WHY A ‘NAME-YOUR-OWN-PRICE’ CHANNEL MAKES SENSE FOR SERVICE PROVIDERS

(OR: WHO NEEDS PRICELINE, ANYWAY?)

Tuo Wang Assistant Professor of Marketing

532 Business Administration Building, P.O Box 5190, Kent State University, Kent, OH 44242-0001

Email: twang3@kent.edu; phone: 330-672-1258; fax: 330-672-5006

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 15260 E-mail: esther@katz.pitt.edu; phone: 412-648-1722, fax: 412-648-1693

Rabikar Chatterjee Professor of Business Administration,

340 Mervis Hall, Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260

E-mail: rabikar@katz.pitt.edu; phone: 412-648-1623, fax: 412-648-1693

Version dated May 10, 2005

Preliminary draft only – please do not quote.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.

WHY A ‘NAME-YOUR-OWN-PRICE’ CHANNEL MAKES SENSE FOR SERVICE PROVIDERS

(OR: WHO NEEDS PRICELINE, 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 posted-price 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, (2) 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.

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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 2000; Kannan and Kopalle 2001). 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 2000; Elkind 1999; Leiber 2002) and, more

recently, from a research perspective (Fay 2004a; Hann and Terwiesch 2003; Terwiesch, Savin,

and Hann 2005). 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

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traditional posted-price channels1. 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 2004a; Hann and

Terwiesch 2003; Terwiesch, Savin, and Hann 2005) 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 2002 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).

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• 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)?

1.2. 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.2 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

2 “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).

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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 2002; Canadian

Lodging Outlook 2002).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, 2001, 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 2004a; Hann and Terwiesch 2003). 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 32 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.

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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.

1.3. 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.

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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, (2) 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 §2, 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.

2. Related Literature

Previous research on the NYOP model has focused on two separate issues: (1) online

haggling (repeat bidding7) between an NYOP retailer and a set of consumers; and (2) the

rationality of consumers’ repeat bidding behavior at the NYOP channel. On the first issue, Hann

and Terwiesch (2003) 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 200 Euros. Terwiesch, Savin, and Hann (2005) 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.

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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 (2004a) 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 2004a; Hann and Terwiesch 2003;

Terwiesch, Savin, and Hann 2005) 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 (2003) 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.”

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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

(2005) 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 2003; 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 2000; Coughlan et al. 2001; Deleersnyder et al. 2002; Geyskens et al.

2002; Lal and Sarvary 1999; Zettelmeyer 2000).

Conceptually, our basic framework is more closely related to the theoretical literature on

product line decisions (e.g., Balachander and Srinivasan 1994; Desai 2001; 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.

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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 Lazier (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 (2004b) 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 (2004b)’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 (§3.2), 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).

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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

iv Reservation price of consumer i for one unit of the service [0,1]

1- d Extent of opacity [0,1] HP Posted price [0,1] LP Minimum acceptable price at NYOP channel [ LL PP , ]

iB Optimal bid submitted by consumer i. [0, HP ]

K Capacity of the service in units c Cost of capacity per unit [0,1) δ A random variable measuring the density of consumers who

participate in the posted price market [0,2]

y Signal of δ that is observed privately by the service provider

[0,2]

h Precision of y as a signal of the random variable δ [0,1]

µ Average density of the NYOP market [0,2]

v Threshold consumer who is indifferent between buying at posted price and bidding in the NYOP channel

v The lowest valuation consumer who participates in the NYOP channel

0 ≤ v ≤ v ≤ 1

3.1. 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 ~ [0,1]iv ,

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

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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 ]1,0[∈d and idv 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 1d = , 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):

• At the beginning of the first stage, the service provider chooses the price HP for the posted-

price 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

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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 2005). After observing the posted price,

consumers decide on whether to buy at the posted price or to bid at the NYOP channel10.

• 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 ( LP ) 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 iB .for consumer i) in the

second stage.

• During the second stage, the NYOP retailer receives the bids from the consumers, and

transacts with any consumer whose bid iB is higher than the minimum acceptable price LP .

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.

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Figure 1 Timeline of the Game

The service provider chooses the posted price

HP

Early consumers decide whether or not to buy, and if so, whether

to do it via the posted price

Buy via posted price

Not buy via posted price

Pay the posted price HP

Consumers bid with optimal bid B if interested in buying the

service

STAGE ONE: Posted Price Channel Only

STAGE TWO: Both Posted and NYOP Channels

The service provider sets the minimum acceptable

price LP

Signal of demand observed by service provider Late consumers decide whether or

not to buy, and if so, whether to do it via the posted price channel

Not buy via posted price

The NYOP retailer

Buy via posted price

Pay the posted price HP

LB P≥

Bid accepted, transaction occurs

Bid rejected, no transaction

LB P<

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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) v1 and v2 buy

tickets at the posted price, the volume of the posted-price market is δ (v2 – v1). We assume that

δ is uniformly distributed over the interval [0,2]∆ = , 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. Let ( )f yδ

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designate the conditional density function of δ given the realization of y ; then the above

assumptions imply that for some [0,1]h∈ , and y ∈ ∆ ,

if ( ) 1(1 ) if

2

h yf y

h y

δδ

δ

==

− ≠

(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 1h = , the service provider has perfect

information of the value of δ at the end of the first stage, and when 0h = , 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.)

