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Joint Opaque Selling Systems for Online Travel Agencies

Malgorzata Ogonowska et Dominique Torre
p. 111-139

Résumés

Cet article analyse les ventes opaques qui constituent un canal de distribution alternatif aux canaux traditionnels. Deux variantes sont pratiquées. La première, développée par Hotwire.com repose sur des prix affichés et un service garanti par le vendeur dès le paiement. La seconde, proposée par Priceline.com, fonctionne sur la base d’une sorte de système d’enchères, les clients potentiels formulant un prix pour une offre qui leur sera d’autant plus accessible que le prix proposé est élevé. Nous proposons un modèle analytique permettant de comparer l’application individuelle et simultanée de ces deux variantes par une agence de voyages en ligne en situation de monopole et faisant face à une demande hétérogène. Deux situations sont explorées : une information complète mais imparfaite et une information incomplète et imparfaite. Les résultats obtenus montrent qu’en information complète et imparfaite l’adoption simultanée des deux systèmes n’améliore pas les profits du monopoleur. En revanche, dans le cas où l’information est incomplète, ce qui semble le plus pertinent, l’utilisation des deux canaux opaques accroît le profit joint de la compagnie et de l’intermédiaire, ce qui jette un doute sur le bien-fondé des stratégies retenues actuellement par les intermédiaires.

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The authors acknowledge valuable comments from Laurence Saglietto and Régis Chenavaz. The authors thank Giacomo Del Chiappa, Milena Gradeva, Ulrike Gretzel, Miriam Scaglione, Dejan Trifunovic, and participants in the ENTER 2012 Conference in Helsingborg, Sweden and the 27 JMA in Angers, France, for comments and suggestions on preliminary versions of the paper.

1. Introduction

  • 1 Longhi [2004, 2009]; http://www.journaldunet.com/cc/10_tourisme/tourisme_marche_fr.shtml; http://ww (...)
  • 2 CheapOAir, Expedia, Opodo, Orbitz, Priceline.
  • 3 Acquired by Expedia in 2003.
  • 4 Which has since acquired Booking.com in 2005, Agoda in 2007 and most recently Kayak in 2012, and si (...)
  • 5 http://www.traveldividends.com/programs/online-travel-agency-programs/

1The emergence of the Internet has radically changed the tourism industry, the organization of tourism markets and the pricing mechanisms developed by tourism firms. Tourism is the best developed and most innovative online business,1 supported by the emergence of various types of online travel agencies (OTAs) and sophisticated pricing and segmentation strategies. There are some leading global OTAs2 that dominate the distribution of travel and tourism services; however, the spread of the Internet has allowed the emergence of niche players. Most of these smaller players specialise in specific market segments focused on particular destinations or services; some have experimented with innovative pricing models including opaque selling. Hotwire3 and Priceline4 are the two companies that have been the most successful in exploiting this latter strategy on the US market. They offer opaque products, that is, airline tickets and hotel rooms where the airline and travel schedule, the hotel name and exact location are only revealed when the payment is completed. Priceline has developed an online pricing mechanism which it calls Name-Your-Own-Price (NYOP), where, instead of posting a price, the seller receives offers from potential buyers which it can then accept or reject. Opaque models offer significant discounts to price conscious consumers with relatively low valuations of the product as the counterpart to opacity and uncertainty, and simultaneously allow suppliers to ‘sell their excess inventory through a “brand-shielded model”, thus enabling suppliers to maintain overall pricing integrity for their inventory’5 and helping them to manage dynamically demand fluctuations for a fixed short-term supply.

  • 6 TravelClick Distribution Channel Performance Outlook Report, 1st Quater 2012, www.travelclick.com/i (...)
  • 7 Data from Experian Hitwise, http://www.tnooz.com/article/priceline-narrows-gap-on-expedia-top-us-tr (...)

2According to TravelClick,6 opaque selling OTAs accounted for 6% of the hotel reservations of major hotel brands in 2011. In addition, some 10,000 of 70,000 unsold airline tickets are sold daily through Priceline.com to leisure travellers, who account for over 90% of its customers. Priceline and Hotwire are ranked among the top 10 of most popular travel websites in the US, recording respectively 10.23% and 6.23% of overall US-based OTA’s visits in March, 2012.7 These evidences raise several questions. What are the advantages of such pricing systems for suppliers, intermediaries and consumers? Why would hotels and airline companies be willing to sell their products through Priceline/Hotwire and lose the advantage (and profit) provided by product differentiation (Shapiro and Shi, 2008)? Why are firms willing to deviate from the standard practice of posting a take-it-or-leave-it offer? Do the firms find these strategies profitable?

3The recent literature on opaque selling addresses these and similar questions. However, to our knowledge, there are no papers that compare the two strategies developed by Hotwire and Priceline and account for the opaque features of the products offered. The question we focus on is whether, since there are many variants of opaque selling systems, is there advantage to be gained from the simultaneous use of more than one distribution channel?

4The remainder of the paper is organized as follows. Section 2 provides a review of the literature. It highlights the specific characteristics of opaque products and the advantages of opaque systems in tourism industry. It investigates the unique properties of the NYOP channel introduced by Priceline. Section 3 presents the analytical model. We are interested in the types of opaque selling systems that might be implemented by a given online monopoly to distribute airline tickets. We compare an opaque posted-price (PP) “Hotwire system” with a NYOP system with no possibility of rebidding, and the joint implementation of these two systems. We find that in a situation of imperfect (the travellers do not know the type and number of tickets that are available), but complete information (potential clients know their number and their respective propensity to pay), it is equivalent to implement the most efficient system (the NYOP system) or both systems in parallel. In section 4 we introduce the assumption of incomplete information (the travellers know their number, but not their relative propensity to pay). In this case, we find that, under moderate uncertainty, joint implementation of both booking systems dominates implementation of the NYOP channel only. The proofs are provided in the appendix.

2. Opaque Selling: A Literature Review

5We survey the literature on opaque selling, which focuses on either PP opaque selling or the NYOP channel. Opaque selling includes the PP models developed by Hotwire.com, Top Secret by LastMinute.com, and the NYOP mechanism developed by Priceline.com. There are no studies that combine these two types of opaque booking mechanisms within the same intermediation structure.

6With the exceptions of Wang et al. [2009], Shapiro, Zillante [2009] and Anderson, Wilson [2012], most work on NYOP selling mechanism ignores the question of product opacity. In this literature survey, we first present the contributions related to the opaque characteristics of the products and then focus on research on the NYOP booking channel.

