Optimal Information-Sharing Behaviors among Hotels: Game-Theoretical Approach

Abstract

The lodging industry uses diverse pricing strategies to maximize revenues. Given the uncertain nature of decision parameters (demand conditions), sharing information among competitors can dramatically affect hotels’ profits. This study examines the decisions of hotels to share or not to share private information with competitors to maximize profits via a game-theoretic model. In a two-stage model, hotels decide whether to share information in the first stage, and then, in the second stage, they compete in setting prices along the lines of a standard price competition model. Results include that hotels share demand information with their competitors if there is a low demand signal but conceal information if the demand signal is high. This study provides a standard price competition model that can assist hotel managers in decision making on revenue management, including room pricing strategy.

Keywords

game-theoretical model information sharing Nash equilibrium price competition model lodging industry revenue management

The lodging industry is a highly competitive market as the room inventory continues to increase with the establishment of new hotels, resorts, and other facilities (Angelo & Vladimir, 2017). There are approximately 17.5 million hotel rooms globally, with more than 5 million (about 28.6%) located in the United States (STR Global, 2019). Moreover, guestroom rates change based on the season or the day of the week. For example, due to the perishable nature of the product (i.e., room nights), hotels offer discount rates when demand is weak but not during strong demand. This way, hotels need to sell more rooms daily even though the prices may be discounted as empty rooms represent a lost opportunity to generate revenues (El Haddad, 2015; Saito et al., 2016). Given the competitive nature of the industry, it is critical for decision makers (e.g., hotel managers) to understand the dynamics of average daily rates (ADR) and occupancy. This would assist them in determining optimal guestroom rates or pricing strategies to generate profits and further secure financial stability and growth.

Meanwhile, due to the uncertain nature of decision parameters—such as cost, price, and demand conditions—sharing information among competitors can dramatically affect firms’ pricing strategies (Gal-Or, 1986; Kuhn & Vives, 1995; Van Zandt & Vives, 2007; Zhou et al., 2019). Such information sharing can occur in a variety of ways. Often, hotels use mediated communication mechanisms via trade associations to whom private information is submitted, which then make it available to other hotels (Krishna, 2007). Trade associations periodically gather sales information from participating hotels, and then aggregate information is disseminated. For example, the American Hotel & Lodging Association (AH&LA), an industry trade association, publishes a “Lodging Report” on a regular basis that disseminates information from participating hotels about occupancy and ADR (Lodging Market Data Book, 2018). Similarly, Smith Travel Research (STR) periodically reports information about hotel performance related to ADR, revenue per available room (RerPAR), demand, supply, and revenue by each respective hotel based on regions or cities. This type of report is available monthly unless hotels request on a quarterly, bimonthly, weekly, or daily basis. Hotels that participate in STR are both senders and receivers of such confidential information.

In addition, hoteliers often check prices of their competitors via hotel sites or independent online travel websites, such as Expedia, Orbitz, and Travelocity (Best Hotel for Any Budget, 2018; O’Connor, 2003). While some information about room prices is easily determined from such websites, many factors of significance cannot be learned from the respective websites. Although discounted pricing information is available, direct indicators, such as occupancy rate, average room rate, gross operating profit, marginal cost, and room sales are not (Chattopadhyay & Mitra, 2019; O’Neill & Mattila, 2006; Saito et al., 2016). This information is only fostered through information systems whereby managers have access to historical data used for budgeting and financial decisions.

In a situation where decision makers interact with each other, game-theoretic models (or game theory) can assist hotel managers to comprehend timely and prognostic information (Rasmusen, 2007). In strategic games, a decision maker selecting a strategy to maximize profits must take into account the strategies of competitors. In particular, information sharing can enhance their ability to find successful strategies when there is competition in a market environment (Osborne, 2009; Zhou, et al., 2019). Game-theoretic models help characterize the incentives for firms to share or not to share private information with competitors (Cason, 1994). The basic way in which game-theoretic models incorporate strategic interactions is through the notion of Nash equilibrium (Osborne, 2009; Rasmusen, 2007). In the hotel setting, being at a Nash equilibrium means that each hotel has correct beliefs about what other hotels are doing and given these beliefs act rationally.

The existing literature on information sharing has developed several insights that may not fully apply to the hotel industry. Among the insights are that, under price competition, firms might raise profits when they share their demand information with competitors (Kuhn & Vives, 1995; Rodriguez, 2003; Van Zandt & Vives, 2007; Zhou, et al., 2019) but would not share private cost information (Gal-Or, 1985). However, when firms compete by choosing quantities, not prices, then sharing their private cost information raises their expected profits (Shapiro, 1986). Cason (1994) further expanded on this argument by showing that firms would conceal cost information if the goods were substitutes but would share cost information if they were complements. Collectively, these results suggest that firms’ optimal strategies vary with the type of competition. Furthermore, the nature of goods also creates variations in the firms’ information-sharing strategies.

In the hospitality industry, the nature of the product sold is quite different from that of traditional products, such as automobiles and computers. The focus of the product in the hospitality industry is intangible, and after consumption of the product, there is no tangible rate of return (Kotler et al., 2017). Additionally, the nature of the product in the hotel business is perishable, so more rooms need to be sold although the prices are significantly discounted. Also, hotels in a marketplace may differ significantly from each other in their costs and qualities, whereas the existing models assume that all firms in an industry are essentially identical. In this regard, competitive conditions (price or demand competition) and the nature of the products create further combinations of different scenarios. For each scenario, an applicable solution exists based on theoretical reasoning and mathematical modeling.

