2 L 30, if ej1 4 or ej1 6 and b 1.6. 1 H=E1 H S -E1 H NS 1 L=E1 L S -E1 L NS 2 H=E2 H S -E2 H NS and 2 L=E2 L S -E2 L NS

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96 Table 4-5. Sensitivity analysis for proposition 3: 1 L1 H2 L2 H 1 a1L a1H a2L a2H 1 L 1 H 2 L 2 H < 168 < 302 30 a1 L 120< 216 > 0 > 0 168 302.4 120 216 > 0 > 0 175 315 125 225 > 0 > 0 182 327.6 130 234 > 0 > 0 189 340.2 135 243 > 0 > 0 196 352.8 140 252 > 0 > 0 203 365.4 145 261 > 0 > 0 210 378 150 270 > 0 > 0 217 390.6 155 279 > 0 > 0 224 403.2 160 288 > 0 > 0 > 224 > 403.2 > 160 > 288 > 0 > 0 Other parameters: c2 c1 z, if ej1 4 or ej1 6 b 1.9, a2 L z, a2 H wz, a1 L tz, a1 H wtz, where z 30, c2 15, w9 5 and t7 5 1 H=E1 H S -E1 H NS 1 L=E1 L S -E1 L NS 2 H=E2 H S -E2 H NS and 2 L=E2 L S -E2 L NS Table 4-6. Sensitivity analysis for proposition 3: 1 H2 H 0 and 1 L2 L 1 a1L a1H a2L a2H 1 L 1 H 2 L 2 H < 168 < 302 30 a1 L 120< 216 > 0 > 0 168 302.4 120 216 > 0 > 0 175 315 125 225 > 0 > 0 182 327.6 130 234 > 0 > 0 189 340.2 135 243 > 0 > 0 196 352.8 140 252 > 0 > 0 203 365.4 145 261 > 0 > 0 210 378 150 270 > 0 > 0 217 390.6 155 279 > 0 > 0 224 403.2 160 288 > 0 > 0 > 224 > 403.2 > 160 > 288 > 0 > 0 Other parameters: c2 c1 z, if ej1 4 or ej1 6 b 1.9, a2 L z, a2 H wz, a1 L tz, a1 H wtz, where z 30, c2 15, w9 5 and t7 5 1 H=E1 H S -E1 H NS 1 L=E1 L S -E1 L NS 2 H=E2 H S -E2 H NS and 2 L=E2 L S -E2 L NS

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97 Table 4-7. Sensitivity analysis for proposition 4: 1 H2 H2 L 0 and 1 L 1 a1L a1H a2L a2H 1 L 1 H 2 L 2 H < 168 < 302 30 a1 L 120< 216 > 0 < 0 168 302.4 120 216 > 0 < 0 175 315 125 225 > 0 < 0 182 327.6 130 234 > 0 < 0 189 340.2 135 243 > 0 < 0 196 352.8 140 252 > 0 < 0 203 365.4 145 261 > 0 < 0 210 378 150 270 > 0 < 0 217 390.6 155 279 > 0 < 0 224 403.2 160 288 > 0 < 0 > 224 > 403.2 > 160 > 288 > 0 < 0 Other parameters: c2 c1 z, if ej1 4 or ej1 6 b 1.9, a2 L z, a2 H wz, a1 L tz, a1 H wtz, where z 30, c2 15, w9 5 and t7 5 1 H=E1 H S -E1 H NS 1 L=E1 L S -E1 L NS 2 H=E2 H S -E2 H NS and 2 L=E2 L S -E2 L NS Table 4-8. Sensitivity analysis for proposition 5: 1 H2 L 0 and 1 L2 H 1 a1L a1H a2L a2H 1 L 1 H 2 L 2 H < 600 < 1080 30 a1 L 120< 216 > 0 0 > 600 1080 120 216 > 0 0 > 625 1125 125 225 > 0 0 > 650 1170 130 234 > 0 0 > 675 1215 135 243 > 0 0 > 700 1260 140 252 > 0 0 > 725 1305 145 261 > 0 0 > 750 1350 150 270 > 0 0 > 775 1395 155 279 > 0 0 > 800 1440 160 288 > 0 0 > > 800 > 1440 > 160 > 288 > 0 0 > Other parameters: c2 c1 z, if ej1 4 or ej1 6 b 2.3, a2 L z, a2 H wz, a1 L tz, a1 H wtz, where z 30, c2 15, w9 5 and t 5. 1 H=E1 H S -E1 H NS 1 L=E1 L S -E1 L NS 2 H=E2 H S -E2 H NS and 2 L=E2 L S -E2 L NS

