WHY A NAME-YOUR-OWN-PRICE CHANNEL MAKES SENSE FOR SERVICE PROVIDERS (OR: WHO NEEDS PRICELINE, ANYWAY?)

Transcription

1 WHY A NAME-YOUR-OWN-PRICE CHANNE MAKES SENSE FOR SERVICE PROVIDERS (OR: WHO NEEDS PRICEINE, ANYWAY?) Tuo Wang Assistant Professor of Marketing 53 Business Administration Building, P.O Box 5190, Kent State University, Kent, OH twang3@kent.edu; phone: ; fax: Esther Gal-Or Associate Dean for Research; Glenn Stinson Chair in Competitiveness and Professor of Business Administration and of Economics, 368A Mervis Hall, Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA esther@katz.pitt.edu; phone: , fax: Rabikar Chatterjee Professor of Business Administration, 340 Mervis Hall, Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA rabikar@katz.pitt.edu; phone: , fax: Version dated May 10, 005 Preliminary draft only please do not quote. Comments are welcome. The authors thank Scott Fay and Jinhong Xie for their helpful comments on an earlier version of this paper.

2 WHY A NAME-YOUR-OWN-PRICE CHANNE MAKES SENSE FOR SERVICE PROVIDERS (OR: WHO NEEDS PRICEINE, ANYWAY?) ABSTRACT The Name-Your-Own-Price (NYOP) channel, exemplified by Priceline, is a popular online alternative to other, more traditional channels, through which service providers such as airlines, hotels, and car rental companies offer their products to customers. This paper is motivated by the importance of developing an understanding of the market implications of this pricing and distribution model, especially from the perspective of the service provider. An important objective of our analysis is to explain why a service provider would seek to distribute its products through an NYOP retailer, in light of concerns among service providers of the adverse consequences of cannibalization of the business generated through traditional postedprice channels. We employ a stylized game theoretic model to capture the behavior of the service provider and consumers. Our analysis provides a theoretical rationale for the existence of the NYOP channel without haggling cost, based on four critical factors: (1) the presence of demand uncertainty, () some degree of opacity (in the form of incomplete information) in the product offered by the NYOP channel, (3) prices in the posted price channel that are stickier than those in the NYOP channel, and (4) a denser market for the NYOP channel. Key words: Pricing; Name-your-own price channel; Bidding; Bayesian Nash equilibrium; E- commerce.

3 1. Introduction 1.1. Motivation and Research Questions The Name-Your-Own-Price (NYOP) channel, exemplified by Priceline, is a popular online alternative to other, more traditional channels, through which service providers such as airlines, hotels, and car rental companies offer their products to customers. Under its patented system, Priceline collects individual customer offers (price bids guaranteed by a credit card) and communicates the information directly to participating sellers or to their private databases. It operates on a commission plus the difference between the consumer bid and the price it pays the service provider (Dolan and Moon 000; Kannan and Kopalle 001). For their part, customers are required to place their bids under a certain degree of opacity about the product, in the sense that certain pertinent product information (such as the flight time, number of stops, hotel location, and/or the specific identity of the airline or hotel) is not available at the time of bidding. Further, unlike most other auction models, consumers are effectively allowed only a single bid for an item. Since its inception in April 1998, Priceline has generated $3 billion in total revenue and has emerged as the dominant NYOP retailer in the U.S. and some other countries, focusing on travel-related services including airline tickets, hotel rooms, rental cars, vacations, etc. Fluctuations in Priceline s stock price have been accompanied by a persistent debate over the merits and the viability of the NYOP business model, which has been examined from a practitioner-oriented perspective (Dolan and Moon 000; Elkind 1999; eiber 00) and, more recently, from a research perspective (Fay 004a; Hann and Terwiesch 003; Terwiesch, Savin, and Hann 005). There is no clear consensus on either the future of this model or the impact of this mechanism on the market. For example, there have been serious concerns among some service providers that the NYOP channel may extensively cannibalize business through - 1 -

4 traditional posted-price channels 1. Others have cast doubt on the long-term viability of the NYOP model after the failure of Priceline WebHouse Club and Perfect Yardsale. On the other hand, there have been similar services launched by Priceline s competitors (e.g., Expedia s PriceMatcher). More than 4,000 hotels signed up to offer unsold rooms through Priceline within its first year of operation (Collins 1999). We believe it is important to fully understand the market implications of this important pricing and distribution model from the perspectives of the service providers, the NYOP retailers, and the consumers. Our focus is primarily from the perspective of the service provider (such as an airline, a hotel or a car rental firm), in contrast to previous literature in this area (Fay 004a; Hann and Terwiesch 003; Terwiesch, Savin, and Hann 005) which looks at bidding models from the perspective of the NYOP retailer. As discussed below, the pricing decisions (as well as the decision to employ an NYOP channel in the first place) are made by the service provider, making the perspective of the service provider especially relevant. An important objective of our analysis is to explain why a service provider would seek to distribute its products through an NYOP retailer, in light of concerns among service providers of the adverse consequences of cannibalization of the business generated through traditional posted-price channels. Our research attempts to address the following issues: From the service providers perspective: Under what conditions does it make economic sense to contract with an NYOP? What prices should the service provider set for the posted-price channel and as the minimum acceptable price for the NYOP channel? 1 Northwest Airline discontinued its relationship with Priceline on June 00 for being increasingly concerned with Priceline's business model (CNET news). Hotel industry expressed similar concern on the long-term risk of Priceline in cannibalization of sales from primary selling channels (Collins 1999). - -