To this end, a model based on game-theoretical reasoning can offer an opportunity to investigate information-sharing behavior under price competition in the hospitality discipline. The rationale is that the equilibrium for firms with respect to sharing of private information with competitors may differ compared with traditional firms. Since game-theoretic models have not been tested in the context of information sharing in the hospitality business, the potential implications to the discipline and the business could be impactful. Therefore, the objective of this study is twofold. First, a price competition model is developed based on the most significant indicators for hotel managers (e.g., revenue manager), including hotels’ ADR, occupancy rate, marginal cost, and market demand. In particular, a two-stage model is developed where hotels share decisions in the first stage and then, in the second stage, compete with each other based on the standard price competition model. Second, all strategies in the two-stage model are examined to further determine Nash equilibrium, which ensures that the predominant outcomes are based on rational behavior by hotels’ managers. More specifically, the purpose of this exploratory research is to answer the following question: What are Nash equilibria hotel pricing strategies in a price competition model with respect to information-sharing behaviors between different types (i.e., upscale, midscale, and economy) and similar size hotels?

Theoretical Background

Game theory is the study of multiperson decision problems (Osborne, 2009). Such problems arise frequently in economics and social and behavioral sciences (Arenoe et al., 2015; Chung, 2000; Huang, 2010; Rasmusen, 2007). For example, oligopolies present multiperson problems, where each firm must consider what the others will do, since there is interdependence between their actions. The consequences to a business (e.g., hotel) in employing a specific pricing strategy depend on the pricing strategies of competitors (Chung, 2000; Huang, 2010). At the micro level, models of trading processes (e.g., bargaining and auction models) involve game theory (Kokott et al., 2019; Osborne, 2009; Rasmusen, 2007). At an intermediate level, aggregation, labor, and financial economics include game-theoretic models of firm’s behavior (Kagel & Roth, 2016). At the macrolevel, international economics includes models in which countries compete or collude in choosing tariffs and other trade polices (Kagel & Roth, 2016). As Rasmusen (2007) states, there are multiperson problems even within a firm. For instance, many workers may vie for one promotion or several divisions may compete for the corporation’s investment capital.

A variety of different approaches exist within game theory to analyze such situations. One basic division is between cooperative and noncooperative models (Osborne, 2009; Rasmusen, 2007). In cooperative game theory, participants can form coalitions that can make enforceable agreements. The analysis revolves around which coalition will form, determined largely by what different coalitions can achieve. Specific strategies and actions by individual participants are generally not specified. In noncooperative game theory, every participant makes independent decisions, and the analysis focuses on the particular strategies that are available to each of them (Rasmusen, 2007). Cooperation may be an outcome of the players’ independent choices, but it occurs because none of them gain by deviating, and not because they have agreed to an enforceable contract (Avinadav et al, 2019; Kagel & Roth, 2016; Mailath, 1998; Van Zandt & Vives, 2007; Yan & Pei, 2011). While information sharing among firms may seem to be a cooperative arrangement, noncooperative game theory seems the more appropriate way to analyze its occurrence. Whether firms share their information about demand or costs will be a voluntary decision by each that will happen only if it is a noncooperative equilibrium (Osborne, 2009; Rasmusen, 2007).

Noncooperative games can be divided between those with complete and incomplete information (Rasmusen, 2007; Schmidt, 2003). In a game with complete information, every player knows the complete structure of the game, which includes knowing the full set of strategies and the payoffs of every player. In a game of incomplete information, a player lacks full knowledge of some aspects of the game, usually something about other players such as their strategy space or payoffs. Lacking full information, a player is typically assumed to have beliefs in the form of a probability distribution over the payoffs or strategies of the others (Rasmusen, 2007). Although it may provide a useful starting point in analyzing many situations, a game of complete information rarely exists in games between real-world firms (Osborne, 2009; Zagare, 1984). This is especially true when considering information sharing. Each firm has private information about its costs or demand, which is not known to others. If information is not shared, the players are clearly in a situation of incomplete information. If all of them share their information, the game is turned into one of complete information (Schmidt, 2003).

Another distinction is between static and dynamic games (Osborne, 2009; Rasmusen, 2007). In a static game, the players can be viewed as if they make a one-time decision about their actions without adjusting what they do because they learn about the actions of others. In a dynamic game, players take some actions, learn something about the actions of others, and then take other actions. Consider the information-sharing context. Firms take a sequence of actions: first, they decide whether or not to share their private information, and then, after learning whether or not others decided to share and, if they did share, what the information that they had was, firms then take particular market actions such as choosing a price (Gibbons, 1992; Kagel & Roth, 2016; Rasmusen, 2007). An information-sharing game is thus innately dynamic between the two decisions. However, each decision is typically made simultaneously. The firms must decide whether to share their information without knowing whether or not others will share. Once sharing decisions are made and carried out, the firms simultaneously set their prices (Gibbons, 1992; Mailath, 1998; Osborne, 2009; Rasmusen, 2007; Rodriguez, 2003).