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98 Table 4-9. Sensitivity analysis for proposition 6: 1 H2 H2 L 0 and 1 L 1 a1L a1H a2L a2H 1 L 1 H 2 L 2 H < 600 < 1080 30 a1 L 120< 216 > 0 0 < 600 1080 120 216 > 0 0 < 625 1125 125 225 > 0 0 < 650 1170 130 234 > 0 0 < 675 1215 135 243 > 0 0 < 700 1260 140 252 > 0 0 < 725 1305 145 261 > 0 0 < 750 1350 150 270 > 0 0 < 775 1395 155 279 > 0 0 < 800 1440 160 288 > 0 0 < > 800 > 1440 > 160 > 288 > 0 0 < Other parameters: c2 c1 z, if ej1 4 or ej1 6 b 2.3, a2 L z, a2 H wz, a1 L tz, a1 H wtz, where z 30, c2 15, w9 5 and t 5. 1 H=E1 H S -E1 H NS 1 L=E1 L S -E1 L NS 2 H=E2 H S -E2 H NS and 2 L=E2 L S -E2 L NS Table 4-10. Sensitivity analysis for proposition 7: 1 H2 H2 L 0 and 1 L 1 a1L a1H a2L a2H 1 L 1 H 2 L 2 H < 168 < 1512 30 a1 L 120< 360 > 0 < < 168 1512 120 360 > 0 < < 175 1575 125 375 > 0 < < 182 1638 130 390 > 0 < < 189 1701 135 405 > 0 < < 196 1764 140 420 > 0 < < 203 1827 145 435 > 0 < < 210 1890 150 450 > 0 < < 217 1953 155 465 > 0 < < 224 2016 160 480 > 0 < < > 224 > 2016 > 160 > 480 > 0 < < Other parameters: c2 c1 z, if ej1 4 or ej1 6 1.5 b 2.4, a2 L z, a2 H wz, a1 L tz, a1 H wtz, where c2 15, w 3, and t7 5 1 H=E1 H S -E1 H NS 1 L=E1 L S -E1 L NS 2 H=E2 H S -E2 H NS and 2 L=E2 L S -E2 L NS

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99 Table 4-11. Sensitivity analysis for proposition 8: 1 H2 H1 L2 L 0 a1L a1H a2L a2H 1 L 1 H 2 L 2 H < 168 < 1512 30 a1 L 120< 360 < < < < 168 1512 120 360 < < < < 175 1575 125 375 < < < < 182 1638 130 390 < < < < 189 1701 135 405 < < < < 196 1764 140 420 < < < < 203 1827 145 435 < < < < 210 1890 150 450 < < < < 217 1953 155 465 < < < < 224 2016 160 480 < < < < > 224 > 2016 > 160 > 480 < < < < Other parameters: c2 c1 z, if ej1 4 or ej1 6 2.4 b 2.8, a2 L z, a2 H wz, a1 L tz, a1 H wtz, where c2 15, w 3, and t7 5 1 H=E1 H S -E1 H NS 1 L=E1 L S -E1 L NS 2 H=E2 H S -E2 H NS and 2 L=E2 L S -E2 L NS Table 4-12. Actual information sharing behavi ors of five hotels in Marion County, FL (20062007) Hotels Segment Own Type Information Sharing Occupancy Rate ADR Market Share A Hotel Upscale Hotel by chain No 92.02% $102.74 9.64% B Hotel Mid-scale Hotel by chain Yes 83.05% $74.24 16.32% C Hotel Mid-scale Hotel by chain Yes 86.14% $80.69 16.93% D Hotel Mid-scale Hotel by chain Yes 82.00% $79.08 9.12% E Hotel Economy Hotel by chain Yes 66.99% $52.22 4.47% (Source: Smith Travel Research; results of phone interview)

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100 Table 4-13. Monthly trend of pri ces and demand in Marion County, FL Month Year Occupancy (%) ADR ($) Room Supply Room Demand June 2006 64.0 67.99 107,250 68,639 July 2006 61.6 68.71 110,825 68,248 August 2006 54.9 66.41 110,825 60,879 September 2006 54.1 70.29 107,250 58,059 October 2006 60.1 69.19 110,825 66,616 November 2006 60.4 70.81 107,250 64,774 December 2006 55.5 69.34 110,825 61,523 Total year 2006 64.2 71.91 1,304,875 837,735 January 2007 65.0 76.78 116,281 75,611 February 2007 77.2 85.79 105,028 81,118 March 2007 77.1 86.56 116,281 89,615 April 2007 62.8 77.16 112,530 70,681 May 2007 54.4 72.56 116,281 63,288 June 2007 57.0 72.42 118,770 67,699 July 2007 48.7 72.09 122,729 59,735 August 2007 45.2 69.47 122,729 55,430 September 2007 43.5 72.78 118,770 51,720 October 2007 51.6 70.78 126,480 65,260 November 2007 52.8 73.69 125,370 66,145 (Source: Smith Travel Research, 2007)