5 How much information about consumer demand does the service provider need to have before he contracts with the NYOP retailer? From a public policy perspective, what are the welfare implications of the presence of NYOP channels (such as Priceline)? 1.. Modeling Approach We employ a game theoretic model to capture the behavior of a service provider and consumers. More specifically, we consider a market with a monopoly service provider distributing its products through two channels, one posted-price and the other NYOP. The population of potential customers of the service is heterogeneous in the individual valuations of the service. These rational consumers can choose either to buy from the posted-price channel (assumed in our model to be the service provider s direct channel) or to place a single bid at the NYOP channel. Before their bids are accepted, bidders on the NYOP channel do not have all the information about the product available to posted-price channels customers. The extent of missing product information (referred to as opacity ) is common across consumers, and greater opacity lowers consumers willingness to pay. We model the process as a two-stage game, with uncertain demand. In the first stage, the service provider sets the posted price for the product (e.g., hotel rooms or airline seats for a specified future date) before it receives information on the state of demand for the product. After observing the posted price, consumers decide whether to buy at the posted price or to bid on the NYOP channel. In our model, the service provider cannot adjust the posted price as additional In exchange for your flexibility on flight times, the airlines allow you to save money off their lowest published fares! Exact flight times on Name Your Own Price tickets will be shown after purchase. (Priceline.com, FAQ section). Note that in reality, part of the opacity comes from not knowing the identity of the service provider. In our stylized framework with a monopoly service provider, the opacity would come from lack of knowledge of the particular flight (given multiple flights over the day) or the exact location of the hotel (given multiple locations in the destination city)

6 information about demand becomes available, capturing the idea that posted prices are sticky relative to prices on the NYOP channel (we address this issue in detail later in the paper). At the beginning of the second stage, the service provider observes a signal of the state of the demand, and then contracts with the NYOP retailer while specifying a minimum acceptable price, indicating that only bids in excess of this price should be accepted. The assumption that the minimum acceptable price is set by the service provider instead of the NYOP retailer is consistent with extensive industry reports and other sources (Ecommerce Guide 00; Canadian odging Outlook 00). 3 Consumers who participate in the NYOP process submit their bids in the second stage. The NYOP retailer receives the bids from the consumers, and transacts with any consumer whose bid is higher than the minimum acceptable price. The notion that the posted price is available in advance of the prices on the NYOP channel is entirely consistent with observed practice. 4 We consider two versions of the model: one where the capacity (airline seats, hotel rooms, rental cars) available to the service provider is fixed and the other where the service provider can choose the level of capacity optimally. Hotels may better fit the first case (at least 3 In the airlines and hotel category, Priceline operates on commission plus the difference between the consumer bid and the price the airline/hotel charges Priceline (Kannan and Kopalle, 001, P76). In other words, Priceline does not have a new retail price other than the wholesale price provided by the service provider. A transaction occurs as long as the bid price is higher or equal to the wholesale price (unknown to the consumers). Unlike the traditional posted-price retailer, the minimum acceptable price is unknown to the consumers and the demand (in the form of consumers reservation prices) has already been collected with the NYOP process. Plus, any price difference between a bid and the wholesale price will always be pocketed by the NYOP retailer. There is no strategic reason for the NYOP retailer to set a higher price above the service provider s wholesale price. This is different from some previous NYOP models in which the NYOP retailer sets the minimum acceptable price above which the bids will be accepted (Fay 004a; Hann and Terwiesch 003). 4 For example, we noted the posted price and the price on an opaque channel (Hotwire.com it is impossible to observe prices on Priceline) for a Pittsburgh-Atlanta round trip ticket, for departure dates starting from the day of our enquiry to 330 days in the future (which is as far as advance bookings are permitted on the posted price channel). Prices on Hotwire were simply not available for travel 3 weeks in the future. Furthermore, the difference between the posted price and the opaque price virtually disappeared for travel dates eight weeks and beyond into the future. (The gap in prices declined from a high of $70 to just $7 in the eighth week and even lower beyond.) Thus, in effect, the opaque channel is in play only for tickets purchased for travel less than 8 weeks in the future