3.2. 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 LP to

reflect the information he has about the state of demand in the posted-price market;

specifically, +→ RyP L ]2,0[:)( . 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 ],[ LL PP where )0(LL PP = and )2(LL PP = . In the sequel, we show

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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 iB to maximize her net expected payoff:12

max ( ) Pr{ ( )}i

Li i i iB

CS dv B B P y= − ≥ (2)

Given the conjecture that ( )LP y is uniformly distributed over the interval [ , ]L LP P , the

above maximization reduces to

max ( )i

Li

i i i L LB

B PCS dv BP P

−= −

−, (3)

yielding the solution,

*( )2

Li

i idv PB v +

= . (4)

Substituting this solution back into the objective function (3), yields the payoff the

consumer can expect when participating in the NYOP process. Specifically,

2( )( )4( )

LNYOP i

i L L

dv PCS vP P

−=

−. (5)

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 HP , 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. 12 Strictly speaking, the expression in (2) should include a term that captures the surplus consumers with vi > PH 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 2 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.)

- 17 -

( ) ( )posted Hi iCS v v P= − 13. Note that the degree of opacity has an adverse effect on the expected

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 ( )iR v as the added benefit derived by a consumer of type iv

when purchasing the product in the posted-price instead of the NYOP channel. Specifically,

2( )( ) ( ) ( ) ( )4( )

Lposted NYOP H i

i i i i L L

dv PR v CS v CS v v PP P

−= − = − −

− .

We assume that (.)R is a strictly increasing function of iv . 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 (0) 0R < and (1) 0R > , we are guaranteed that both

channels are active. We summarize these restrictions in Assumptions 1 and 2.

Assumption 1: ( ) 0R′ ⋅ > .

Assumption 2: (0) 0 and (1) 0R R< > .

The above assumptions imply that the population of consumers can be divided into three

segments as depicted in Figure 2.

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 2003)

- 18 -

Figure 2 Market Segmentation

Consumers whose valuation falls short of v withdraw from the market. Those in the

interval [ , ]v v place bids in the NYOP channel (in Stage 2), and those in the interval [ ,1]v

purchase the service in the posted price channel (in Stage 1 or 2). The threshold consumer v is

indifferent between buying the service in the posted price and the NYOP channel, implying that:

2( )4( )

LH

L L

dv Pv PP P

−− =

−. (6)

The threshold consumer v submits a bid that is just equal to the minimum acceptable

price imposed by the service provider. From (4), therefore,

( )2

LLdv P P y+

= .

Hence, the threshold consumer v satisfies the equation

2 ( )( )L LP y Pv y

d−

= . (7)

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

0 1 v v

Do not participate

NYOP market

Posted-price market

v

- 19 -

provider observes a higher realization of y. In the sequel, we demonstrate that ( )LP 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 )(yv derive a non-negative net

payoff from transacting with the NYOP retailer. It is easy to show that if ( )LP y is increasing,

this implicit assumption is, indeed, valid.

3.3. 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 HP is fixed14,

( )LP 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 ( )LP y in a manner that

guarantees full utilization of his capacity (as long as 0LP > .)15 Assuming that the average

14 Our analysis can be easily extended to allow for the possibility of adjustments in HP 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.

- 20 -

density of the NYOP market is [0, 2]µ ∈ 16, the service provider anticipates that the demand in

the NYOP channel amounts to ( )v vµ − . The value of the signal y indicates that the expected

demand facing the service provider in the posted-price channel is equal to (1 ) ( )v E yδ− . Hence,

the service provider chooses ( )LP y so that

( ) (1 ) ( )v v K v E yµ δ− = − − (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 ( )LP y as a function of v and K in

Lemma 1.

LEMMA 1 (OPTIMAL MINIMUM ACCEPTABLE PRICE IN THE NYOP CHANNEL): The optimal

minimum acceptable price submitted to the NYOP retailer at the beginning of second stage is

( ) (1 ) (1 ) (2 )( )2

L d v K d v d v h yP y µµ µ µ

− − − −= + − , 0 2y≤ ≤ . (9)

PROOF: See Appendix 1.

Note that the schedule of the minimum acceptable price is a strictly increasing function of

y (for 1v < and 0h > ). 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 .