A subgame is a part of a game that can be separated from the rest and be played (or analyzed) on its own independent of what happens elsewhere in the game (Rasmusen, 2007). A situation where players’ behaviors satisfy the conditions of Nash equilibrium not just in the whole game but also on every subgame is called a subgame perfect Nash equilibrium. In this setting of a multistage noncooperative game of incomplete information, the Nash equilibrium can be found by working backward (Gibbons, 1992; Osborne, 2009). In the second stage, after the information-sharing decisions have been made, firms are in a complete information subgame if all of them reveal their information, or are in an incomplete information subgame if at least some have chosen not to share. In whatever subgame exists, a Nash equilibrium has each firm choosing its price to maximize its expected profits given its beliefs about any information it does not have and its beliefs about the prices other players are setting. Thus, maximization is one part of Nash equilibrium. The second part of Nash equilibrium is that each player’s beliefs must be consistent with other aspects of the game. Beliefs about unlearned information must be consistent with what that information could be. Beliefs about the prices chosen by others must be consistent with what the others actually chose (Avinadav et al., 2019; Rasmusen, 2007). Then, consider the first stage. A player decides whether to share information looking ahead to the different second-stage equilibria arising from different sharing decisions. Again, a Nash equilibrium has each player deciding on whether to share information based on what maximizes its profits given its beliefs about the information of others and about their sharing decisions (Avinadav et al., 2019; Gibbons, 1992; Li et al., 2018; Osborne, 2009; Osborne & Rubinstein, 1994; Rasmusen, 2007; Van Zandt & Vives, 2007). Essentially, beliefs must be consistent with what others actually do and with the equilibrium in the next stage.

One important thing to note is that strategies used by players can be either pure or mixed (Gibbons, 1992; Osborne, 2009; Rasmusen, 2007). A pure strategy is when a player in a particular circumstance does one specific thing. A mixed strategy is when a player in a particular circumstance randomly chooses what to do from the set of available pure strategies. From the beginning of formal game-theoretic analysis by Borel and von Neumann in the 1920s, the importance of mixed strategies was recognized. To understand the role of mixed strategies, consider a pricing game between two competing identical hotels. Assume that one of them plays a pure strategy of definitely pricing rooms at some particular price and assume that the other hotel can either observe or deduce this price. The second hotel can take much business from the first simply by undercutting the first hotel’s price by a small amount. The first hotel can defend against this by using a mixed strategy so that the second hotel cannot know for sure what the first hotel’s price will be and thus cannot do a simple undercut of it. In general, the role of mixed strategies is to at least partially hide from its opponents what a player is going to do (Rasmusen, 2007).

Model Building

The formal model is based on price competition between two hotels that provide differentiated products and that have uncertainty about demand. Demand uncertainty and information sharing is modeled on the approach of Vives (1984), where firms know their own demand but are imperfectly informed about that of their competitors. In the presence of this uncertainty, hotels decide whether to share or conceal their private information to maximize expected profits. The model here makes three major modifications to that noted in Vives (1984). First, instead of having to decide whether to share information before receiving their private information, hotels first learn the value of their demand intercept and then decide whether to share this information. Since this complicates the analysis, the second modification is to simplify the random structure to maintain tractability. Randomness in the demand intercept is assumed to be discrete instead of continuous, taking on either a high or a low value. Third, hotels are not assumed to be symmetric but can have different costs or demands. This allows for considering competition between different types of hotels, an important real-world consideration.

Costs and Demands

Each hotel has a constant marginal cost (operating costs) for each unit sold (Gu, 1997; Saito et al., 2016), but different hotels can have different costs. An upscale hotel would have higher marginal costs than a midscale one, which in turn would have higher costs than an economy hotel. These hotels may also differ in their fixed costs, but such fixed costs do not directly affect information-sharing decisions, so they are not specifically modelled. In this duopoly model, each hotel faces a linear demand curve where the quantity (occupancy rates) sold equals an amount (the demand intercept) that it would sell at a zero price less decreases due to having its own price being positive plus increases due to its competitor selling at a positive price. The demand intercept can be of a high or a low value. Hotels could be large, medium, or small in scale and thus could differ in size (i.e., the total number of rooms they have available). Both demand and costs vary among different types of hotels. A hotel’s demand is assumed to be more responsive to its own price than to that of its competitors. Basically, when hotels’ own price effect is closer to the cross effect, the market is more competitive. However, when they differ significantly, the market is less competitive and more segmented. The difference between these effects reflects whether hotels are similar or different in their nature. Similar hotels would be highly competitive, whereas different types of hotels would be significantly less competitive.

Timing and Information

Nature (i.e., a term in game theory for any randomly determined variables such as demand intercepts) first chooses the demand intercept for each hotel. This creates what is called a state of nature based on random outcomes. There are four possible states of nature denoted as $(L, L)$ , $(L, H)$ , $(H, L)$ , and $(H, H)$ , where, for example, $(L, L)$ means each hotel has randomly gotten a low demand. Then, the hotels decide simultaneously whether to share or conceal demand information based on their own respective demands. Hotels simultaneously set prices following an assessment of their demand and based on any particular information about their competitors that they may have. This game is one of incomplete information since hotels may not know their competitor’s type. Given the structure of the game, the basic solution concept used is subgame perfect Nash equilibrium. To apply that notion in this context, the game is solved backward. For example, equilibrium prices can be found to be conditional on the hotels’ information and on sharing decisions in the final stage. Using these equilibrium prices, the level of expected profits for each hotel in each circumstance can be computed. Using these expected profits, hotels make decisions on whether or not to share information. The equilibrium-sharing decisions are found in the first stage of the game. The timing of actions and the strategies at each state are presented in the game tree in Figure 1.