7 in the short run), while car rentals might have the flexibility in capacity to represent the second scenario. In the latter case, we assume that this choice is made in an initial stage prior to the two stages of the game as described above Summary of Key Results We derive the Bayesian Nash equilibrium solution for both variants of the two-stage game. Some key results are summarized qualitatively below: An increase in the level of the fixed available capacity may reduce the proportion of the potential market purchasing at the posted price. When the precision of the signal is sufficiently high, the service provider can make better pricing decisions in the NYOP channel, and therefore may be motivated to reserve more of the available capacity for this channel, by raising his posted price. Reduced opacity of the NYOP offering or increased precision of the demand signal observed by the service provider at the end of the first stage result in countervailing forces affecting the service provider s profit from the NYOP channel. On the one hand, there is the direct positive effect of lower opacity (which increases the consumers willingness to pay) and higher precision (which improves the quality of the pricing decision). On the other hand, there is an indirect negative effect stemming from the cannibalization of the higher margin posted-price market. The service provider will find it profitable to distribute through both its own posted-price channel and an independent NYOP channel if the degree of opacity is not too large and the NYOP market is sufficiently dense relative to the posted price market. 5 This result is driven by the tradeoff between the two countervailing effects discussed earlier. The expected profit for the service provider is the highest for some intermediate value of the precision of the demand signal. Once again, the same tradeoff is in effect here while greater signal precision makes it possible to align prices with the state of demand, it also implies a transfer of sales from the posted-price channel (where the service provider controls 5 As discussed later in the paper, it is reasonable to expect the high valuation end of the market (the posted price customers) to be thinner than the lower-middle segment of the market in terms of valuation, which is likely to consist of leisure travelers, typically comprising the entire family

8 prices) to the NYOP channel (where control is shared with consumers and to some degree the retailer). This paper provides, as its key contribution, a theoretical rationale for the existence of the NYOP channel, based on four critical factors: (1) the presence of demand uncertainty, () some degree of opacity in the product offered by the NYOP channel, (3) prices in the posted price channel that are stickier than those in the NYOP channel, and (4) a denser market for the NYOP channel. 6 The rest of this paper is organized as follows. In, we review the relevant literature to position our research. Next, in 3, we develop the model and present our analysis and results. Finally, in 4, we conclude with a discussion of the managerial implications of our findings as well as directions for future research in this important area.. Related iterature Previous research on the NYOP model has focused on two separate issues: (1) online haggling (repeat bidding 7 ) between an NYOP retailer and a set of consumers; and () the rationality of consumers repeat bidding behavior at the NYOP channel. On the first issue, Hann and Terwiesch (003) consider the NYOP process in a bargaining framework to measure the haggling cost of repeat bidding at a European NYOP retailer. They find that when repeat bidding is allowed, the haggling cost is significant to consumers and is equivalent to about 5.5 Euros for a product costing around 00 Euros. Terwiesch, Savin, and Hann (005) further investigate the impact of consumer haggling on the NYOP retailer s optimal pricing strategy. 6 One may ask why the service provider does not own the NYOP channel. While our focus is on providing a theoretical rationale for the existence of an NYOP channel such as Priceline and not on investigating whether such a channel should be company-owned rather than independent, a plausible reason in the presence of several service providers is that an independent NYOP channel can be more efficient by consolidating supply across all participating service providers, from both cost and traffic-generation perspectives. (From the consumer s perspective, comparison shopping across several service provider-owned NYOP channels would be almost impossibly cumbersome.) 7 When repeat bidding is allowed, a bidder whose offer has been rejected can invest in additional haggling effort and increment his/her offer

9 The major decision variable for the NYOP retailer is a constant minimum acceptable price above which all offers are accepted. Because of the research setting between a German NYOP retailer and a set of consumers, it does not consider the profit implications of the NYOP process to the service provider, who has the ultimate pricing power in the Priceline business model. Fay (004a) studies the optimal design of the NYOP mechanism. Using a game theoretic model, he suggests that Priceline may be better off by encouraging re-bidding behavior, which is different from the company s current single-bid policy. The basic objective of these three papers (Fay 004a; Hann and Terwiesch 003; Terwiesch, Savin, and Hann 005) is to improve the NYOP retailer s decision with regard to setting a minimum acceptable price and/or bidding rules. However, the assumption in the above papers that the NYOP retailer is setting the minimum acceptable price may be questionable under Priceline s current model. In contrast, we consider the service provider as setting both the posted price and the minimum acceptable price in the NYOP channel. We treat the NYOP retailer as an agent with information advantage over both the service provider and consumers. Furthermore, all three papers allow re-bidding activity to differing degrees. On the other hand, we assume a single-bid mechanism following Priceline s current practice. 8 Thus, our analysis is based on what we believe are more realistic assumptions regarding the Priceline model and with the service provider s role in the pricing decision. From the consumer perspective, Spann and Tellis (003) test consumers rationality with reference to their bidding behavior, using data of bid sequences for airline tickets at a European NYOP retailer. They find that greater experience seems to be associated with more irrational 8 This practice is reflected in the following advice for potential bidders on Priceline s website in the FAQ section: Put your best foot forward when naming your price. Since you can only make one offer per itinerary (same price, city, check-in and check-out dates and star-level) in any 3-day period with Priceline you'll want to be sure your first offer is your best offer