2.1. Opaque Products

7First, we analyse the characteristics of opaque products and the advantages of opaque selling. We focus on the contributions that consider what, in our opinion, is the most important feature of opaque selling, that is, that some key product’s attributes or characteristics are concealed by the seller. This forces consumers to make their purchase decisions blind. From the service providers’ point of view, we can identify two opposite effects. On one hand, by employing opaque selling the provider loses the advantages of product differentiation because, to consumers, opaque goods are indistinguishable and are perfect substitutes (Shapiro, Shi [2008], Jerath et al. [2010]). On the other hand, since it is not always beneficial to fully inform consumers about the market prices in case their price sensitivity increases and downward price pressures emerge, opaque selling enables service providers to generate incremental revenues without disrupting existing distribution channels or retail pricing structures (Smith et al. [2007], Shapiro, Shi [2008], Zouaoui, Rao [2009], Gal-Or [2011]). Opaqueness allows the service provider to distribute a distressed inventory at discounted prices through opaque intermediaries, which enable it to reach a different demand segment than can be achieved by traditional, transparent sales channels (Dolan, Moon [2000], Chen, Iyer [2002], Jiang [2007], Pizam [2011], Anderson, Wilson [2011]). Hence, it is beneficial for service providers to implement multichannel distribution using mechanisms that provide different levels of market transparency (Grandos et al. [2008], Anderson, Xie [2012]). In order to increase its revenues, the service provider might vary the price differential across different selling mechanisms and thus, successfully price discriminate clients (Fay [2008], Jiang [2007], Grandos et al. [2008], Shapiro, Shi [2008]), because consumer valuation of the product may be represented as a function of the channel’s opacity (Anderson, Xie [2012]). In the case of competition between service providers, an issue that we do not tackle in the present paper, the introduction of an opaque channel increases the price competition for the low-value consumers’ segment, but decreases it for the high-value consumers (Shapiro, Shi [2008]). This result is particularly important if high value consumers are sufficiently brand-loyal. On the other hand, if consumers’ brand loyalty is rather low, the introduction of opaque selling may have the opposite effect (Fay [2008]).

8Opaque selling can be regarded also as probabilistic selling, in which the opaque good is considered as a gamble involving a probability of getting any one of the sets of multiple distinct items (Fay, Xie [2008], [2010], [2012]). In this case, also, market segmentation is based on consumer uncertainty and heterogeneity in the uncertainty levels they can bear. In addition, since opaque intermediaries distribute the products of different service providers, opaque selling provides the seller with a buffer against its own uncertainty about the identity of the most popular product. Finally, the introduction of opaque selling is beneficial not only for the intermediary, it also affects overall welfare by enabling very price sensitive consumers to travel (Jiang [2007]).

2.2. Name-Your-Own-Price selling mechanism

9NYOP is a popular method of selling excess inventory over the Internet. It was developed in 1998 by Priceline.com, which remains the largest NYOP seller worldwide. It is sometimes described in the literature as an auction (Spann, Tellis [2006], Bernhardt, Spann [2010], Anderson, Wilson [2011], Gal-Or [2011]) since NYOP and auctions have several similarities. When a consumer visits the website of Priceline (or some other NYOP intermediary), in presenting her query, she is asked to name the price she would like to pay for the product, and to complete all requested data (name, e-mail address, credit card number). Priceline then checks the prices of corresponding services, loaded into its database (GDS Worldspan) by the service providers. If it finds a product whose price is lower than the consumer’s bid, the transaction takes place. Priceline keeps the difference between the listed price and the price paid by the client, which represents its margin (identified with another type of margin – informational – as the two sources of intermediary’s profits by Hann and Terwiesch [2003] and Gal-Or [2011]). In the literature, it is usually assumed that the intermediary sets a threshold price above which it accepts the bids. If it does not find an appropriate product at a price corresponding to the consumer’s bid, this bid is rejected. In the case of a declined bid, the consumer cannot reformulate the same query for 24h, but she can rebid immediately by changing at least one of the product’s attributes (e.g. date, destination or departure airport in the case of bidding for an airline ticket, hotel location or star rating in the case of accommodation search). In this paper, we adopt this single-bid restriction in line with Wilson, Zhang [2008], Wang et al. [2009], Anderson, Xie [2012], Gal-Or [2011], Shapiro [2011]; however, the question of relaxing this restriction i.e. allowing multiple bidding remains an important issue in existing literature since perfect enforcement of the single-bid policy is not always possible (Fay [2004], Bernhardt, Spann [2010]). Fay [2004] shows that some consumers use illegitimate practices to bypass this restriction (e.g. a different credit card number and e-mail address), which is detrimental to the intermediary’s profits. In practice, some NYOP sellers implement a multiple bidding policy and allow consumers to engage in online haggling (Hann, Terwiesch [2003], Terwiesch et al. [2005], Joo et al. [2012]), and progressively to raise their bids (Cai et al. [2009]) towards their reservation prices (Spann et al. [2004]) if their initial bids are rejected. Fay [2004] shows that, surprisingly, single-bid and multiple-bid policies do not modify the level of the intermediary’s profits. Fay and Laran [2009] apply a joint policy of multiple-bidding and varying threshold price. They show that if consumers suppose the threshold price to be constant, their bidding pattern is monotonically increasing. However, if they expect it to vary, their bidding behaviour depends on their patience and the expected degree of threshold price variability. The fact of changing the threshold may attract and retain more customers, and does not necessarily reduce customer satisfaction (Fay, Laran [2009], Hinz et al. [2011]), which contrasts with what might be expected.

  • 8 Following the assumption developed by Fay [2004], we consider that there are two possible threshold (...)

10Another important feature of NYOP system, which is related to its profitability, is the secrecy surrounding the threshold price (Bajari, Hortaçsu [2003], [2004], Hinz, Spann [2010]). For bidders, it is important to learn the maximum on its level in order to bid near to it but not to overbid. In this paper we suppose that potential bidders estimate the thresholds levels,8 perfectly in the case of complete information (i.e. the benchmark case) and imperfectly under uncertainty. In reality, in the context of the Internet, consumers share information on their successful and unsuccessful bids with their online communities and on forums (ex. BiddingForTravel.com, BetterBidding.com). Bidders use the available information in order to update their references prices, product valuations and beliefs about thresholds, in order to derive maximum savings (Joo et al. [2012]), all of which decreases the sellers’ profits. NYOP intermediaries may react different to this information diffusion (Hinz, Spann [2010]). They may adapt their threshold prices levels (Fay, Laran [2009], Hinz et al. [2011]) or they may manipulate the quality and availability of the information diffused (Wolk, Spann [2008], Hinz, Spann [2010], Cai, Cude [2011], Spann et al. [2012]), by contributing to these forums or posting reference prices on their own websites. One possibility is to implement a Select-Your-Price mechanism (Spann et al. [2012]). In this case consumers are influenced by the range of possible candidate bids. Providing a list of possible bids could be perceived as a format that provides more information about the seller’s threshold price and, thus, decreases the customer’s uncertainty about the product’s value. The effective bid amounts and intermediary’s profits, depend on the level of possible bids provided. If they are too low or too high i.e. seem unrealistic or unacceptable, their effect will be negative.