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101 CHAPTER 5 DISCUSSION A hotels p ricing decision is affected by anothe r hotel offering similar, if not necessarily identical, rooms for sale in an imperfect co mpetitive market structure (Shaw, 1984). This imperfect competition creates the pot ential for room rates to be diffe rent in the lodging industry, due to the uncertainty of decision parameters, such as, demand and price conditions (Gal-Or, 1986; Kuhn & Vives, 1995). With imperfect knowledge of markets, hotels decide to share or not to share their private information w ith competitors. The rationale is that in this situation, sharing of information can dramatically a ffect profitability of hotels. Previous literature in price competition models, considered information sharing equilibrium (Cason, 1991; Doyle & Snyder, 1999; Gal-Or, 1986; Kuhn & Vives, 1995; Raith, 1996; Vives, 1984), has usually developed two stages models. In the first stage, firms made a decision regarding the amount of private information th ey wish to truthfully reveal to other firms. Importantly, this decision was made before any info rmation was revealed to firms. In the second stage, firms chose price strategi es based on the information revealed in stage one. In addition, previous literature has generally analyzed only situations in which firms were symmetric in their demands, costs, and information (Cason, 1991; Kuhn & Vives, 1995). The symmetry quality reduces the complications in the model th at makes it more tractable to solve. Similarly, this study also developed a two-stag e pricing competition model. In the first stage, two hotels decide to share or not to shar e their demand information, and then compete with each other in order to maximize their profits in th e second stage. No additional hotel interactions occurred after stage two. The equilibrium concep t is Nash subgame perfection, so that the first stage information sharing decisi ons takes into account how it affects the second stage subgame equilibrium. However, this model greatly differs in two ways when compared to the models in

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102 the literature. First, information sharing decisi ons are only made after ea ch hotel learns its own market demand (low versus high), and not befo re. Second, both symmetric and asymmetric situations about cost and demand in the pr ice competition model were analyzed. The asymmetric situations about di fferent costs and/or demands cr eate various scenarios about the types of competitions among hotels. In this duopoly model, several significant parameters were considered to determine whether or not hotels should share their dema nd information with competitors in order to maximize their profitability. These parameters included cost (ci), demand intercepts (ai j) with which different demand intercepts arise, demand responsiveness to b and d, and probabilities. The probability distribution over different pair s of the demand intercepts for two hotels was f, k, e, and j, which created different correlations be tween the private information of the hotels. The probability of k and f arose when both hotels had low demand and high demand, respectively. Also, the probability of e or j existed when a hotel had low demand signal, and the other had a high signal. In particul ar, two cases were considered where ej1 4 the information was completely independent, while where ej1 6 there was correlation in their demand. In both cases, there was symmetry in th eir information. In each case, a hotel can conjecture the other hotels dema nd when it learns its own demand. However, in this model, ej was not considered due to the complexity of solving the model. This probability would allow an additional type of asymmetry between hotels. The relations between constants (b, d) are worth noting. The value of constant (b) determines how responsive its occupancy rate is to its own price. The value of d specifies how responsive is its occupancy rate to the price of its competitor. Typically, a demand is more responsive to its own prices so that the value of b should be greater than that of d (Cason, 1991).

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103 However, d can be set equal to 1 wit hout loss of generality since d only entered in a ratio with b in all the subgame profit functions. Therefore, b d was the only important parameter regardless of the actual values of each. The ratio b d determines a level of market competition. In this study, the market was more competitive when the own price-effect was closer to the cross-effect. However, the more they differed, the market grew less comp etitive. In other words, with b d between 1 and the closer b d was less to 1, the greater was the competition, while the closer b was to competition existed between hotels. In some of the results, there was a critical value of b at which information sharing behavior changed. For example, in propositions 3 and 4 b 1.9 could have been considered a relatively high-level of competition, while b 1.9 a relatively medium or lowlevel of competition since behavors differed in their regions. Cost (ci) is another important parameter in this study. Each hotel was assumed to have constant marginal costs for each room sold with fixed costs not considered. The analysis on costs was consistent with cost-driven pricing strategies evident in the literature (Gu, 1997; Nagle & Holden, 1995). The absolute value of cost an d demand parameters was irrelevant. However, the value of the cost and the value of cost to the demand intercept creat ed competitions between different types of hotels with a comb ination of all the parameter values. The value of the demand intercept in th e linear demand curve was either high (ai H) or low (ai L). According to their own size, similar type of hotels can be large, medium, and small, which can be set based upon the value of t where at w9 5 The simplified demand parameter values were first used with a1 L a2 L a1 H a2 H, which enabled to analyze competition between similar sized hotels. However, after competing with diffe rent sizes of hotels, the demand variables were