10 bids in their multiple-bid model. However, their results of weak rationality from consumers apply in the case of multiple-bid behavior only, which is significantly different from Priceline s single-bid mechanism. Our model assumes that consumers are rational in arriving at their optimal bids in the NYOP channel. In a different vein, Ding, Eliashberg, Huber, and Saini (005) incorporate the effect of emotion in modeling bidders behavior in Priceline-like channels, considering the excitement of winning or the frustration of losing, depending on whether the bid is accepted or rejected. From the service provider s perspective, the emergence of the NYOP retailer provides the opportunity of adding a new channel to the existing posted price channel. While a new channel can be profitable by serving as a vehicle to increase sales via higher market penetration (Moriarty and Moran 1990), adding a channel can be risky for the service provider, with potential for channel conflict and cannibalization (e.g., Balasubramanian 1998; Chiang, Chhajed and Hess 003; Purohit 1997; and Purohit and Staelin 1994). The cannibalization issue in the context of adding an online channel has received recent research attention (Alba et al. 1997; Brynjolfsson and Smith 000; Coughlan et al. 001; Deleersnyder et al. 00; Geyskens et al. 00; al and Sarvary 1999; Zettelmeyer 000). Conceptually, our basic framework is more closely related to the theoretical literature on product line decisions (e.g., Balachander and Srinivasan 1994; Desai 001; Gabszewicz and Thisse 1979; Moorthy 1984; Mussa and Rosen 1978; and Villas-Boas 1998) in that the products offered on the posted-price and NYOP channels are essentially differentiated in terms of quality (the NYOP channel s product is of lower quality on account of opacity). While we do not explicitly consider the degree of opacity as a decision variable in our framework, it has important implications for our results

11 Demand uncertainty is another important element in our modeling framework, one that turns out to be critical to our rationale for the existence of the NYOP channels. The service provider learns about the state of demand from the signal received from the market in the first period, after setting the price on the posted-price channel but before determining the minimum acceptable price in the NYOP channel. Similar to azier (1986), our framework assumes that the service provider responds to the signal whose precision is exogenously determined, independent of the decision-maker s actions. 9 Fay (004b) investigates the rationale behind the existence of an opaque product offered at Priceline and Hotwire. Using a Hotelling model with two service providers, Fay provides necessary conditions under which a firm benefits from offering an opaque version through an intermediary. In contrast to our approach, Fay (004b) s paper is based on the conventional posted-price model and does not involve a bidding model to sell the opaque product. As we shall show later, the unique nature of the NYOP pricing model significantly influences the behavior of consumers and service provider, thereby impacting on our results. 3. Model and Results In this section, we first describe the model in 3.1. We then derive the optimal bidding strategy of consumers in the NYOP channel ( 3.), the optimal lower bound on bids that is imposed on the NYOP retailer by the service provider ( 3.3), and the optimal posted price and level of capacity chosen by the provider at the start of the game ( 3.4). In the latter section, we also evaluate the consequence of this choice on the expected profit of the service provider. Section 3.5 evaluates the consequences of the choice on the expected profits of the NYOP 9 In contrast, Gal-Or (1988) and Mirman, Samuelson, and Urbana (1993) consider circumstances under which the decision-maker s action influences the precision of the information (consequently affecting the decision-maker s behavior)

12 retailer and the welfare of consumers. Table 1 provides definitions of all the symbols used in our model to denote various variables and parameters. Table 1 Definitions of Variables and Parameters in the Model Variables and Parameters Definition Interval v Reservation price of consumer i for one unit of the service [0,1] i 1- d Extent of opacity [0,1] H P Posted price [0,1] P Minimum acceptable price at NYOP channel B Optimal bid submitted by consumer i. i [0, K [ P, P ] Capacity of the service in units c Cost of capacity per unit [0,1) δ y A random variable measuring the density of consumers who participate in the posted price market Signal of δ that is observed privately by the service provider H P ] [0,] [0,] h Precision of y as a signal of the random variable δ [0,1] µ Average density of the NYOP market [0,] v v Threshold consumer who is indifferent between buying at posted price and bidding in the NYOP channel The lowest valuation consumer who participates in the NYOP channel 0 v v The Model We consider a market with both a posted price channel and a NYOP channel. There is a monopoly service provider and a large population of potential customers of the service whose reservation price for one unit of the service is distributed on the normalized interval v i ~ [0,1], with some density function that captures the concentration of potential customers with a particular reservation price in the interval [0,1]. These rational consumers can either choose to buy at the posted-price channel or to place a single bid at the NYOP channel. Without loss of generality, the posted-price channel is assumed to be the service provider s direct marketing

13 channel (most airlines and hotels have their own websites for direct sales to consumers). In contrast to the products featured in the posted-price channel, bidders in the NYOP channel have limited information about the item when they place their bids and until (if at all) their bids are accepted. We denote the extent of opacity of the featured items in the NYOP channel by (1 d), where d [0,1] and dvi measures the discounted valuation of one unit of the opaque product featured at the NYOP channel. The closer d is to 1, the lower is the opacity associated with the item sold on the NYOP channel. In the limit, when d = 1, consumers view the products sold at both channels as being identical. We assume that the parameter d is common for all consumers. We also assume that there is no value to the item after its service date. Consumers are risk neutral and visit the posted-price channel before deciding on whether to participate in the NYOP process. If they decide to submit bids in the NYOP channel, they can do so only once before the service date. This latter rule is consistent with the policy of Priceline that prohibits multiple rounds of bids for a given item for a certain period of time. We also assume that when consumers derive the same expected surplus from both channels, they prefer the posted price channel. Also, when consumers expect zero probability of bid acceptance, they do not submit any bids. We model the process as a two-stage game, with the following timeline (see Figure 1): H At the beginning of the first stage, the service provider chooses the price P for the postedprice channel. Since there is demand uncertainty, the service provider is forced to make this decision before the state of the demand is realized. Moreover, he cannot adjust the posted price as additional information about the state of the demand becomes available at the end of the first stage. This assumption warrants some discussion, since it is clearly a simplification of reality. We certainly observe variations in posted prices of, for example, air tickets (both over time and across product variants e.g., fully refundable versus nonrefundable). What our assumption captures is the idea that posted prices are significantly stickier than prices in