Figure 1

Game Tree

Model Formalization

The constant marginal costs of the two hotels are denoted as $c_{1}$ and $c_{2}$ . It is convenient to specify demand in the form of inverse demand functions, which present the prices as functions of quantities, instead of specifying the ordinary demand, which gives quantities as a function of prices. These inverse demand functions are denoted as

p_{1} = a_{1} - b q_{1} - d q_{2}

(1)

p_{2} = a_{2} - b q_{2} - d q_{1}

(2)

where $a_{1}$ and $a_{2}$ are the demand intercepts, $q_{1}$ and $q_{2}$ are the quantities (occupancy rate), and b and d are constants (coefficients) related to their own and cross-price effects.

Solving the Equations (1) and (2) for $q_{1}$ and $q_{2}$ yielded the ordinary demand functions:

q_{1} = (\frac{a_{1} b - a_{2} d}{b^{2} - d^{2}}) - (\frac{b p_{1} - d p_{2}}{b^{2} - d^{2}})

(3)

q_{2} = (\frac{a_{2} b - a_{1} d}{b^{2} - d^{2}}) - (\frac{b p_{2} - d p_{1}}{b^{2} - d^{2}})

(4)

The demand intercepts $a_{1}$ and $a_{2}$ could each take on one of two values—high or low—denoted as $a_{1}^{H}$ and $a_{1}^{L}$ for Hotel 1 and $a_{2}^{H}$ and $a_{2}^{L}$ for Hotel 2. Nature randomly chose the value of these demand intercepts. The probability distribution over different pairs of the intercepts for the two hotels is illustrated in Table 1.

Table 1

Probability Distribution

	a₂ ^L	a ₂ ^H
a₁ ^L	k	e
a₁ ^H	j	f

Note: $k + e + j + f = 1$ , and $k, e, j, f \geq 0 .$

This general specification contained different special cases. One polar case with only common uncertainty would arise if $e = j = 0$ . Then, each hotel would know exactly the other hotel’s demand when it learned about its own. On the other hand, if $k / (k + e) = j / (j + f)$ (which also implies that $k / (k + j) = e / (e + f)$ ), then each hotel’s uncertainty is purely private. When a hotel learned about its own demand intercept, this conveyed no information about the other hotel. The probability that the other hotel has a high or a low intercept is unaffected by a hotel’s own intercept value. In between situations with $(k / k + e) > (j / j + f) > 0$ (or equivalently $(k / k + j) > (e / e + f) > 0$ ) would involve a mixture of common and private uncertainty. Hotels partially learned about the other hotels’ demand based on their own demand.

In the final stage, based on what the hotels learned about their own demand and that of their competitors from information sharing, there are nine subgames, divided into three types: complete information, one-sided private information, and two-sided private information. The four complete information subgames occurred for the four states of nature when both hotels shared information in that state. Subgames of one-sided private information arise when one shares information and the other does not. For example, if Hotel 1 has a low demand and shares that with Hotel 2, but Hotel 2 does not share its information, then Hotel 2 knows for certain whether the state of nature is $(L, L)$ or $(L, H)$ , depending on its own information. Hotel 1 does not know for certain the demand of Hotel 2, and hence, it does not know for certain which of those two states is true. Hotel 1 instead has beliefs about the likelihood of which of those states has occurred. These beliefs depend on two considerations: the underlying probabilities of Hotel 2 having a high or a low demand as determined by nature and Hotel 1’s beliefs about the probabilities that Hotel 2 chooses to share information given its level of demand. Denote the equilibrium probabilities with which Hotel 2 shares information given the knowledge of its own type as $α_{2}^{H}$ and $α_{2}^{L}$ . Then, Hotel 1 views $(L, L)$ or $(L, H)$ as arising with probability $(1 - α_{2}^{L}) k / [(1 - α_{2}^{L}) k + (1 - α_{2}^{H}) e]$ and $(1 - α_{2}^{H}) e / [(1 - α_{2}^{L}) k + (1 - α_{2}^{H}) e]$ . Similarly, if nature selects Hotel 1 as H with probability j + f and Hotel 1 shared this information, then, Hotel 1 would believe that $(H, L)$ arose with probability $(1 - α_{2}^{L}) j / [(1 - α_{2}^{L}) j + (1 - α_{2}^{H}) f]$ , while Hotel 2 would know for certain 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-sided incomplete information exists when neither hotel chose to share. Then, neither hotel knows the other hotel’s demand. In this subgame, nature has selected $L$ for Hotel 1 with probability $k + e$ . Hotel 1 knows this outcome but does not know Hotel 2’s type. Hotel 1 does know that Hotel 2 chose not to share information. Thus, Hotel 1 believed that $(L, L)$ arose with probability $(1 - α_{2}^{L}) k / [(1 - α_{2}^{L}) k + (1 - α_{2}^{H}) e]$ and that $(L, H)$ arose with probability $(1 - α_{2}^{H}) e / [(1 - α_{2}^{L}) k + (1 - α_{2}^{H}) e]$ . If, nature selected Hotel 1 as $H$ with probability $j + f$ , that Hotel 1 believes that the probabilities of $(H, L)$ and $(H, H)$ are $(1 - α_{2}^{L}) j / [(1 - α_{2}^{L}) j + (1 - α_{2}^{H}) f]$ and $(1 - α_{2}^{H}) f / [(1 - α_{2}^{L}) j + (1 - α_{2}^{H}) f]$ . Similarly, if Hotel 2 was $L$ (which arose with probability $k + j$ ), it did not know whether Hotel 1 was $L$ or $H$ , viewing $(L, L)$ with probability $(1 - α_{1}^{L}) k / [(1 - α_{1}^{L}) k + (1 - α_{1}^{H}) j]$ and $(H, L)$ with probability $(1 - α_{1}^{H}) e / [(1 - α_{1}^{L}) k + (1 - α_{1}^{H}) e]$ . If Hotel 2 were $H$ , it believes that $(L, H)$ and $(H, H)$ arose with probabiites $(1 - α_{1}^{L}) j / [(1 - α_{1}^{L}) j + (1 - α_{1}^{H}) f]$ and $(1 - α_{1}^{H}) f / [(1 - α_{1}^{L}) j + (1 - α_{1}^{H}) f]$ .