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104 specified as a2 L z, a2 H wz, a1 L tz, a1 H wtz, where t7 5 or t 5, and the value of w was fixed (w9 5 ). The different values of t created competition between different sizes of hotels. The larger the t value, the more they differed in size. The parameters in proposition 1 included c1 c2 a1 L a2 L a1 H a2 H, ej1 4 or ej1 6 and b 1.1. This condition generated competiti on between identical hotels that have the same quality (c1 c2) and the same size since a1 L a2 L a1 H a2 H. In addition, when e was equal to j, each hotel had identical beliefs about it s competitor given its information about its own demand. For example, competition between two convention hotels on Canal Street in New Orleans, which have 1000 guestrooms respectiv ely, can be supported in proposition 1. In this identical hotel case, as sharing in proposition 1 a unique Nash equilibrium existed with 1 H 0, 1 L 1, 2 H 0, and 2 L 1. Each hotel shared its demand information with the other when it had low demand signal in the market The results of this study identified that hotels can increase market information, a nd reduce uncertainty de mand conditions through sharing information with competitors when both hotels faced low demand signal in the market. However, both hotels can conceal demand informa tion when high demand signal is identified in the market. This information sharing equilibriu m should be utilized for hotels in all different levels of market competitions since b 1.1. This theoretical solution also provides an insight for the mid-scale and similar sizes of hotels in Marion County. Their actual information sharing beha vior was sharing information no matter what demand signal was identified in the me dium-level of market competition. However, results of this study theoretica lly suggested that the mid-scal e and same size hotels should

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105 conceal their demand information when high demand signal is identified, while sharing demand information with low demand signal in the market for maximum profitability. The parameters in proposition 2 create competition between different type hotels (c2 c1), and similar size hotels (a1 L a2 L a1 H a2 H). For example, a competition between Sydney Harbor Marriott Hotel (an upscale hotel) with 300 guestrooms and Courtyard Sydney-North Ryde (a mid-scale hotel) with 300 guestrooms on North Ryde in New South Wales can be supported in proposition 2. The parameters include c2 c1 a1 L a2 L a1 H a2 H, ej1 4 or ej1 6 and b 1.6. Similar to the condition of proposition 1, e is equal to j, each hotels uncertainty about its demand condition correlates with one another. Two Nash equilibria were found in proposition 2. These include 1 L1 H2 L2 H 1 in case 81 with ee f f j j kk 0, and 1 H 0, 1 L 1, 2 H 0, and 2 L 1. Since b 1.6, this information sharing equilibr ium cannot be utilized for hotels in the high level of market competition, as b is closer to 1.1, but lower than 1.6. The first information sharing equilibrium indicates that hotels always share information with each other to maximize their profits. However, this information sharing equilibrium was an unusual case because it occurred only if ee f f j jkk 0 in case 21, not case 1 that 1 L1 H2 L2 H 1 with all the values of ee, ff, jj, and kk. Thus, if a hotel deviates from sharing its private information with another hotel, this Nash equilibrium is strictly dominated by the second information sharing equilibrium. In this sense, this equilibrium was not identical to information sharing equilibrium found in the previous literature (Cason, 1991; 1992; Doyl e & Snyder, 1999; Gal-Or, 1996; Raith, 1996; Vives, 1984). Firms should share demand information with competitors, which is case 1 among 81 different possible Nash e quilibria, not case 81 with ee f f j j kk 0. Also, information