14 the NYOP channel. By its very nature, name-your-own-price is as flexible as it gets, with each consumer selecting her bid independent of other consumers; on the other hand, there is significant direct cost (in terms of communications and logistics) attached to changing posted prices, not to mention such indirect costs as customer alienation. Airlines have recently reduced the number of pricing options for these reasons, and indeed, some airlines have begun to guarantee the lowest prices on their web sites (the guarantee does not apply to prices on NYOP channels such as Priceline; Skertic 005). After observing the posted price, consumers decide on whether to buy at the posted price or to bid at the NYOP channel 10. Consumers may become aware of their need to avail of the service early (in the first stage) or late (in the second stage). Those arriving in the first stage decide on whether to purchase the service at the posted price right away or to wait until the second stage to submit their bid in the NYOP channel. Those arriving in the second stage have both posted price and NYOP options available. At the beginning of the second stage, the service provider observes a signal of the state of the demand. This signal y is privately observed by the service provider, and is generated by the consumers bookings at the posted price in the first stage. Following the observation of the signal, the service provider submits a minimum acceptable price ( P ) indicating that only bids in excess of this price should be accepted. The minimum price can be chosen contingent upon the signal of the demand that is observed by the service provider. Consumers who participate in the NYOP process submit their bids (denoted by second stage. B i.for consumer i) in the During the second stage, the NYOP retailer receives the bids from the consumers, and transacts with any consumer whose bid B i is higher than the minimum acceptable price P. Note that the posted-price channel is available to consumers in both stages, while the NYOP channel is available only in the second stage. 10 Since the service cannot be consumed before the service date, there is no time discounting of utility for consumers bidding in stage two instead of buying in stage one

15 Figure 1 Timeline of the Game The service provider chooses the posted price H P Early consumers decide whether or not to buy, and if so, whether to do it via the posted price Buy via posted price Pay the posted H price P STAGE ONE: Posted Price Channel Only Not buy via posted price STAGE TWO: Both Posted and NYOP Channels ate consumers decide whether or not to buy, and if so, whether to do it via the posted price channel Buy via posted price Not buy via posted price Signal of demand observed by service provider Pay the posted H price P Consumers bid with optimal bid B if interested in buying the service The service provider sets the minimum acceptable price P The NYOP retailer B P B < P Bid accepted, transaction occurs Bid rejected, no transaction

16 We consider two versions of the model: (a) where the capacity available to the service provider is fixed (i.e. hotel service), at the level K, and (b) where the service provider can choose the level of capacity optimally (i.e. a rental car service). In the latter case, we assume that this choice is made in an initial stage prior to the two stages described above. We assume that the cost of adding capacity is c per unit, where c < 1 to guarantee that the cost of capacity does not exceed the highest willingness to pay across consumers. We model the demand uncertainty facing the service provider in the form of a random variable δ that represents the density function of the distribution (over reservation prices) of those consumers who are active in the posted-price market. Thus, δ captures the density of the posted-price market, so that if all consumers with reservation prices between (say) v 1 and v buy tickets at the posted price, the volume of the posted-price market is δ (v v 1 ). We assume that δ is uniformly distributed over the interval = [0,], implying an average density of one. At the end of the first stage, prior to transacting with the NYOP retailer, the service provider observes a signal y of the random variable δ. Based upon the early bookings by customers, the service provider observes an initial indication of the extent of demand in the posted-price market. This preliminary information is reflected in the signal y. We utilize the specification proposed by Gal-Or (1991) to measure the precision of y as a signal of the uncertain demand densityδ. Specifically, conditional on a given realization of the signal of the demand, we assume that there is probability h that this signal is perfectly precise, implying that the demand density in the posted market is equal to y. There is, however, probability (1 h) that the signal is completely uninformative, and therefore the demand is distributed over the support according to the original prior density function. et f ( δ y)