Model Analysis

The two-stage competition model was solved by backward induction. First, equilibrium prices and expected profits were determined in the second stage based on hotels’ demand information and sharing decisions. Second, using these expected profits, in the first stage of the game (see Figure 1), hotels simultaneously chose to share or not to share information. As such, the second stage of the model was first examined, followed by the first stage. In the first stage, each hotel knew its type and 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 $α_{1}^{L}$ and $α_{1}^{H}$ for the decisions of the high and the low demand types for Hotel 1, and $α_{2}^{L}$ and $α_{2}^{H}$ for the high and the low demand types for Hotel 2.

The final stage was solved analytically using Mathematica 14.0, 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 among unknown parameters in equations were found analytically, but their intersections were identified numerically using Mathematica 14.0 for a variety of parameter values. The optimal mixed strategies of each hotel type can take on one of three types of values: a pure strategy of sharing with $α_{i}^{D} = 1$ , a pure strategy of not sharing with $α_{i}^{D} = 0$ , or a mixed strategy in which the hotel is indifferent between sharing and not sharing denoted by $α_{i}^{D} = [] . I f α_{i}^{D} = 1$ , then Hotel i of Type D must get higher profits from sharing information, while if $α_{i}^{D} = 0$ , the profits from not sharing must be greater. If the hotel is indifferent, then expected profits are equal. Note then that 3⁴ = 81 different types of equilibrium exist depending on which type of value each $α_{i}^{D}$ took. When multiple equilibria existed during this first stage, equilibrium in which a hotel used a weakly dominated strategy were discarded.

Many possibilities exist given the range of values for the different parameters. One case of interest is when there is competition between an upscale and a midscale hotel, where the upscale hotel has higher costs. The following proposition gives the Nash equilibria in this case.

Proposition: Two pure-strategy Nash equilibria (i) $α_{1}^{H} = α_{2}^{H} = 0$ and $α_{1}^{L} = α_{2}^{L} = 1$ and (ii) $α_{1}^{H} = α_{2}^{H} = α_{1}^{L} = α_{2}^{L} = 1$ exist under the following parameter values: $c_{2} < c_{1} < a_{1}^{L} = a_{2}^{L} < a_{1}^{H} = a_{2}^{H}$ , where $c_{2} = 15, a_{1}^{L} = a_{2}^{L} \geq 30$ if $e = j = 1 / 4$ or $e = j = 1 / 6$ and $b \geq 1.6$ (see Tables 2 and 3).

Table 2

Sensitivity Analysis for Proposition $a_{1}^{H} = a_{2}^{H} = 0$ and $a_{1}^{L} = a_{2}^{L} = 1$

aL1	aH1	aL2	aH2	aL1	aL2
30 ≤ aL1 < 120	30 ≤ aH1 < 120	<120	<160	>	>
120	60	120	160	>	>
120	165	120	165	>	>
120	170	120	170	>	>
120	175	120	175	>	>
120	180	120	180	>	>
125	160	125	160	>	>
125	165	125	165	>	>
125	170	125	170	>	>
125	175	125	175	>	>
125	180	125	180	>	>
130	160	130	160	>	>
130	165	130	165	>	>
130	170	130	170	>	>
130	175	130	175	>	>
130	180	130	180	>	>
135	160	135	160	>	>
135	165	135	165	>	>
135	170	135	170	>	>
135	175	135	175	>	>
135	180	135	180	>	>
140	160	140	160	>	>
140	165	140	165	>	>
140	170	140	170	>	>
140	175	140	175	>	>
140	180	140	180	>	>
>140	>180	>140	>180	>	>