- 21 -

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 ( )LP 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 values17 of v and K, this increased

steepness implies an overall reduction of prices since (2)LP 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 ( )LP 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 ( )LP 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 2) to obtain the limits of the uniform distribution of the price schedule, that

we designated earlier as LP and LP . Substituting those values back into (6) yields a relationship

among the variables HP , v and K as follows:

2[(1 )(1 ) ]4 (1 )

H d h v KP vv hµ

− − −= −

− . (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 HP 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 ( )LP y . However, its steepness is unambiguously greater as h increases.

- 22 -

earlier stages of the game. As a result, the provider’s maximization problem that yields the

optimal values of the decision variables K and HP can be formulated, instead, as a maximization

problem where K and v are chosen18. 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).

3.4. 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 HP ), and in the

latter case he chooses both v and K optimally (or alternatively HP and K). The objective

function of the service provider in either case is:

2 2

0 0

1 1(1 )(1 ) ( )[ (1 )(1 )]2 2

H LDual P v h hy dy P y K v h hy dy cKπ = − − + + − − − + −∫ ∫ . (11)

subject to: 0 1v< < ,

where HP is given in (10) and ( )LP 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 HP from (10) and the value of ( )LP y from (9) into (11), we obtain:

18 There is a one-to-one mapping from ( HP , K) to v and vice versa from ( v , K) to HP , according to (10)

- 23 -

2 22 2

( ) [(1 ) ( 1 )]

1 1 (1 )(1 )(2 ) (1 ) (1 ) [1 ]2 2 4 2 6 4

DualE v v d K v cK

d h h h h hK v K vh h h

π

µ

= − + − + − +

− −− − + − + − − − + +

. (12)

Case (a): Fixed Capacity

For a fixed capacity K, optimization of (12) with respect to v yields19:

22 3

2 3

2 1 32 (1 ) (1 2 ) ( 2 )3

24 (1 ) (1 2 )3

d h hh d h h h dK hv dh d h h h

µ µ

µ

+ −− + + − + − −

=− + + − +

(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. Large 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 HP , 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 .10 ≤≤ v

- 24 -

(i) When21 3

2h hh

µ + −> , 0v

K∂

>∂

, and 0.5v > .

(ii) When 21 3

2h hh

µ + −< , 0v

K∂

<∂

. In particular, if 32

µ < , 0vK

∂<

∂irrespective of the

value of h.

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, PH, and the expected value of the minimum acceptable price in the

NYOP channel, Ey(PL). The effect on the latter, KPE Ly ∂∂ )]([ , is unambiguously negative –

thus, as the available capacity increases, the expected value of the minimum acceptable price in

the NYOP channel decreases. Turning to the posted price, 0<∂∂ KPH 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 PH and Ey(PL) decrease as capacity increases. Part (ii)

of the proposition implies that PH decreases rapidly enough relative to Ey(PL) 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 2.

- 25 -

PROPOSITION 2: For a fixed value of K,

(i)

10 if 210 if 2

vvd v

> >∂ ∂ < <

(ii) 0vµ

∂>

∂, assuming (1 )K v> − .

(iii) vh

∂∂

> 0 if 12

v < ; otherwise, it has an ambiguous sign.

PROOF: See Appendix 1.

According to Proposition 2, 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 21<v , smaller values of d

and bigger values of h result in the shrinking of this population. In contrast, when 21>v , 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., 1K v> − ), larger values of µ result in a smaller

segment of consumers buying in the posted-price channel.

The results reported in Proposition 2 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. Larger values of d

indicate lower opacity experienced by consumers and therefore increased willingness to pay on

their part. Larger values of µ indicate that the density of consumers in the NYOP channel is

- 26 -

higher, thus making this channel more profitable to the provider. Finally, larger values of h

imply that the provider can make better pricing decisions in the NYOP channel, given the more

precise information available to him at the time when he determines the floor for acceptable bids.

We refer to this positive effect of changes in the parameters as the direct effect on the

profitability of the NYOP channel to the service provider.

However, changes in the parameters also give rise to an indirect effect that stems from

the cannibalization of the posted-price market. When the NYOP channel appears more

beneficial to consumers, the service provider ends up transferring sales from a channel where he

has full control over the revenues generated from consumers to one where he shares those

revenues with the NYOP retailer. Moreover, this transfer of sales also implies that consumers

have greater ability to determine the selling price via their bidding, and do not have to consider

the price as given anymore. Such increased flexibility on the part of consumers may also be to

the detriment of the service provider. We refer to this indirect effect on the provider’s profit as

the cannibalization effect.