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106 sharing equilibrium (1 L1 H2 L2 H 1) in the previous literature is assumed to have symmetric information about demand and cost. But, the results of proposition 2 were assumed to have asymmetric information a bout different costs, such as c2 c1. However, the second information sharing eq uilibrium notes that two similar size and different type hotels share their demand informati on when low demand signal is identified in the market. Two hotels conceal demand information with one another when high demand signal is identified in the market. Importantly, this info rmation sharing equilibriu m strictly dominates the first information sharing equilibrium. For ex ample, if a hotel always shares its demand information no matter what demand signal is in the market, another hotel starts to deviate sharing information when high demand signal is identified. Thus, the other hotel does not have an incentive to share information because a hotel that fails to optimize its profit is eventually driven out by market forces (Mailath, 1998). Over se veral interactions, two hotels end up with not sharing information when they face high demand signal in the market competition. Therefore, the results of proposition 2 suggest th at two similar sizes, but different types of hotels should utilize the second information sharing equilibrium in competition, when b is greater than and equal to 1.6. Basically, sharing demand info rmation with low demand signal and concealing demand information with high demand signal in the market. The results of propositions 3 and 4 should be discussed together. Although the critical value of b can be distinguished between two propositions, the parameters in propositions 3 and 4 include c2 c1 z, where z 30, if ej1 4 or ej1 6 with respect to a2 L z, a2 H wz, a1 L tz, a1 H wtz, where w9 5 and t7 5 These parameters create competition between similar types of hotels, but the hotels differ in their size. For example, competition between Handerly Union Square hotel ( boutique hotel) with 200 guestrooms and Omni hotel (upscale

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107 hotel) with 350 guestrooms in downtown, San Fr ancisco can be supported in propositions 3 and 4. Two Nash equilibria were found from th e results of proposition 3, which has b 1.9. These equilibria were 1L 1 H 2 L 2 H 1 in case 21 with ee f f j j kk 0 and 1 H 0, 1 L 1, 2 H 0, and 2 L 1. Also a unique Nash equilibr ium was sought as results of proposition 4, which had b 1.9. This equilibrium included 1 H 0, 1 L 1, 2 H 0, and 2 L 0. Response to the value of b, proposition 4 can create a comp etition in a relative high level of competition as b is closer to 1.1, while propositi on 3 can create a competition in a relative low or medium level of competition. Also, the results of proposition 3 and 4 were assumed to have asymmetric inform ation about different demands with a2 L z, a2 H wz, a1 L tz, a1 H wtz, w9 5 and t7 5 But, if the value of z is lower than 30, the Nash equilibria are not revealed along with all the different parameter values. Similar to the results of proposition 2, the first Nash equilibrium in proposition 3, which was 1L 1 H 2 L 2 H 1 in case 21 with ee f f j j kk 0, was strictly dominated by the second Nash equilibrium, 1 H 0, 1 L 1, 2 H 0, and 2 L 1. Two similar types and different size hotels share demand information with a demand signal, while hotels conceal demand information with high demand signal in the market. However, the results of proposition 4 indicate when the market competition increases as b is closer to 1.1, a relatively small size of hotel will conceal its demand information with a relatively larger size of hotel with low demand signal. Theoretically, the results of propositions 1, 2, and 3 are identical under different parameter values. The rationale is that one hotel can co njecture the other hotels demand signal, regardless of what it shares or chooses not to share its demand information; the hotel always shares their

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108 demand information with low demand signal, while the hotel always conceals demand information with high demand signal. In this se nse, one-side and two-si de private information subgames in propositions 1, 2, and 3 should be identical to complete information subgames. The results of propositions 5 and 6 also need to be discussed together. The parameters in propositions 5 and 6 include c2 c1 z, if ej1 4 or ej1 6 and a2 L z, a2 H wz, a1 L tz, a1 H wtz, where z 30, w9 5 and t 5. These conditions created competition between similar types of hotels that differed in size. For example, one hotel is at least 5 times larger than the other hotel. Thus, competiti on between Handerly Union Square hotel (boutique hotel) with 200 guestrooms and Hilton San Francisco (upscale hotel) with 1000 guestrooms in downtown, San Francisco can be suppor ted in propositions 5 and 6. Two Nash equilibria were found from th e results of proposition 5, which has b 2.3. These equilibria include 1L 1 H 2 L 2 H 1 in case 81 with ee f f j j kk 0 and 1 H 0, 1 L 1, 2 H 1, and 2 L 0. Also a unique Nash equili brium was found from results of proposition 6, which had b 2.3. This equilibrium was 1 H 0, 1 L 1, 2 H 0, and 2 L 0. Depending upon where the value of b exists between 1 and a different level of market competition is created. Since b is less than 2.3 in proposition 4, this creates competition in a relative high level of competition as b is closer to 1.1, while proposition 6 create competition in a relative low or medium level of competition. Also, the results of propositions 5 and 6 were assumed to have asymmetric inform ation about different demands with a2 L z, a2 H wz, a1 L tz, a1 H wtz, w9 5 and t5. But, if the value of z is less than 30, the Nash equilibria are not found along with all the different parameter values.