Note: Other parameters: $c_{2} < c_{1} < a_{1}^{L} = a_{2}^{L} < a_{1}^{H} = a_{2}^{H}$ , where $c_{2} = 15, a_{1}^{L} = a_{2}^{L} \geq 30$ if $e = j = 1 / 4$ or $e = j = 1 / 6$ and $b \geq 1.6$ . $a_{1}^{H}$ = $E (\prod_{1 H}^{S})$ - $E (\prod_{1 H}^{N S})$ , $a_{1}^{L}$ = $E (\prod_{1 L}^{S})$ - $E (\prod_{1 L}^{N S})$ , $a_{2}^{H}$ = $E (\prod_{2 H}^{S})$ - $E (\prod_{2 H}^{N S})$ , and $a_{2}^{L}$ = $E (\prod_{2 L}^{S})$ - $E (\prod_{2 L}^{N S}) .$

Table 3

Sensitivity analysis for proposition: $a_{1}^{L} = a_{1}^{H} a_{2}^{L} = a_{2}^{H} = 1$

aL1	aH1	aL2	aH2	aL1	aL2
30 ≤ aL1 < 120	30 ≤ aH1 < 120	<120	<160	>	>
120	160	120	160	>	>
120	165	120	165	>	>
120	170	120	170	>	>
120	175	120	175	>	>
120	180	120	180	>	>
125	160	125	160	>	>
125	165	125	165	>	>
125	170	125	170	>	>
125	175	125	175	>	>
125	180	125	180	>	>
130	160	130	160	>	>
130	165	130	165	>	>
130	170	130	170	>	>
130	175	130	175	>	>
130	180	130	180	>	>
135	160	135	160	>	>
135	165	135	165	>	>
135	170	135	170	>	>
135	175	135	175	>	>
135	180	135	180	>	>
140	160	140	160	>	>
140	165	140	165	>	>
140	170	140	170	>	>
140	175	140	175	>	>
140	180	140	180	>	>
>140	>180	>140	>180	>	>

Note: Other parameters: $c_{2} < c_{1} < a_{1}^{L} = a_{2}^{L} < a_{1}^{H} = a_{2}^{H}$ , where $c_{2} = 15, a_{1}^{L} = a_{2}^{L} \geq 30$ if $e = j = 1 / 4 o r 1 / 6$ and $b \geq 1.6$ . $a_{1}^{H}$ = $E (\prod_{1 H}^{S})$ - $E (\prod_{1 H}^{N S})$ , $a_{1}^{L}$ = $E (\prod_{1 L}^{S})$ - $E (\prod_{1 L}^{N S})$ , $a_{2}^{H}$ = $E (\prod_{2 H}^{S})$ - $E (\prod_{2 H}^{N S})$ , and $a_{2}^{L}$ = $E (\prod_{2 L}^{S})$ - $E (\prod_{2 L}^{N S}) .$

The two equilibria in this proposition are really the same. In both, full information about demand, whether high or low, is revealed. This is clearly true in equilibrium (ii) since the firms explicitly reveal their high demands. It is also true in equilibrium (i) when high demands are not explicitly shared. Since the low demands are always revealed, a firm can infer that a competitor who did not share information must have a high demand. Other equivalent equilibria would also exist using mixed strategies. A firm could share with any probability when it has high demand as long as it always shared with low demand since high demand could then be inferred even when not shared.

Different results occur in other cases. For example, when an upscale hotel and an economy hotel were competing, there was never a Nash equilibrium in which the hotels shared information. This is consistent with this type of hotels not considering the other to really be a competitor given their target markets (Kotler et al., 2017).

Discussion

Theoretical Implications

As per the theoretical complications in imperfect competitive market structures (Shaw, 1984), a hotel’s pricing decision is affected by offering similar, not necessarily identical, rooms for sale in the market competition. Also, the pricing decision is based on demand relative to the available supply of guestrooms, as well as factors in the availability of their competitors, considering the quality of the rooms. Accordingly, a potential for room rate differences in the lodging industry is due to an imperfect knowledge of competitors’ prices. To this end, sharing information among competitors dramatically affects hotels’ pricing decision given the uncertainty of decision parameters, such as demand and price conditions (Gal-Or, 1986; Kuhn & Vives, 1995; Rasmusen, 2007; Van Zandt & Vives, 2007; Zhang et al., 2019).

In this study, the two-stage price competition model was developed with consideration of the lodging industry that is characterized by an imperfect competition market structure. This ensures that hotels obtain asymmetric information quality about demand, ADR, and other indicators without major simplifications. Also, the information structure in the model is modified so that information quality is asymmetric. Basically, this model enables understanding the relationship between price and demand, where price is directly relevant to the operating costs and demand is regarded relative to the available supply of guestrooms, as well as the competitors. This notion of price parameter in a price competition model is consistent with cost-based pricing method in the lodging industry (Nagle & Holden, 1995). But cost-driven pricing drives overpricing in off-seasons and underpricing during high seasons (Bitran & Mondschein, 1997; Chattopadhyay & Mitra, 2019; Chung, 2000). Also, in the lodging industry, where fixed costs are high and variable costs are low, costs play a secondary role to demand in pricing. In this regard, in addition to cost variables, ADR is mainly utilized for price parameters in price competition model to overcome a shortcoming of cost-based pricing method.