11In relation to the distribution of threshold prices, the most common customer belief, which we adopt in the paper, is that the threshold is uniformly distributed across an interval (Hann, Terwiesch [2003], Fay [2004], Terwiesch et al. [2005], Fay, Laran [2009], Wang et al. [2009]). In this paper, we adopt the assumption of uniformity of threshold distribution as a consequence of customers’ uniform reservation price distribution. In our model consumers’ valuations of tickets are uniformly distributed (on two identical segments). The literature includes similar settings (Fay [2004], Almadoss, Jain [2008], Wang et al. [2009], Anderson, Xie [2012], Shapiro [2011], Fay, Xie [2012]).

12This paper compares the use of an opaque NYOP channel, an opaque PP channel, and their joint implementation. In the model, once the customer’s bid is rejected, she cannot purchase the product via the opaque PP channel. This is the same assumption as in Wang et al. [2009]. The nonsequentiality of the booking mechanism is an important point, and it distinguishes our setting from the frameworks in the literature. In particular, Anderson and Xie [2012] consider a firm which tends to set optimal full information prices, opaque prices and an optimal threshold policy at the NYOP retailer. Although these prices are set simultaneously, sequential use of distribution channels is possible in this setting. Customers choose one of channels or, in the case of rejected bids, the sequence of channels. They make their decisions based on their valuation, PP levels, and on the probability of their bid being accepted. For the firm it is always optimal to post both full information and opaque prices, especially if the opaque price, as a function of the channel’s opacity, converges to a full information price. However, in this framework, it is not always optimal to implement the NYOP channel. Shapiro [2011] compares a non-opaque NYOP and PP channels with risk adverse buyers. He shows that in the case of risk neutral buyers the NYOP profits coincide with the PP profits. If buyers are risk-averse, the NYOP profits outweigh the PP benefits. Then, like Anderson and Xie [2012], Shapiro considers a NYOP intermediary which adds to its offer a PP option. This option captures the demand of rejected bidders. Finally, Shapiro considers the same situation with the presence of a competitive alternative PP option. In this case, the seller needs to be cautious about modifying the PP in order not to lose its clients. This framework explains why Priceline has developed a PP non-opaque system on its website. The main differences with our paper and our contributions to knowledge, are that: first, we consider that the use of both models is simultaneous and following a rejected bid the customer has no possibility of acquiring the ticket; second, that the products are opaque; and third, that capacity is limited. In the opposite cases, the intermediary and potential clients would adopt different behaviour, therefore, the issue would not be the same (Cai et al. [2009], Fay, Xie [2012]).

3. Diversification of opaque channels with complete information

13Despite the extensive literature, there is one question that has not been addressed, that is, since many variants of opaque systems exist, is there an advantage in using simultaneously more than one distribution channel? This is the question addressed in this paper.

14The answer is complex and depends on many circumstances, mainly the competitive environment. If we consider a competitive game, in which every competitor chooses one channel, the equilibrium could be asymmetric, where each intermediary specialises and distributes on a specific channel. If Agencies A, B and C compete on alternative channels: opaque PP, transparent Last Minute and opaque NYOP channel, each should specialise in different types of selling and should serve specific demand segments.

15If there is only one agency in a monopoly position and the objective is to find the best allocation of potential travellers on alternative channels, the best solution, theoretically, would be first-degree price discrimination. As in many other cases, this strategy is not implementable due to its complexity, and because the consumers’ willingness to pay is private information and there is no incentive for its revelation. The NYOP opaque solution (the Priceline system) seems to be the most similar. Suppose that the population of travellers is risk-neutral, fully informed about the characteristics of unsold tickets (airline, departure time, etc.) and knows perfectly the distribution of other potential travellers’ propensities to pay, each consumer is able to bid (or not) a price corresponding to her reservation price, given the uncertainty about the number of seats available and their attributes. However, this result depends on the level of incompleteness of the potential traveller’s information. Suppose for instance that potential travellers with a high propensity to pay are less well informed about the ticket distribution and the propensity to pay of other agents. In this case, they will likely over-estimate the utility they can derive from the NYOP channel and bid a lower price than they would under complete information. In this case, implementation of a last minute channel would be a better strategy. However, this solution has one main inconvenience: it has a negative effect on the existing pricing structure, by creating a downward pressure. In this paper we consider the last minute selling channel as complementary to the opaque channel.

16It is complicated to decide whether two or more forms of opaque channels can coexist. Consider, for instance, the opaque NYOP Priceline and the opaque PP Hotwire channels. Both channels are opaque, i.e. do not give precise information to the would-be travellers about the quality of the travel. Again, if all passengers had complete information on flight frequency and other ticket attributes, and if they knew precisely the distribution of the other consumers’ propensities to pay, all would choose to use only the NYOP system, and would quit the PP channel, which would be rendered redundant. In the following subsection we try to confirm this intuition.

3.1. The model

There are 2n potential travellers distributed in two sub-populations of n agents, both willing to travel from city 1 to city 2. The travellers belonging to the sub-population A prefer the 7:00 flight and the sub-population B – the 18:00 flight. Each subset of n potential travellers is distributed uniformly on a segment Image 10000000000000240000001912DCDA6E.jpg with Image 100000000000002400000012EE148AAE.jpg. The gross utility of traveller i, located at the point Image 1000000000000028000000167F74D573.jpg on the segment Image 10000000000000240000001912DCDA6E.jpg is Image 100000000000003A00000019AAE2C0EE.jpg, Image 10000000000000390000001502E3C1E7.jpg when she travels at her preferred time and only Image 100000000000001800000016A6C139B2.jpg when she takes the other flight. All travellers are risk neutral, i.e. they care only about maximizing their utility. If a traveller decides not to purchase the product and not to bid, or her bid is not accepted, her utility vanishes. In the case of a rejected bid, the unsuccessful bidder has no possibility of rebidding or buying the ticket on the PP channel.

  • 9 Priceline.com benefits from a monopoly position in the U.S. market due to its booking system Name-Y (...)
  • 10 It receives a commission after each booking, but makes no commitment on inventory, therefore it tak (...)

17There is one OTA, which is in a monopoly position9 and implements an adapted opaque selling system in order to distribute flight tickets from city 1 to city 2 for given airlines. It maximizes its and the airlines’ profits. To keep the results simple, we consider that the OTA does not bear any costs; for any costs level, the analysis yields the same insights. We suppose that the OTA receives a fixed percentage of each ticket sold since it operates under a merchant model10.

Each day there are two flights from city 1 to city 2: the first leaves at 7:00 and the second at 18:00. The number and the nature of available seats are estimated with a small error just a few days before the flight departure date. There are five possible states of the world, defined in Table 1. The OTA knows their distribution and the potential travellers’ number and locations on the two segments. There are always more potential travellers than available seats in all states of the world, i.e. Image 100000000000002D0000000F74CB8247.jpg. Tickets are sold on a first-come-first-served basis.