17 designate the conditional density function of δ given the realization of y ; then the above assumptions imply that for some h [0,1], and y, h if δ = y f( δ y) = 1 (1 h) if δ y (1) The parameter h reflects the quality of the signal y in predicting δ, or a measure of the precision (or informativeness) of this signal. When h = 1, the service provider has perfect information of the value of δ at the end of the first stage, and when h = 0, the demand uncertainty remains unresolved for the second stage of the game. For intermediate values of the parameter h, higher values indicate that y is a more precise signal of the random variable δ. We can interpret h as being tied to the duration of the first stage of the game the longer the stage, the more precise the signal. (Thus, h = 0 implies that there is, in effect, no first stage, and the service provider announces his posted price and the minimum acceptable price in the NYOP channel simultaneously in a single-stage game.) 3.. Consumer s Optimal Bidding Strategy Consumers who plan to participate in the NYOP process are aware of the fact that the service provider can observe the signal y of the state of demand at the end of the first stage. Therefore, they know that the service provider can adjust the minimum acceptable price P to reflect the information he has about the state of demand in the posted-price market; + specifically, P ( y) :[0,] R. Moreover, since we assume that the distribution function of δ and y (prior as well as posterior distributions) are public information, rational consumers can infer the possible range of minimum acceptable prices that can arise at equilibrium. We designate this range as [, P P ] where P = P (0) and P = P (). In the sequel, we show

18 that since y and δ are uniformly distributed, the minimum acceptable price defined over the interval above is also uniformly distributed. 11 The consumer chooses her bid B i to maximize her net expected payoff: 1 max CS = ( dv B ) Pr{ B P ( y)} () Bi i i i i Given the conjecture that P ( y) is uniformly distributed over the interval [ P, P ], the above maximization reduces to Bi P max CSi = ( dvi Bi) B i P P, (3) yielding the solution, B( v ) i i dvi + P =. (4) Substituting this solution back into the objective function (3), yields the payoff the consumer can expect when participating in the NYOP process. Specifically, CS NYOP ( dvi P ) ( vi ) =. (5) 4( P P ) In deciding on whether to submit a bid at the NYOP channel, each consumer compares this expected payoff to the one she can expect by purchasing directly from the service provider. When purchasing at the posted price P H, the net payoff of the consumer is equal to 11 This ensures analytical tractability, and is the reason for the manner in which we model demand uncertainty. 1 Strictly speaking, the expression in () should include a term that captures the surplus consumers with v i > P H obtain if their bid is rejected, in which case these customers can buy at the posted price. However, the service provider sets the minimum acceptable price in Stage to clear capacity. When doing so, he gives priority to newly arriving customers in this stage who buy immediately at the posted price. Therefore, customers whose bids are rejected cannot expect to return to the posted-price market. The customer knows this, and therefore does not include this additional term in her payoff. (One might add that, in practice, there are additional disincentives for such customers to wait, which are not included in our model posted prices are typically higher nearer the service date, the most desirable seats may be taken, and there is less time to plan other aspects of the trip.)

19 posted H CS ( v ) = ( v P ) 13. Note that the degree of opacity has an adverse effect on the expected i i surplus of a consumer who buys from the NYOP retailer. It does not, however, affect her payoff when buying directly from the provider. In order to identify the group of consumers who will find it optimal to participate in the bidding, we define the function R( v i ) as the added benefit derived by a consumer of type v i when purchasing the product in the posted-price instead of the NYOP channel. Specifically, posted NYOP H ( dvi P ) Rv ( i) = CS ( vi) CS ( vi) = ( vi P ) 4( P P ). We assume that R(.) is a strictly increasing function of v i. This monotonicity assumption (which has been referred to as the single crossing property in the economics literature) guarantees that consumers with a higher valuation are more inclined to use the posted-price rather than the NYOP channel. Moreover, if R (0) < 0 and R (1) > 0, we are guaranteed that both channels are active. We summarize these restrictions in Assumptions 1 and. Assumption 1: R ( ) > 0. Assumption : R(0) < 0 and R(1) > 0. The above assumptions imply that the population of consumers can be divided into three segments as depicted in Figure. 13 We assume zero haggling cost at the NYOP channel because of the single-bid policy at Priceline. A positive value on the haggling cost is likely to be the case if repeat bidding is allowed (Hann and Terwiesch 003)

20 Figure Market Segmentation Do not participate NYOP market Posted-price market v 0 1 v v Consumers whose valuation falls short of v withdraw from the market. Those in the interval [,] vv place bids in the NYOP channel (in Stage ), and those in the interval [ v,1] purchase the service in the posted price channel (in Stage 1 or ). The threshold consumer v is indifferent between buying the service in the posted price and the NYOP channel, implying that: H ( dv P ) v P =. (6) 4( P P ) The threshold consumer v submits a bid that is just equal to the minimum acceptable price imposed by the service provider. From (4), therefore, dv+ P = P ( y). Hence, the threshold consumer v satisfies the equation P ( y) P vy ( ) =. (7) d Note that while the value of the threshold consumer v is determined independently of the realization of the signal y, the value of the threshold consumer v does depend upon this realization. In particular, if the minimum acceptable price is an increasing function of y, the threshold consumer who participates in the market has a higher valuation for the service if the