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109 Similarly, the first Nash equili brium in proposition 5, which is 1L 1 H 2 L 2 H 1 in case 81 with ee f f j jkk 0, is strictly dominated by the second Nash equilibrium, 1 H 0, 1 L 1, 2 H 1, and 2 L 0. Nash equilibrium in proposition 5 demonstrates an interesting way of sharing privat e information. A relatively small-size hotel shares its demand information with low demand signal, while this hotel conceals demand information in high demand. Conversely, a large size hotel shares its demand information with high demand, while it conceals demand information when low demand in the market. However, the results of proposition 6 indicate when the ma rket competition decreases as b is closer to a large size hotel conceals its demand information with a relatively small size hotel with high demand in the market. The results of propositions 3 and 4 are compared with the results of propositions 5 and 6. The parameters in these propositions are identical, but the value of t creates a different size of hotels (t7 5 versus t 5). As per the value of t changes, the critical value of b is also changed (b 1.9 versus b 2.3). This result offers an insight that as the value of t increases, the critical value of b increases. That is, when hotels, which differ in size by the value of t, compete with each other, their information shar ing equilibrium may change accord ing to the critical value of b. The results of propositions 7 and 8 also need to be discussed together. The parameters in propositions 7 and 8 include c2 c1 z, where z 30 if ej1 4 or ej1 6 and a2 L z, a2 H wz, a1 L tz, a1 H wtz, where w 3, and t7 5 This condition creates a competition between similar types of hotels, but the hotels differ in size by 7 5 Importantly, the value of w creates the fluctuation of demand of a hotel. For example, define z as 100. Then, a2 L 100,a2 H 300, a1 L 140, anda1 H 420. Hotel 2s low demand is equal to 100, while its

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110 high demand is 300, which means that their demand fluctuates by 200 according to a demand signal in the market. Therefore, competition betw een two mid-scale of reso rt hotels on Atlantic Avenue in Daytona Beach, Florida can be s upported in propositions 7 and 8. Also, since e is equal to j, each hotel has identical beliefs about it s competitor given its information about its own demand. A unique Nash equilibrium was found in th e results of proposition 7 with respect to 1.5 b 2.4. These include 1 H 0, 1 L 1, 2 H 0, and 2 L 0. Since the value of b is between 1.5 and 2.5, this equilibrium was not su pported for hotels in th e high and low level of market competition where b was closer to 1.1 and respectively. Tw o similar types and different size of hotels conceal demand information with high demand. But, relatively small size hotels always share demand information with low demand, while a relatively larger size hotels always conceal demand information with low dema nd in the market. However, the results of proposition 8 noted that two similar types and different size hotels always conceal demand information irrespective of demand signals as b is between 2.4 and 2.8. Also, the results of propositions 7 and 8 are compared with the results of propositions 3 and 4. The parameters in these propositions are identical, but the value of w, which creates a relatively different demand for two different hotel sizes (w9 5 versus w3). As per the value of w changes, the critical value of b is also changed (b 1.9 versus b 2.6). That is, when hotels, which differ in their relative demand (by the value of w), compete with each other, their information sharing equilibrium changes according to the critical value of b. Overall, the results of this st udy demonstrate that constant (b) is the most significant indicator in the price competition model with resp ect to all the parameter values. The constant (b) creates a different level of competition. Th is finding supports the study of Rogers (1980) and

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111 Cason (1991), which explains a major influence on the demand function is the competitive structure of the industry where firms operate. Firms may not ignore their vulnerability to the effects of decisions made by their competitors in varying degrees of competitions (Rogers, 1980). This interdependence of fi rms intensifies the degree of uncertainty in the market (Cason, 1991; Gal-Or, 1986; Kuhn & Vives, 1995). To this end, the findings of this study are valuable with respect to the information-sharing equilibria. The rationale is that these equilibria indicate the incentive for hotels to share or c onceal information with competitors. Conclusions and Implications The lodging industry has establis hed diverse pricing strategies via yield management to optimize revenue and profitability in the high ly competitive markets (Kimes, 1989; 1994; Lewis & Shoemaker, 1997; Orkin, 1989). However, given the competitive and uncertain nature of the lodging industry in demand and supply, it is critical for hotel managers to capture the dynamics of ADR and occupancy rate in real time through communication mechanisms (Kirby, 1988; Krishna, 2007). This information-sharing process enhances the quality of pricing indicators in determine pricing strategies against competitors. By using these, pricing strategies can be effectively determined to maximize profits, and fu rther secure financial st ability and growth of lodging businesses. Previous literature in economics and opera tional research noted that sharing demand information in Bertrand model is always better of f in order to increase profits (Cason, 1992; GalOr, 1985; Moorthy, 1998; Shaked & Sutton, 1982; Vandenbosch & Weinberg, 1995; Vives, 1984). Nonetheless, the results of this study revealed th at information sharing equilibrium varies with different scenarios in the l odging industry. First, similar sizes and types of hotels generally share their demand information with each other wh en low demand signal is identified, while they conceal demand information with high demand signal, regardless of the competitive nature of the