Table 1. Available seats for the flights from city 1 to city 2 on a given date

States of the world

Number and type of available seats

Probability

1

m at 7:00

1/4

2

m at 18:00

1/4

3

2m at 7:00

1/8

4

m at 7:00

m at 18:00

1/4

5

2m at 18:00

1/8

18The OTA implements either:

  1. an opaque PP system;

  2. an opaque NYOP system;

  3. both systems jointly.

19The sequence of actions is as follows:

  • At stage 1, the OTA chooses among (i), (ii) and (iii). If it selects (i) or (iii), then at the same moment it sets the price of the PP channel. If the OTA chooses (ii) or (iii), it launches a single bidding process for the tickets.

  • At stage 2, if the OTA initially chose (i), potential travellers will decide to buy or not a ticket on the PP channel. If the OTA selected (ii), they will choose to post or not a single bid. If the OTA chose (iii), potential travellers will decide to buy a ticket on the PP channel, or to bid on the NYOP channel, or to reserve.

  • At stage 3, the OTA knows the exact number and nature of the available seats on each flight. If (i) or (iii) was chosen at stage 1, the OTA delivers the tickets to its clients on the PP channel. If (ii) or (iii) was selected, the agency fixes the threshold price for the NYOP channel and sells the tickets to those bidders whose bids exceeded this threshold. Each successful bidder pays the rate she posted.

20The relevant equilibrium concept is a Stackelberg equilibrium, where the OTA is the leader. The game is solved by backward induction. At stage 3, the OTA chooses the best action (i.e. it fixes the threshold price of the NYOP channel if (ii) or (iii) was selected), given potential travellers’ actions at stage 2. At stage 2 potential travellers choose their own best options, given the OTA’s decisions at time 1 (the distribution system chosen and the PP channel rate, if strategies (i) or (iii) were implemented), OTA’s expected decisions at stage 3, and the probability of their bids being accepted. At stage 1, the OTA chooses the appropriate distribution strategy and the rate applied on the posted-price channel if strategy (i) or (iii) is implemented.

21We suppose that information is imperfect, but complete, i.e. travellers know the states of the world and their respective probability, but they do not know which is realized.

3.2. The optimal choices of the OTA

22Let us consider the three OTA solutions in order.

  • 11 Theoretically, the OTA could sell more than m tickets, because in some states of the world there ar (...)

(i) If the opaque PP channel is implemented on its own, the OTA at stage 1 sets the price Image 100000000000001C000000182A31D08F.jpg, which maximizes the airlines’ and OTA’s joint profit Image 100000000000006100000018B265F1CC.jpg. The number of seats available for the channel is fixed at stage 1 as m, which is the highest number of seats always available at stage 3 in all states of the world.11 Then, the level of Image 100000000000001C000000182A31D08F.jpg is such that the OTA extracts the whole surplus of the last traveller choosing the PP channel. Whatever the rate for this channel fixed at stage 1, the potential travellers, whose net utility is greater than or equal to zero at this rate, will choose to buy a ticket via this channel at stage 2. Then, the best solution for the OTA is to charge a rate that clears the last potential PP channel client’s surplus. These travellers are located on each segment at points Image 100000000000001100000018FF31F2D6.jpg, such as Image 100000000000007A00000018D0EA2786.jpg, i.e. at Image 100000000000007900000018B1602075.jpg. The resulting value of Image 10000000000000170000001893D00997.jpg, which wipes out the net utility of agents located at Image 100000000000001100000018FF31F2D6.jpg, then is Image 100000000000008B000000186FABB317.jpg, since the states of the world and the distribution of agents on the segments Image 10000000000000240000001912DCDA6E.jpg are common knowledge. Then, we obtain Image 10000000000000BE000000187AE50A20.jpg and

Image 1000000000000101000000186422DE1B.jpg (1)

(ii) If the opaque NYOP channel is the only channel implemented at stage 3 and in each state of the world, the OTA chooses the higher threshold value, such that travellers, whose bids are greater than or equal to this threshold, clear the market. Since the OTA determines this value after observing the state of the world, there are two possibilities. If only m tickets are available, the price Image 1000000000000018000000182C80B30D.jpg is high: it corresponds to the reservation price of the Image 100000000000003900000018EAA89D7C.jpg traveller if potential buyers are ranked according to their increasing propensity to pay. If the number of available tickets is 2m, the price Image 10000000000000190000001293CA7B3D.jpg is lower because it corresponds to the propensity to pay of the Image 100000000000004100000018F6ACE40B.jpg traveller, who integrates uncertainty in her expected utility function. At stage 2, the bidders are able to take account, in their decisions, of the optimal choices of the OTA and, among other things, to consider the possibility of their bids being accepted. If they are able to understand the NYOP system correctly, they will be able to calculate the last successful bid in each state of the world and may post it if it is lower than or at least equal to their reservation price. In the case of imperfect, but complete information, there exist two possible bids: Image 1000000000000018000000182C80B30D.jpg, which guarantees the travel in all states of the world, and Image 100000000000001800000018DF34C136.jpg, which makes the travel uncertain. Potential travellers bid only Image 100000000000001800000018DF34C136.jpg or Image 1000000000000018000000182C80B30D.jpg: their net expected utility is then defined by Image 100000000000006E000000189480E7EB.jpg if they decide to bid Image 1000000000000018000000182C80B30D.jpg, and Image 10000000000000870000001C9F963D88.jpg, if they decide to bid Image 100000000000001800000018DF34C136.jpg. Elementary calculus allow us to deduce the threshold values Image 100000000000001600000018C15F49E2.jpg and Image 100000000000001B000000181DA617F7.jpg separating on each segment Image 100000000000002300000015A9540F3D.jpg potential travellers choosing not to bid and potential travellers bidding Image 100000000000001800000018DF34C136.jpg, potential travellers choosing to bid Image 100000000000001800000018DF34C136.jpg and potential travellers who bid Image 1000000000000018000000182C80B30D.jpg respectively. These values are Image 100000000000006E00000018D5CEFE1C.jpg and Image 10000000000000830000001811CCEA8D.jpg. Then we can deduce the equilibrium threshold prices Image 10000000000000AB00000018EEF56DC0.jpg and Image 10000000000000BA0000001832E5D3CB.jpg, and the joint airlines’ and OTA’s profit Image 100000000000008700000018AF1380E2.jpg or

Image 100000000000014F00000018FAC1AFC3.jpg (2)

(iii) If both channels are implemented jointly, the OTA allocates the first set of m seats to the PP channel, targeting customers with a higher propensity to pay. The second set of m seats is assigned to the NYOP channel, serving the travellers with lower propensity to pay. At stage 1, the OTA chooses the price of the PP channel and offers the travellers the possibility to bid on the NYOP channel. As in case (i), the price of the PP channel is Image 10000000000000BE000000187AE50A20.jpg. The NYOP channel attracts the next m travellers and the threshold price is Image 10000000000000AB00000018EEF56DC0.jpg. The joint profit of the airlines and the OTA then is Image 10000000000000930000001890A75A96.jpg or:

Image 1000000000000150000000181ABEAAFB.jpg (3)

23Consequently, we can hypothesize that:

24Proposition 1. If potential low rate travellers are completely informed about the random number and distribution of available seats, and the other agents’ propensities to pay, it is equivalent for the airlines and the OTA to implement a NYOP channel alone or to implement the PP and NYOP channels jointly.