21 provider observes a higher realization of y. In the sequel, we demonstrate that P ( y ) is indeed an increasing schedule. Hence, when the signal y indicates a high level of demand in the posted price market, the service provider imposes a higher minimum acceptable price on the NYOP retailer, since he does not anticipate significant excess capacity remaining to be sold by the NYOP retailer. As a result, only consumers having higher valuation for the service find it possible to submit bids that are acceptable to the service provider. Also note that in (7) we implicitly assume that consumers with valuation above threshold v(y) derive a non-negative net payoff from transacting with the NYOP retailer. It is easy to show that if P ( y) is increasing, this implicit assumption is, indeed, valid Optimal Pricing Strategy of the Service Provider in the Second Stage Even though the service provider cannot adjust his posted price, he does have the option to sell any anticipated idle capacity via the NYOP retailer. Moreover, the minimum acceptable price imposed on this retailer reflects the information that is available to the service provider concerning the state of the demand in the posted price market. Hence, while P H is fixed 14, P ( y) is a schedule that can depend upon the realization of the demand signal y. Since the salvage value of unsold capacity is zero, it is easy to show that the service provider finds it optimal to choose the minimum acceptable price P ( y ) in a manner that guarantees full utilization of his capacity (as long as P > 0.) 15 Assuming that the average 14 Our analysis can be easily extended to allow for the possibility of adjustments in P H as well. As long as the flexibility of adjustment in pricing is greater in the NYOP channel than in the posted price channel, our results remain qualitatively similar. The assumption that drives our characterization is that there is greater rigidity in pricing in the posted price market. 15 Proof of this result can be provided by the authors upon request

22 density of the NYOP market is µ [0, ] 16, the service provider anticipates that the demand in the NYOP channel amounts to µ ( v v). The value of the signal y indicates that the expected demand facing the service provider in the posted-price channel is equal to (1 ve ) ( δ y). Hence, the service provider chooses P ( y ) so that µ ( v v) = K (1 v) E( δ y) (8) Note that at the beginning of stage two, the demand uncertainty in the posted price market δ is not entirely resolved. In fact, only by the end of the game can the service provider perfectly observe the realization of δ. However, the service provider does have access to some partial information concerning the state of the demand as indicated by the signal y. According to (8), he uses this signal in setting the minimum acceptable price to be imposed on the NYOP retailer. We use equation (8) to derive the schedule of P ( y ) as a function of v and K in emma 1. EMMA 1 (OPTIMA MINIMUM ACCEPTABE PRICE IN THE NYOP CHANNE): The optimal minimum acceptable price submitted to the NYOP retailer at the beginning of second stage is ( ) (1 ) (1 ) ( ) ( ) µ v K d v d P v h y y = +, µ µ µ 0 y. (9) PROOF: See Appendix 1. Note that the schedule of the minimum acceptable price is a strictly increasing function of y (for v < 1 and h > 0 ). Hence, as the service provider observes better news about the state of the demand in the posted-price market, he raises the floor that the NYOP retailer should consider 16 Even though we do not introduce a random variable to capture the state of the demand in the NYOP market, it is straightforward to model the demand in this market similar to the way we do it for the posted price channel. It turns out that the analysis depends only on the expected value of this random variable, which we designate by µ

23 in accepting bids from consumers. When anticipating improved demand in the posted price market, the service provider is less concerned about idle capacity, thus finding it optimal to raise the floor dictated to the NYOP retailer. Notice, also, that the schedule P ( y ) is steeper as the precision of the signal y improves. When h is bigger the signal is a more reliable indication of the state of the demand, thus leading the service provider to respond more aggressively to changes in the realization of the signal y. Note that for fixed values 17 of v and K, this increased steepness implies an overall reduction of prices since P () is a constant independent of h. As pointed out earlier, we assume rational expectations on the part of consumers, implying that they can anticipate the functional form of the price schedule P ( y ), as derived in (9). They can infer, therefore, how the price floor for bids is distributed. Given that y is uniformly distributed, so is P ( y ), since this schedule is a linear function of y. Hence our initial conjecture about the distribution function that characterizes the minimum acceptable price is, indeed, confirmed at the equilibrium. Moreover, consumers can substitute into (9) the boundary values of y (i.e., 0 or ) to obtain the limits of the uniform distribution of the price schedule, that we designated earlier as among the variables H P P and P. Substituting those values back into (6) yields a relationship, v and K as follows: d [(1 h )(1 v ) ] P K H = v 4 µ (1 vh ). (10) From equation (10), the value of the threshold consumer v, who is indifferent between buying the service in the posted-price channel and participating in the NYOP process, is uniquely determined once the variables H P and K have been chosen by the service provider in 17 In the sequel, we show that when h changes, the equilibrium values of v and K change as well. Hence, apriori, it is unclear how the value of the parameter h affects the level of the schedule P ( y ). However, its steepness is unambiguously greater as h increases