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112 market. Second, similar sizes but different type s of hotels also share demand information with low demand signal, while they conceal demand information with a high signal if there is a medium or low-level of competitor, but share inform ation if there is a high level of competition. Third, hotels that are similar in type, but diffe r in size share their demand information with each other when each hotel faces low demand signal if th ere is a medium or high level of competition. However, as market competition increases, the relatively smaller sized hotels conceal demand information against larger hotels when the sm all sized hotels face low demand signal with a high-level of competition. These hotels con ceal demand information when high demand signal is identified regardless of the extent of competition. Fourth, in a competition between similar types of hotels, which differ in size, the small size hotels share their demand information when the hotels face high demand signal if there is a high or medium level of competition. As level of competition decreases (b is closer to ), the hotels conceal demand information with low demand signal no matter which level of competition exusts. However, the larger hotels (at least 5 times bigger) share demand information with low demand signal, while these hotels conceal de mand information when high demand signal is presented, irrespective of competition. Lastly, hotels, which are similar in type, but differ in size, and face a fluctuation in demand (seasona lity) conceal their demand information with high demand signal when there is a low-level of competition. But, relatively larger hotels, which also have higher demand fluctuation, share demand information when they encounter low demand signal in low-level competitions. This study has contributed valuable insight into information-sharing behaviors among hotels and optimal pricing strategi es. This may consequently resu lt in greater collaboration and alliances in the lodging industry in the future This study identified market competition,

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113 marginal cost, market demand, size of hotel and fluctuation of demand (seasonality) as significant indicators in resolving or establishi ng optimal pricing strategy in associated with information-sharing behavior s in the lodging industry. Based on the results of this study, the fo llowing recommendations are proposed for the lodging industry. In yield management, information-shar ing behavior should be considered Acquire dynamic information about ADR and occupancy rates from different communication mechanisms (e.g., personal re lationships; phone cal ls; Smith Travel Research; third party websites) Information-sharing is not always better o ff in optimizing revenue and profitability Information-sharing equilibrium varies depending on a level of competition Depending on demand fluctuation (high versus low), information sharing equilibrium (optimal information-sharing behaviors) varies in the low-level of competition. More specifically, o Managers should share demand information in competition between similar type hotels that differ in size, if there is low demand signal o Managers should conceal demand information in competition between similar types of hotels that differ in size, if there is high demand signal Information-sharing equilibrium varies with respect to type and si ze of hotels. More specifically, 1) competition between similar sizes and types of hotels: o Share demand information with low demand signal o Conceal demand information with high demand signal

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114 2) competition between similar sizes and different types of hotels in the medium or low level of competition: o Share demand information with low demand signal o Conceal demand information with high demand signal 3) competition between different sizes and sa me types of hotels in the medium or low level of competition: o Share demand information with low demand signal o Conceal demand information with high demand signal 4) competition between the different sizes and same types of hotels in the high level of competition: o Conceal demand information with high demand signal For a relatively small size of hotels: o Share demand information with low demand signal For a relatively larger sizes of hotels: o Conceal demand information with low demand signal 5) competition between the different sizes and same types of hotels in the high or medium level of competition, for relatively small size of hotels: o Share demand information with low demand signal o Conceal demand information with high demand signal For the relatively larger size of hotels: o Share demand information with high demand signal o Conceal demand information with low demand signal