Proof: Expressions (1), (2) and (3) represent the airlines’ and OTA’s joint profits at Stackelberg equilibriums associated respectively with the implementation of the PP or NYOP channels and both channels jointly. Comparison among (1), (2) and (3) proves that, whatever the values of the parameters Image 100000000000003500000014015A7F7E.jpg, and m, Image 100000000000006700000018595FD57E.jpg, it is equivalent for the OTA to implement the NYOP or both systems jointly.

According to the previous intuition, the opaque PP channel is not an optimal solution for potential travellers if it is implemented on its own. The travellers with a higher propensity to pay are indifferent between this selling mechanism and its joint implementation with the opaque NYOP channel, while the travellers with a low propensity to pay prefer the other two distribution strategies. We observe also that it is equivalent for high propensity travellers to pay Image 100000000000001C000000182A31D08F.jpg on the PP channel or to use the NYOP channel.

4. Joint opaque channels with incomplete information

There is a first type of information incompleteness that is associated with travellers’ uncertainty concerning the stochastic distribution of demand on traditional channels. The seasonal, daily and hourly evolution of traditional demand follows complex laws which are not easily understandable by travellers. The statistical distribution of demand variations during the period could involve information incompleteness or information asymmetries, on the one hand between the OTA and the travellers, and on the other hand among the travellers. However, it is advantageous for airlines to partly adapt their supply to these variations. Consequently, it is advantageous for airlines and the OTA to spread the appropriate statistics on the available seat distribution for each destination, during every time sub-period. Then, we can assume that this lack of information is not the main reason for travellers’ uncertainty, and can focus on the second type of information incompleteness. Bidders generally lack relevant information on other consumers’ propensities to pay. The important number of potential travellers makes it difficult for each bidder to perceive the propensities to pay distribution. This lack of information has dramatic consequences: under information completeness, our example provides only two bid prices when the NYOP or the PP system and the NYOP jointly are implemented. In this case, whatever the traveller’s propensity to pay, it will never be interesting for her to bid a price different from Image 100000000000001800000018DF34C136.jpg or Image 1000000000000018000000182C80B30D.jpg.
In contrast, under incomplete information, travellers cannot perfectly estimate
Image 100000000000001800000018DF34C136.jpg or Image 1000000000000018000000182C80B30D.jpg. Then, it might be rational for them to bid different prices if the selling system is the NYOP mechanism.

4.1. The general setting

Let us consider the segment that accommodates all potential travellers preferring the 7:00 (resp. the 18:00) flight, and assume that travellers do not know their precise position on this segment. This uncertainty implies that their estimations of the other travellers distribution on the segment, and especially the distance Image 10000000000000280000001953372CEC.jpg between their own location and the location of the agent with the highest propensity to pay, are imprecise. Then, we suppose that the agent located on Image 100000000000000F0000001642D6B12D.jpg estimates Image 100000000000000E0000000EF03DBF0A.jpg as Image 100000000000000E000000125865FA49.jpg:

Image 10000000000000E3000000194DE86BC8.jpg (4)

When Image 100000000000002400000015C94E7A46.jpg, there is full uncertainty on Image 100000000000000E0000000EF03DBF0A.jpg’s position and the traveller locates herself in the middle of the segment Image 100000000000002300000015A9540F3D.jpg. When Image 10000000000000210000001514EEA273.jpg, the information on her position is perfect, so she can perfectly estimate the threshold levels, as described in the previous section. When Image 100000000000000E000000113B7AEA54.jpg is strictly comprised of between 0 and 1, the uncertainty about the agent’s location is more or less moderate. We suppose that the OTA is aware of the agents’ confusion about their relative propensities to pay. Thus, we can consider the three possible strategic choices among the implementations of alternative selling mechanisms.

(i) If only the PP channel is implemented with price Image 100000000000001C000000182A31D08F.jpg, all the travellers have information on prices when taking their decision at time 2. Their behaviour is unchanged compared to the behaviour in Section 3. They buy tickets if Image 100000000000008B00000018E4C1C930.jpg and do not if Image 100000000000008B00000018559BE0B9.jpg. The result is the same as in case of complete information, i.e., Image 10000000000000BE000000187AE50A20.jpg and

Image 1000000000000101000000186422DE1B.jpg (5)

(ii) If only the NYOP channel is implemented, at time 2 the bidders estimate the probability of their bid being successful. Given (4), they still compare Image 100000000000006E000000189480E7EB.jpg (their estimated net utility if they choose to bid Image 1000000000000018000000182C80B30D.jpg and expect to travel, in all states of the world) and Image 10000000000000870000001C9F963D88.jpg (their estimated net utility if they choose to bid higher than Image 100000000000001800000018DF34C136.jpg, but lower than Image 1000000000000018000000182C80B30D.jpg, and accept the possibility of not travelling if there are only m tickets available) and 0 (their estimated net utility if they decide not to bid). In this case, they are bound in their individual estimations of Image 100000000000001600000018C15F49E2.jpg and Image 100000000000001B000000181DA617F7.jpg to evaluate Image 100000000000001800000018DF34C136.jpg and Image 1000000000000018000000182C80B30D.jpg. Given (4), they calculate Image 10000000000000D000000018FA8773A1.jpg and Image 10000000000000E10000001873CF2106.jpg,
and then deduce
Image 100000000000010800000018978367B2.jpg and Image 1000000000000026000000188D1870CA.jpgImage 10000000000000F100000018EB850F93.jpg – the threshold prices (depending on their location Image 100000000000000F0000001642D6B12D.jpg, when the total number of seats is respectively m and 2m). The higher the propensity to pay of the traveller located in Image 100000000000000F0000001642D6B12D.jpg, the greater high and low threshold prices for the NYOP channel she will expect. Potential travellers located at Image 100000000000000F0000001642D6B12D.jpg on one of the segments Image 10000000000000240000001912DCDA6E.jpg consider themselves marginal agents between travellers choosing the reservation and agents bidding at a low rate if Image 10000000000000E900000018E747C1BC.jpg,
i.e. Image 10000000000000F6000000187994B906.jpg. Similarly, agents located on the
same segment at
Image 100000000000010200000018D507E181.jpg, i.e. Image 100000000000003F000000180DD163A3.jpg consider themselves as limit agents between the low rate and high rate bidders. Note that these thresholds depend on Image 100000000000000E000000113B7AEA54.jpg, i.e. on the level of travellers’ uncertainty about their relative positions on Image 10000000000000240000001912DCDA6E.jpg. Then, at stage 2, potential travellers bids depend, first, on their position on Image 10000000000000240000001912DCDA6E.jpg and, second, on the level of uncertainty. Note that given (4), Image 1000000000000048000000189D23F83B.jpg. Then, at stage 3, there are three possible cases based on parameter values and uncertainty levels:

case 1: Image 10000000000000920000001865F8859A.jpg,

case 2: Image 100000000000009200000018ADA7FB1A.jpg,

case 3: Image 100000000000009200000018F034B19B.jpg.