Overall, the results show that demand signals in the market were the most significant indicators in the model although a level of market competition, which was created by the relationship between b and d, influences Nash equilibrium (optimal pricing strategy) with respect to the information-sharing equilibrium. However, these parameters (b, d) do not seem to change the Nash equilibrium associated with the information-sharing equilibrium within the same competitive market in competition between different types (i.e., upscale, midscale, and economy) and similar size hotels. This finding supports the study of Rogers (1980), Cason (1994), and Rodriguez (2003), which explains that 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 (Kagel & Roth, 2016; Rodriguez, 2003; Rogers, 1980). This interdependence of firms intensifies the degree of uncertainty in the market (Cason, 1994; Gal-Or, 1986; Kuhn & Vives, 1995; Rodriguez, 2003; Van Zandt & Vives, 2007; Zhou, et al., 2019). To this end, the findings of Nash equilibrium with respect to the information-sharing equilibria are valuable since these equilibria indicate the incentive for hotels to share or conceal information with competitors.

An information-sharing equilibrium was found in the competition between different types and similar size hotels: $α_{1}^{H} = α_{2}^{H} = 0$ and $α_{1}^{L} = α_{2}^{L} = 1$ , in which both types of hotels always shared their information only if they faced a low demand signal in this market. Through sharing private information with competitors, hotels can increase market information and reduce uncertain demand conditions (Gal-Or 1986; Van Zandt & Vives, 2007; Yang et al., 2020). Thus, it helps generate profits when hotels face a low demand signal in the competitive market. However, when hotels have a high demand signal in this market, the hotel’s optimal information-sharing behavior is concealing information to maximize revenue and profitability. Hotels share their private information via trade associations to acquire the right information about prevailing market conditions, which helps generate profits (Raith, 1996; Van Zandt & Vives, 2007; Vives 1984; Yan & Pei, 2011). To this end, hotels can better correlate pricing decisions to actual market conditions to optimize profitability in the marketplace. A stochastic market environment restricts collusion since firms are not sure of precise market conditions as long as information is imperfect (Christodoulou et al., 2019; Clarke, 1983; Green & Porter, 1981; Kagel & Roth, 2016; Rasmusen, 2007). In other words, hotels are not sure of precise market conditions since information is asymmetric within imperfect market conditions (Stigler, 1964). In addition, when information is private (not shared), firms may hold divergent views about market conditions.

Previous theoretical research about price competition model with demand uncertainty has focused on symmetric models where all firms have equal information quality (Cason, 1994; Kuhn & Vives, 1995). The rationale is that it provides a clear solution while reducing the complications caused by the uncertainty parameters in the model. However, this focus may ignore several important characteristics of markets, which have firms with different information quality (Cason, 1994; Yan & Pei, 2011). This study generated an asymmetric condition with the assumption that $c_{1}^{L} = 5 / 4 c_{2}^{L}$ and $c_{1}^{H} = 5 / 4 c_{2}^{H}$ in a competition between an upscale and a midscale hotel and $c_{1}^{L} = 8 / 5 c_{2}^{L}$ and $c_{1}^{H} = 8 / 5 c_{2}^{H}$ in a competition between an upscale and an economy hotel. However, these results are indifferent to those generated via a symmetric condition in this model. This implies that cost variable in price competition model associated with demand uncertainty is not a significant indicator to estimate Nash equilibrium—information-sharing equilibrium. Interestingly, hotels in the same market will face different demand conditions according to their target markets, thus generating asymmetric demand information, which mimics the lodging industry. In this regard, this study created two different demand conditions in price competition model. First, a series of different demand conditions caused by uncertainty were tested in symmetric and asymmetric conditions in the model. Like the cost variable, a succession of different demand conditions did not influence Nash equilibrium with information-sharing equilibrium. This is due to oligopolistic markets where firms focus on competitive responses to a pricing decision more than demand responses (Shaw, 1984).

Managerial Implications

The finding of this study provided several insights for hotel operators, including revenue managers with respect to information-sharing behaviors of hotels and optimal pricing strategy. Despite the general critical elements to determine hotels’ optimal information-sharing behaviors (Nash equilibrium) in previous research, this study identified market demand as the most significant indicator in determining hotels’ information-sharing behaviors. As previous research (Krishna, 2007; O’Connor, 2003; Saito et al., 2016) indicated, hotels use several different tools (e.g., web scrapping services, STR reports) to learn about competitors’ private information (e.g., key performance indicator or KPI). However, it is hotels that determine whether they should submit their private demand information to STR, which makes it available to other hotels in the marketplace, or they should publish information to the third parties. According to Lodging Market Data Book (2018) not all the hotels in regions or cities shared their private information with their competitors in the marketplace. But it wasn’t obvious for hotels when to share or conceal their private information via trade associations (e.g., STR) to optimize their revenue. Essentially, this study suggests that hotels can make such a decision based on a market demand signal, as well as on the types of hotels. But the types of hotels (e.g., similar size hotels) were not significant in determining information-sharing behavior. More specifically, based on the results of this study, the following recommendations have been proposed for revenue managers in the lodging industry.

In revenue management, information-sharing behavior should be considered.

Market demand is a critical indicator for hotels to know when to share their demand information with competitors to maximize revenues; hotels should share demand information when they face a low demand signal in the marketplace.

Demand information can be revealed implicitly as well as explicitly. Thus, revenue managers should make inferences when competitors choose not to reveal information.

If hotels decide to share demand information, acquisition of dynamic information about KPI from different communication mechanisms (e.g., personal relationship, phone calls, STR, websites) is critical.

Information sharing is not always better off to optimize revenue and profitability.