24 earlier stages of the game. As a result, the provider s maximization problem that yields the optimal values of the decision variables K and H P can be formulated, instead, as a maximization problem where K and v are chosen 18. For reasons of analytical tractability, we find it simpler to adopt the latter in our subsequent analysis, given the quadratic functional form obtained in (10) The Bayesian Nash Equilibrium of the Entire Game As mentioned earlier, we consider two different variants of the model, one in which the level of capacity is fixed and the other in which the capacity is optimally selected. In the former case, the service provider chooses the single decision variable v (or alternatively P H ), and in the latter case he chooses both v and K optimally (or alternatively P H and K). The objective function of the service provider in either case is: H 1 1 π Dual = P (1 v)(1 h + hy) dy + P ( y)[ K (1 v)(1 h + hy)] dy ck. (11) 0 0 subject to: 0< v < 1, where H P is given in (10) and ( ) P y is given in (9). The first and second terms of the objective function of the service provider correspond to the expected profit from the posted-price and NYOP channels respectively. Notice that in the first stage, the service provider is uncertain about the demand at the posted price channel and, as a result, is uncertain about the unsold capacity that is available for the NYOP channel. Substituting the value of H P from (10) and the value of P ( ) y from (9) into (11), we obtain: 18 There is a one-to-one mapping from ( P H, K) to v and vice versa from ( v, K) to - - H P, according to (10)

25 E( π ) = v[(1 v) + d( K 1 + v)] ck + Dual d h 1 h 1 h h (1 h) K v K v µ h 4h 6 4h (1 )( + ) (1 + ) (1 ) [1 + + ]. (1) Case (a): Fixed Capacity For a fixed capacity K, optimization of (1) with respect to v yields 19 : v = d 1+ 3h h µ 3 µ d 3 4 h(1 d) + (1+ h h + h ) µ 3 3 h(1 d) + (1+ h h + h ) dk( h) (13) It is interesting to note from (13) that the segment of consumers participating in the posted-price channel is not necessarily bigger if the installed capacity is larger (i.e. the sign of v/ K is not necessarily negative.) When h and µ are sufficiently large v/ K is positive, implying that a larger capacity leads to a smaller segment of consumers obtaining the service via the posted price channel. arge values of h and µ make the NYOP channel a more attractive option for the service provider. As the extent of informativeness of the signal y improves (as measured by h), the provider can make much better pricing decisions in the NYOP channel than in the posted-price channel, where the price has to remain fixed independent of the anticipated state of the demand. Further, as the relative size of the NYOP market gets larger (as measured by µ ) the provider has greater incentives to reserve capacity for this channel. Hence, he finds it optimal to raise P H, which leads to smaller participation of consumers in the posted price market. We summarize the above observations formally in Proposition 1. PROPOSITION 1: For a fixed level of capacity K, 19 From (13), it is clear that there is a limit on the capacity K to ensure that 0 v

26 (i) (ii) 1+ 3h h v When µ >, > 0 h K, and v > h h v When µ <, < 0. In particular, if h K value of h. µ < 3, v < K 0 irrespective of the PROOF: See Appendix 1. According to part (ii) of the proposition, if the anticipated demand density of the NYOP market is not much greater than the expected density in the posted price channel (recall that E(δ) = 1 in the posted price market) then higher capacity results in a greater proportion of the customers obtaining the service directly from the service provider. We can gain further insight by examining the direction of the effect of the (fixed) capacity on the posted price, P H, and the expected value of the minimum acceptable price in the NYOP channel, E y (P ). The effect on the latter, [ E ( P )] K, is unambiguously negative y thus, as the available capacity increases, the expected value of the minimum acceptable price in the NYOP channel decreases. Turning to the posted price, P H K < 0 when h and µ are sufficiently small (as in part (ii) of Proposition 1), but its sign is ambiguous otherwise. Thus, when h and µ are sufficiently small, both P H and E y (P ) decrease as capacity increases. Part (ii) of the proposition implies that P H decreases rapidly enough relative to E y (P ) to prompt a greater proportion of customers to buy at the posted price. On the other hand, when h and µ are sufficiently large (corresponding to part (i) of Proposition 1), increasing capacity implies that the extent of decrease in the expected minimum acceptable price is significantly larger than that in the posted price, such that a smaller proportion of customers buys at the posted price. A comparative statics analysis to evaluate how changes in the parameters affect the value of the threshold consumer v, yields the result reported in Proposition

27 PROPOSITION : For a fixed value of K, (i) 1 > 0 if v > v d 1 < 0 if v < v (ii) > 0, assuming K > (1 v). µ (iii) v h > 0 if 1 v < ; otherwise, it has an ambiguous sign. PROOF: See Appendix 1. According to Proposition, changes in the degree of opacity of the NYOP channel or the extent of informativeness of the signal y may have ambiguous implications on the size of the population that purchases directly from the service provider. When v < 1, smaller values of d and bigger values of h result in the shrinking of this population. In contrast, when v > 1, the size of this population shrinks when d increases. The effect of h on this size is unclear. The expected size of the NYOP channel, as measured by µ, has an unambiguous effect of the value of v. Specifically, as long as the level of capacity is sufficient to at least cover the expected demand in the posted price channel (i.e., K > 1 v ), larger values of µ result in a smaller segment of consumers buying in the posted-price channel. The results reported in Proposition stem from the existence of two counteracting effects on the profitability of the NYOP channel to the service provider. On the one hand, large values of the parameter d, µ, and h increase the profitability of this channel. arger values of d indicate lower opacity experienced by consumers and therefore increased willingness to pay on their part. arger values of µ indicate that the density of consumers in the NYOP channel is - 5 -