(iii) If the NYOP system is implemented jointly with the PP channel, the OTA still allocates the first set of m seats to the PP, targeting customers with a higher propensity to pay. The price of the PP channel Image 100000000000001C000000182A31D08F.jpg is unchanged. The second set of m seats is still assigned to the NYOP channel and distributed to potential travellers with a lower propensity to pay. At time 2 the bidders estimate the probability of their bids being successful. Given (4), they still compare Image 10000000000000870000001C9F963D88.jpg (their estimated net utility if they choose to bid higher than Image 100000000000001800000018DF34C136.jpg) and 0 (their estimated net utility if they decide not to bid). In this case, they use their individual estimations of Image 100000000000001600000018C15F49E2.jpg to evaluate Image 100000000000001800000018DF34C136.jpg. Similar to the NYOP only strategy, they calculate Image 10000000000000D3000000182D050BCB.jpg, and then deduce the threshold price Image 100000000000010800000018978367B2.jpg. Again, the potential travellers located at Image 100000000000000B00000016623A5655.jpg on one of the segments Image 10000000000000240000001912DCDA6E.jpg consider themselves marginal agents between travellers choosing reservation and travellers bidding at a low rate if Image 10000000000000EE00000018345356BE.jpg, i.e. Image 10000000000000F6000000187994B906.jpg. Note that the threshold depends on Image 100000000000000E000000113B7AEA54.jpg, i.e. the level of travellers’ uncertainty about their relative positions on Image 10000000000000240000001912DCDA6E.jpg. Then at stage 2, potential travellers’ bids depend, first, on their position on Image 10000000000000240000001912DCDA6E.jpg and, second, on the level of uncertainty. Finally, under the joint implementation strategy, at stage 3 the three cases defined in (ii) still hold.

  • 12 For an extensive analysis of this issue see Chernev [2003], Kamins et al. [2004], and Wolk, Spann [ (...)

The first case is the most representative of the reality and, thus, is the case we analyse below. We dismiss the second case because according to the huge amount of easily available information, including information on external reference prices,12 it is unrealistic to consider high levels of consumer uncertainty. We dismiss the third case because it implies a large number of tickets Image 10000000000000390000001294988DE1.jpg (compared with the number of potential travellers), which means that, in the absence of an additional clearance channel (opaque PP or opaque NYOP or even classic last-minute), airlines would experience a huge excess capacity. Although during the crisis period, the trend among most airlines has been to reduce capacity to an optimum level in order to minimize excess capacity, consequently we consider this third case to be unrealistic.

4.2. Average number of tickets, moderate uncertainty

  • 13 Remained that a potential traveller is someone interested in travelling at a positive utility rate: (...)

In the first case we suppose that the number of available tickets is less than half the number of potential travellers, Image 100000000000003900000012F2E91FA2.jpg. In this case all served travellers are located on the segment between Image 100000000000001F00000012A64734FC.jpg and Image 100000000000000E0000000EF03DBF0A.jpg, i.e. Image 100000000000006A000000188CE45F83.jpg.13 By moderate uncertainty we mean that Image 1000000000000046000000151AC18731.jpg, which implies that Image 100000000000001D00000018EB3DD081.jpg is lower than Image 100000000000001B000000181DA617F7.jpg.

Figure 1.Case 1, 2m tickets available

Image 10000000000001E0000000728D38EB34.jpg

  • 14 As compared to , the threshold level in situation of complete information.

In this case, when the NYOP system is implemented, as illustrated in Figure (1), the threshold between the bids of those who expect to travel in all states of the world and those who expect to travel only if a large number of tickets is available, is higher than in the case of complete information. Consequently, travellers under-estimate the number of travellers able to travel in all states of the world. Therefore, bidders located between Image 10000000000000210000001826C57793.jpg and Image 100000000000000E0000000EF03DBF0A.jpg pay higher (and different) rates than in the case of complete information (and they are sure of travelling in all states of the world), while the travellers located between Image 100000000000001B000000181DA617F7.jpg and Image 10000000000000210000001826C57793.jpg pay lower (and also different) rates (and suffer the same level of uncertainty of their bid being accepted as in the case of complete information). At the same time, the travellers located between Image 100000000000001D00000018EB3DD081.jpg and Image 100000000000001B000000181DA617F7.jpg pay relatively high14 (and different) rates and travel only if 2m tickets are available. Finally, potential travellers located between Image 100000000000001600000018C15F49E2.jpg and Image 100000000000001D00000018EB3DD081.jpg do not bid because, under the prevailing uncertainty, they believe that the lower threshold price Image 10000000000000180000001849CEAF81.jpg corresponds to the relative propensity to pay of the agent located at Image 100000000000001D00000018EB3DD081.jpg and, consequently, that their bid would not be sufficiently high. When the number of available tickets is 2m, the result again is an extra-profit for the OTA and the airlines, derived from selling tickets to the subset of travellers located between Image 100000000000001D00000018EB3DD081.jpg and Image 100000000000001B000000181DA617F7.jpg, and the remaining unsold tickets corresponding to potential travellers located between Image 100000000000001600000018C15F49E2.jpg and Image 100000000000001D00000018EB3DD081.jpg.

When the PP channel is implemented on its own, only the travellers located between Image 100000000000001B000000181DA617F7.jpg and Image 100000000000000E0000000EF03DBF0A.jpg choose to travel at the uniform posted rate corresponding to Image 100000000000001B000000181DA617F7.jpg on the segment.

  • 15 Compared to .

When the PP and NYOP systems are implemented jointly, the travellers located between Image 100000000000001B000000181DA617F7.jpg and Image 100000000000000E0000000EF03DBF0A.jpg still choose the PP system, while the travellers located between Image 100000000000001D00000018EB3DD081.jpg and Image 100000000000001B000000181DA617F7.jpg still choose to bid relatively high15 (and different) prices and travel only if 2m tickets are available. Then, the PP channel remains dominated by the joint implementation of the two systems. The relevant comparison is between only implementation of the NYOP channel, and its joint implementation with the PP system and, especially, from the OTA’s point of view, the profits generated by the travellers located between Image 100000000000001B000000181DA617F7.jpg and Image 100000000000000E0000000EF03DBF0A.jpg in case of NYOP and joint implementation.