Operational cost is not a vital factor to determine information-sharing equilibrium.

Limitations and Recommendations

Several limitations were identified in this exploratory study due to the nature of game-theoretical model (or game theory). In the theoretical background, the game-theoretical model was discussed as the study of two players and multiplayers’ decision problems. Due to the current mathematical skills, as well as the complexity of the model, only the model with two-players games were analyzed mathematically and analytically, which might not reflect the reality of the lodging industry. Also, the cost parameter for hotels was set in either high or low cost and was assumed to have constant marginal costs, without consideration of fixed costs of hotels. In a reality of the lodging industry, however, the cost variable varies according to location, type, and year of hotels with respect to fixed costs (El Haddad, 2015; O’Neill & Mattila, 2006). Thus, the generalizability of the results derived from a simple and convenient custom in this theoretical model to the entire lodging industry was limited.

In addition, hotels make decisions about the amount of private information disclosure and need to decide whether to truthfully reveal or conceal information. This decision is made before any uncertainty is resolved through information-sharing behavior (Agastya et al., 2007). In this exploratory study, however, the assumption that hotels truthfully revealed their information was implied. It is also possible that a hotel revealed untruthful or false information.

Several areas were recognized for future research, which include Cournot competition, cost uncertainty, demand segments, and economic experiments. First, although this study analyzed the price competition model (the Bertrand competition), the Cournot competition model (the demand competition model) is also related to incentives to share or conceal information (Krishna, 2007; Kuhn & Vives, 1984; Osborne, 2009; Vives, 1984). It is because the type of competition determines the slope of the hotel’s reaction function in game-theoretical model. Therefore, the optimal information-sharing behaviors, along with Nash equilibrium, in the Cournot competition model may not be identical to those in the Bertrand competition model. As per the nature of the lodging industry, the quantity is not controlled; Cournot competition model with respect to information-sharing equilibrium could be examined in different settings. Second, the source of uncertainty (demand vs. cost) influences the incentives to share information (Cason, 1994; Osborne & Rubinstein, 1994; Rasmusen, 2007; Rodriquez, 2003; Yang et al., 2020; Zhang et al., 2019). Especially, the uncertainty source, along with the information-sharing decision, determines the degree of correlations between firms’ strategies. The rationale is that reduced correlation has either a negative or a positive effect on profit functions depending on the type of competition. To this end, cost uncertainty in game-theoretical competition model needs to be further examined.

In the lodging industry, both product and timing heterogeneity induce several different demand schedules (Kotler et al., 2017). It is also common for the lodging businesses to provide numerous pricing strategies for different market segments (Collins & Parsa, 2006; El Haddad, 2015; Kotler et al., 2017; Vives et al., 2018). Therefore, it would be useful to develop a Bertrand or Cournot model based on market segments with consideration to off-season and high season in the lodging industry. In addition, other than the size of hotels in the Bertrand or Cournot model, other variables (e.g., location), might be considered because location is one of the pricing decision-making variables, which could influence hotels’ information-sharing decisions. Last, the economic experiment is worth noting. Altman (2004) notes that the deduced results from a game-theoretical model may be different from the actual game results. Instead of a pure theoretical deduction, thus, the game results would be verified using experiments. In this way, the results of a game-theoretical model would be more reliable, which can reflect the reality of the lodging industry.

Conclusion

There are ongoing debates about methods to establish the effective pricing strategy in the lodging industry (Collins & Parsa, 2006; El Haddad, 2015; Gu, 1997; Lee at al., 2011; Nagle & Holden, 1995; Saito et al., 2016). Overall, the previous literature notes that the effective pricing strategy is determined depending on demand and supply, cost, seasonality, and competition. Based on a demand uncertainty model (Vives, 1984), this study developed a two-stage price competition model within a lodging context to show how such a model is useful for determining effective strategies with respect to information sharing. In the first stage of Nash equilibrium, hotels simultaneously decided to share or conceal information, and then in the second stage, hotels simultaneously chose prices given the first-stage outcomes. To mimic the lodging industry, especially, this study considered an asymmetric condition in cost, which created different types of hotels (e.g., a competition between an upscale and a midscale hotel), as well as in demand, creating a low and a high demand in the marketplace. Because of these assumptions, which are significantly different as compared with previous research (Gal-Or, 1986; Jiménez-Martínez, 2006; Shapiro, 1986; Vives, 1984; Yan & Pei, 2011), this study examined competitions between different types of hotels considering different market demand signals. This study found that hotels share their private demand information if there is a low demand signal but conceal private information if the demand signal is high in the marketplace. The finding of this study provided several insights for hotel operators, including revenue managers with respect to information-sharing behaviors of hotels and optimal pricing strategy.

Footnotes

ORCID iD

Sungsoo Kim

Sungsoo Kim, PhD (e-mail: sungsoo.kim@usm.edu), is an associate professor at the School of Marketing, College of Business, University of Southern Mississippi, Hattiesburg, MS. Steven M. Slutsky, PhD (e-mail: slutsky@ufl.edu), is a professor at the Department of Economics, University of Florida, Gainesville, FL. Brijesh Thapa, PhD (e-mail: bthapa@hhp.ufl.edu), is a professor at Department of Tourism, Hospitality and Event Management, University of Florida, Gainesville, FL.

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