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115 6) competition between the different sizes and same types of hotels in the low level of competition, for relatively small size hotels: o Share demand information with low demand signal o Conceal demand information with high demand signal For relatively larger size hotels: o Share demand information with high demand signal o Conceal demand information with low demand signal 7) competition between the different sizes a nd same types of hotels, for the relatively larger sizes of hotels (a t least 5 times bigger): o Conceal demand information For the relatively small sizes of hotels: o Share demand information with low demand signal o Conceal demand information with high demand signal Limitations Three limitations were identified in this e xploratory study. First, the main study (Phase 1) was mathematically solved with three different correlations (i.e., c1 c1; c15 4 c1; c18 5 c1). These correlations were induced ba sed upon the actual price information, not on their actual cost information with respect to three different types of hotels (upscale; mid-scale; economy). Also, the cost parameter for hotels was set in either high and low cost, and was assumed to have constant marginal costs, with out consideration of fixed costs of hotels. However, in a reality of the lodging industry, the cost variable varies according to location, type, and age of hotels with respect to fixed co sts (ONeill and Mattila, 2006). Thus, the generalizability of the results (i.e., information sh aring behavior; Nash equilibria) derived from a

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116 simple and convenient assumption in this theore tical model to the entire lodging industry was limited. Second, hotels make decisions about the amount of private information disclosure, and need to decide whether to truthfully reveal or co nceal information. This decision is made before any uncertainty is resolved through information sharing behavior (A gastya, Menezes, and Sengupta, 2006). However, in this explorator y study, the assumption that hotels truthfully revealed their information was implied. It is also possible that a hotel revealed untruthful or false information. Lastly, in Phase 2 of this expl oratory study, the phone intervie ws were used to identify the actual information sharing behaviors of five hotels in order to conf irm the relevance and implication of two stages of price competition m odel in the tourism and hospitality context. The participants of the phone interview were only selected from ge neral managers of five hotels in Marion County, FL. More interviews with subjects in different positions (e.g., hotel executives; sales managers; the front desk) and markets (e.g ., Las Vegas; Orlando) would have been useful data. The rationale is that interviewing ot her employees might provide further insight in information sharing behaviors with respect to the optimal pricing strategies (Nash equilibria). Furthermore, only five hotels were employed fr om the study site, which was not representative of all hotels. Recommendations for Future Study Several areas were recognized for future res earch. These include: 1) Cournot competition; 2) cost uncertainty; 3) demand segments; a nd 4) independent hotel vs. hotel by chain Cournot Competition The type of competition (Bertrand vs. Cournot) is also related to incentives to share or conceal information (Kuhn & Vives, 1984). It is because the type of competition determines the

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117 slope of the firms reaction function in game theoretical competition model (Cason, 1991; 1994; Vives; 1984). Therefore, the optimal informati on sharing behaviors along with Nash equilibrium in Cournot competition model (demand competition model) may not be identical to those in Bertrand model (price competition model). However, as per the nature of the lodging industry, the quantity is not controlled, Cournot model with respect to information sharing equilibrium could be further examined in different settings. Cost Uncertainty Similarly, the source of uncertainty (demand vs. cost) influences the incentives to share information (Cason; 1991; 1994; Kuhn & Vives, 1995). Especially, the uncertainty source along with the information-sharing decision determin es the degree of correlation between firms strategies. The rationale is that reduced correl ation either has a negativ e or positive effect on profit functions depending on the type of competition. To this end, cost uncertainty in gametheoretical competition model (e.g., price or demand competition model) needs to be further examined. Demand Segments In the lodging industry, both product and timing heterogeneity induce several different demand schedules (Shaw, 1984). Also, it is common for the lodging businesses to provide numerous pricing strategies for different market segments (Collins & Parsa, 2006). Therefore, it would be useful to develop a Bertrand model ba sed on market segments with consideration to off-season and high season within the lodging industry. Independent Hotel vs. Hotel by Chain Information sharing behaviors of independent and chain-affiliated hotels would likely be different due to the varying management philosophy. In general, there are more chain-affiliated hotels than independent properties in the market place. Chain affiliated hotels usually depend on

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118 the business traveler and meetings/convention ma rkets, and are likely to have negotiated room rates. Conversely, independents are usually smaller properties that tend to focus on the independent traveler and leisure market that associates with discounted room rates. Given the differences in property type, si ze, and management philosophy, it would be useful to develop price competition model with respect to information sharing between chain affiliated and independent properties.

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126 BIOGRAPHICAL SKETCH Sungsoo Kim, a Korean, has spent his life in introducing strategic m arketing modeling into the filed of tourism and hospitali ty management during his study at UF. Also, e-service quality with special reference to visual images on Internet compromise within his research foci. He received his Ph.D. in 2008. He has found he feels most alive when laughing, playing with math, traveling, and spending time on the ocean. He used to live in Gainesville, Florida with his pet, Jolly.