25If the NYOP channel is implemented alone, the OTA profits are expressed by (6)

Image 10000000000000DE0000001882777320.jpg (6)

26with

Image 10000000000001B80000006176E85CEC.jpg

27and

Image 100000000000018D000000619948D788.jpg

where Image 100000000000007C0000002B4F37F3EA.jpg and Image 100000000000008C0000002BAE2EDC5E.jpg, given the level of uncertainty corresponding to case (1), represent the number of tickets obtained by travellers bidding high and getting a ticket in all states of the world, and the number of tickets obtained by travellers, who bid low for a ticket if 2m tickets are available.

28If the OTA decides to implement both systems jointly, its profits are given by equation (7):

Image 10000000000001C80000004827EE2B3D.jpg(7)

Let us begin with an illustration of joint implementation of the PP and NYOP systems strongly dominating implementation of only the NYOP or only the PP channels. We choose the case where n = 9 and m = 4. In this case, each subset of n agents is located on the segment Image 100000000000002300000015A9540F3D.jpg.

In the case of complete information, travellers 8 and 9 are able to fly in all states of the world and travellers 6 and 7 are able to travel only when there are 8 tickets available (recall that there are 2n travellers located on two segments). We normalize a = 1 and settle the threshold values Image 100000000000004D000000189577E9FA.jpg and Image 10000000000000510000001892CAB14F.jpg, which correspond respectively to the reservation prices of the 6th and 8th travellers.

Then, we consider the case of incomplete information. We choose q = 35/36, which corresponds to a very moderate level of uncertainty (with q = 1, the potential travellers have complete information on other bidders’ reservation prices). Since in this case Image 10000000000000210000001826C57793.jpg is located between Image 100000000000001B000000181DA617F7.jpg and a, when only the NYOP system is implemented, only the traveller 9 chooses to bid high (which makes her flight certain), while travellers 7 and 8 choose to bid low (with the probability p = 1/21 to travel), and agent 6 does not bid. When there are m = 4 tickets available, only agents 8 and 9 travel and (in this case) at very different rates. Given the parameter values, we obtain Image 100000000000004F00000018AE5E4DDC.jpg, which can be deduced from the general formula Image 100000000000010400000018A5B13C48.jpg, which, when m and n are small, overtakes the approximation Image 10000000000000E40000001832C109C6.jpg. The first traveller’s bid corresponds to Image 1000000000000055000000188C8C203C.jpg, while the second traveller’s bid: Image 100000000000004F00000018B26DA183.jpg. The sum of their bids 1.472, is the OTA’s profit obtained by distribution to the high rate population when only the NYOP system is implemented. When both systems are implemented jointly, agents 8 and 9 choose the PP system and each pays the PP, which corresponds to the reservation price of agent 8: Image 100000000000004E000000186AA50B93.jpg. The resulting profit for the OTA is 1.666, compared to the profit obtained when the NYOP system is implemented on its own, of 1.427. Since agent 7 still bids the same amount Image 100000000000001D0000001869B83DEA.jpg with or without the PP system and agent 6 still does not bid, joint implementation of these two systems provides higher profits to the OTA.

29We generalize this observation in the following proposition:

Proposition 2. When n, m and q are such that Image 10000000000000920000001865F8859A.jpg,
joint implementation of the PP and NYOP is always the best solution for the OTA.

30Proof: see Appendix 1.

When we compare joint implementation of these systems with implementation only of the NYOP channel, consumers located between Image 100000000000001600000018C15F49E2.jpg and Image 100000000000001B000000181DA617F7.jpg choose the same options. Therefore, we focus on travellers located between Image 100000000000001B000000181DA617F7.jpg and a. In the case of joint implementation, all these consumers travel and pay the same opaque PP of Image 100000000000001C0000001499C8DD33.jpg. If only the NYOP system is implemented, the same agents pay very different prices. Consumers located between Image 10000000000000210000001826C57793.jpg and a are sure of being able to travel in all states of the world by bidding high prices, evaluated individually, Image 1000000000000018000000186F1A804B.jpg. These bids are higher than the opaque PP would have been. Alternatively, consumers located between Image 100000000000001B000000181DA617F7.jpg and Image 10000000000000210000001826C57793.jpg are convinced that the threshold price, which guarantees travel in all states of the world, is higher than their reservation price and, thus, bid much lower prices, evaluated individually, Image 10000000000000180000001849CEAF81.jpg, which enable them to travel only if there are 2m tickets available. Their estimation of their position on the segment is much lower than the reality. Whatever the number of available tickets, they will be able to travel. The bids Image 10000000000000180000001849CEAF81.jpg are lower than the opaque PP Image 100000000000001C0000001499C8DD33.jpg would have been. These bids converge to the reservation price of the agent who considers she would be the last to travel, if there were 2m tickets available, i.e. Image 100000000000001D00000018EB3DD081.jpg. The profit surplus resulting from high bids does not compensate the profit loss from low consumer bids.

The spread between the two profits as a function of the number of tickets available Image 100000000000004B00000015EF7744A0.jpg, increases with the uncertainty, as illustrated in Figure 2a,b,c. Figure 2a illustrates the case of relative uncertainty, q = 0.7 ; Figure 2b illustrates moderate uncertainty, q = 0.8, and finally Figure 2c illustrates the case of no uncertainty, q = 1, when both profits are equal. All other parameters remain unchanged and are normalized to: a = 20, u = 15, Image 100000000000002B000000122F7456E8.jpg and n = 75.

Figure 2.Comparison between NYOP and joint implementation in case 1

Image 10000000000003040000010518186BCD.jpg

5. Conclusion

31Drawing on the literature reviewed, which illustrates the extent of the questions raised by opaque selling in tourism, this paper considered the possibility of joint implementation of two different opaque systems by the same OTA. The first is the PP channel; the second takes the form of an auction where only travellers bidding over the unknown (hidden) threshold prices are sure to travel in all states of the world.

32We built a three-stage game model describing the optimal choices of a travel agent facing the population of potential travellers with differentiated reservation prices. We studied this game in the context of potential travellers’ imperfect, but complete information. In this case, potential travellers do not know the exact number and characteristics of available seats, but they do know the states of the world and their corresponding probabilities. They also know the number of potential travellers and their respective reservation prices. These assumptions are usual in the first strand of developments of an opaque pricing strategy analysis. With these types of assumptions, and assuming risk neutrality to analyse the travellers bids in the NYOP case, we find that joint implementation of the NYOP and PP systems provides no advantages over single implementation of the NYOP channel. Obviously, since, all things being equal, risk adverse travellers tend to prefer the PP system to the more risky NYOP auction, risk aversion might be a reason for implementing the PP system as an alternative to NYOP. Since travellers’ risk aversion of travellers is not easily observable and probably less important for the low valuation traveller sub-population, the choice of only the NYOP system is the best solution since, joint implementation of the two systems would increase operational costs and probably complicate the traveller’s choice for no good reason.

33We next extended the model to the case of incomplete information. In this case, the individual traveller does not know the characteristics of any other traveller. We limit this unawareness to reservation price levels and suppose that the number of potential travellers is known. This case has never been considered explicitly in the literature despite its relevance for real-life contexts, where the number and other statistical characteristics of given potential travellers are difficult for other bidders to identify. Several cases can be considered, related to the proportions of potential travellers and available tickets in each state of the world. We focus on the case we consider the most relevant: average number of available tickets relative to the number of potential travellers, and moderate uncertainty related to the distribution of other agent characteristics. We find that in this setting joint implementation of the PP and NYOP systems always dominates single implementation of the NYOP channel, even with the risk neutrality hypothesis we assume in this study.

34A first basic extension would be to consider the other two cases. For instance, the context of strong uncertainty and the PP system on its own dominating, could have interesting properties. More interesting, would be to consider competition among OTAs in a market with a small number of intermediaries. Would a ‘separating’ solution be the best in this case, with the opaque PP system chosen by one OTA and the opaque NYOP by another, or would these competing agents reap advantage from each implementing both systems?

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Annexe

Appendix 1: Proof of Proposition 2

Given that potential travellers located between and choose the same action whether the NYOP is implemented alone or jointly with the PP system, we consider only the optimal actions of potential travellers located between and a. According to the relative values of n, m and q, every agent j belonging to this subset chooses to bid prices Image 10000000000000180000001B9131E738.jpg or Image 10000000000000180000001B5A3213D7.jpg, according to her own position related to . If the agent is located between and , she chooses to bid a low price Image 10000000000000180000001B5A3213D7.jpg. If she is located between and a, she bids the high price Image 10000000000000180000001B9131E738.jpg. If the two systems are implemented jointly, all potential travellers located between and a pay . Equations (6) and (7) can be expressed by (8) and (9) respectively:

Image 10000000000001C60000005C938C4D12.jpg(8)

and

Image 10000000000001E20000002FF32F0812.jpg(9)

Comparison of the profit equations (8) and (9) shows that it is always more profitable for the OTA to implement both systems jointly than to implement only the NYOP channel. Indeed, there are no possible parameter values that make the profit Image 1000000000000018000000158199BC68.jpg greater than the profit Image 100000000000002700000015701330A1.jpg. In this comparison, we focus on profits driven by consumers located between and a. Indeed, it is more profitable for the OTA to provide these travellers with the opaque PP product rather than letting them bid at different price levels.16

Figure 3.Comparison between NYOP and joint implementation in case 1 according to uncertainty level

Image 10000000000001D60000011B9B6673C0.jpg

Figure 3 (3) illustrates that a decrease in the uncertainty level (corresponding to an increase in q from 0.5 to 1) reduces the spread between Image 10000000000000230000001867ADECAD.jpg and Image 100000000000001900000018F93E8242.jpg. These two profits become equal in the case of no uncertainty i.e. q = 1. All other parameter levels are normalized to: Image 100000000000003900000012A2F01448.jpg with m = 32 and n = 75, a = 20, u = 15 and Image 100000000000002600000012E2B75FE4.jpg.

According to Figures (2) and (3) the conditions on parameters a, u, Image 100000000000000E0000001223D5FC67.jpg, Image 100000000000004700000015F1BE0F41.jpg and the condition Image 100000000000003900000012A2F01448.jpg are sufficient to make Image 100000000000001900000018F93E8242.jpg smaller than Image 10000000000000230000001867ADECAD.jpg in all cases.

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Notes

1 Longhi [2004, 2009]; http://www.journaldunet.com/cc/10_tourisme/tourisme_marche_fr.shtml; http://www.journaldunet.com/ebusiness/commerce/e-commerce-en-france/sites-les-plus-rentables.shtml; http://webaly.co.in/ecommerce.html.

2 CheapOAir, Expedia, Opodo, Orbitz, Priceline.

3 Acquired by Expedia in 2003.

4 Which has since acquired Booking.com in 2005, Agoda in 2007 and most recently Kayak in 2012, and since became one of leading market players. For more extensive information see Priceline.com Incorporated Company Pro le by Marketline, 2013.

5 http://www.traveldividends.com/programs/online-travel-agency-programs/

6 TravelClick Distribution Channel Performance Outlook Report, 1st Quater 2012, www.travelclick.com/infomation-center/bookings-by-channel.cfm

7 Data from Experian Hitwise, http://www.tnooz.com/article/priceline-narrows-gap-on-expedia-top-us-travel-sites-march-3-2012/

8 Following the assumption developed by Fay [2004], we consider that there are two possible thresholds: one when the supply is very limited, and the other when there are more tickets available. However, unlike Fay [2004], we assume the intermediary keeps both levels secret.

9 Priceline.com benefits from a monopoly position in the U.S. market due to its booking system Name-Your-Own-Price being patented.

10 It receives a commission after each booking, but makes no commitment on inventory, therefore it takes no risk.

11 Theoretically, the OTA could sell more than m tickets, because in some states of the world there are 2m tickets available. However, as in case of overbooking it would be sued and it prefers to implement the safety strategy of selling only m tickets.

12 For an extensive analysis of this issue see Chernev [2003], Kamins et al. [2004], and Wolk, Spann [2008].

13 Remained that a potential traveller is someone interested in travelling at a positive utility rate: it is realistic to suppose that there are always potential travellers, especially during holiday periods, which are willing to purchase tickets, if their price decreases sufficiently.

14 As compared to Image 10000000000000150000001631D9D0A8.jpg, the threshold level in situation of complete information.

15 Compared to Image 10000000000000150000001631D9D0A8.jpg.

16 Computation details are available upon request.

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Malgorzata Ogonowska et Dominique Torre, « Joint Opaque Selling Systems for Online Travel Agencies », Revue d'économie industrielle, 147 | 2014, 111-139.

Référence électronique

Malgorzata Ogonowska et Dominique Torre, « Joint Opaque Selling Systems for Online Travel Agencies », Revue d'économie industrielle [En ligne], 147 | 3e trimestre 2014, mis en ligne le 30 septembre 2016, consulté le 22 février 2018. URL : http://journals.openedition.org/rei/5878 ; DOI : 10.4000/rei.5878

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Auteurs

Malgorzata Ogonowska

Université Nice Sophia Antipolis – GREDEG CNRS
malgorzata.ogonowska@gredeg.cnrs.fr

Dominique Torre

Université Nice Sophia Antipolis – GREDEG CNRS
dominique.torre@gredeg.cnrs.fr

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