According to Proposition 2, the direct effect of changes in µ more than offsets the

cannibalization effect, thus implying that bigger values of µ always result in the shrinking of the

population of consumers who buy directly from the provider. On the other hand, the direction of

the net effect of changes in d or h depends upon the overall size of the population of consumers

who participate in the posted-price channel as determined by the location of v .

Case (b): Capacity is Chosen Optimally by the Service Provider

When capacity (e.g., size of rental fleet, or number of hotel rooms or airline seats) can be

chosen optimally by the service provider, we must derive the additional first order condition with

- 27 -

respect to K from (12), ( ) 0DualEK

π∂=

∂. Note that the condition remains the same irrespective of

whether K and v (or alternatively HP ) are chosen sequentially or simultaneously. If K is chosen

sequentially prior to v , total differentiation of ( )DualE π with respect to K yields:

( ) ( ) ( )Dual Dual DualdE E E vdK K Kvπ π π∂ ∂ ∂

= +∂ ∂∂

.

However, the second term of the above derivative vanishes by the Envelope Theorem,

thus reducing the condition to the simple partial derivative mentioned above. Combining the

optimization with respect to K with the optimization we have obtained already with respect to v

yields the following optimal solution for K and v , when capacity can be optimally chosen by the

service provider:

2 22 2

*

2

*

6 [2 (1 3 )]6(1 3 2 ) (12 6 4 ) 21 4 .(8 5 ) (1 4 )12(1 4 ) [12(1 ) ]

(8 5 )6(1 4 ) [6(1 ) ] 6 [2 (1 3 )].(8 5 )12(1 4 ) [12(1 ) ]

c h h hh h h dh h h chK h h d hh dh h

h hh dh h c h h hv h hh dh h

µµ µ µ

µµ

µµ

µµ

− − +− + + − + − −

+= −+ ++ − + + −

++ − + − − − − +

=+

+ − + + −

(14)

The expressions in (14) imply that the optimal level of investment in capacity falls short

of one unit (i.e., K < 1), given our assumption that 2µ < . Moreover, if c is sufficiently small,

*0.5v > . Note also that the optimal investment in capacity is a decreasing function of the unit

cost of capacity c. In contrast, the size of the population that participates in the posted price

channel may or may not decline when c increases. We state this result in Proposition 3.

PROPOSITION 3: When K can be optimally selected by the service provider,

- 28 -

*

0Kc

∂<

∂,

2

*

2

1 3 -0 if 2

1 3 -0 if 2

h hv hc h h

h

µ

µ

+< >∂

∂ + > <

.

The proof follows by inspection of the expressions obtained in (14).

The result reported in Proposition 3 is related to the one derived in Proposition 1, where

K is assumed to be exogenously determined. When µ and h are relatively large, Proposition 1

establishes that increased capacity favors the NYOP channel over the posted-price channel.

Since bigger values of c reduce the level of capacity selected at equilibrium, it is the NYOP

channel that is adversely affected, in terms of its size, and not the posted-price channel. Hence,

*v declines when c increases. The argument is reversed when µ and h are relatively small,

because changes in the level of capacity primarily affect the larger, in this case, posted-price

market.

In Proposition 4 we report on the comparative statics with respect to the remaining

parameters of the model.

PROPOSITION 4: When K can be optimally selected by the service provider,

(i) *

0vd

∂>

∂. Changes in the parameters h and µ may have an ambiguous effect on the

value of the threshold consumer *

v . However, when c is sufficiently small, *

0vh

∂>

∂

and *

0vµ

∂>

∂.

(ii) **

*

0 if is relatively small0 if is relatively large

KKd K

<∂∂ >

* 0 if is relatively small0 if is relatively large

hKhh

>∂ <∂

- 29 -

*

0 if is sufficiently small.K cµ

∂>

∂

PROOF: See Appendix 2.

According to part (i) of Proposition 4, reduced opacity of the NYOP channel results in

fewer customers purchasing the service directly from the provider. Moreover, when the unit cost

of capacity is sufficiently small, the size of the posted price channel shrinks as the relative

density of the NYOP market increases (bigger µ ), or as the demand signal is more precise

(bigger h, improving the quality of information available to the service provider). It follows,

therefore, that the direct effect of changes in those parameters more than offsets the indirect

cannibalization effect discussed earlier. According to part (ii) of the proposition, changes in the

parameters have ambiguous implications on the level of investment in capacity. For instance,

while improved information may lead to higher investment when h is relatively small, it results

in reduced investment if h is relatively large.

Upon substitution of the optimal levels of *K and *

v into the objective function of the

service provider (12), we obtain the following expected profits that accrue to the service provider

if he chooses to operate both channels:

2* *3 12 6 (6 3 2 )( ) (8 5 )12(4 1) [12(1 ) ]

dualh dh dh d dhE cKh hh dh h

πµ

µ

+ − − − −= −

++ − + + −

, (15)

where *K is given by (14).

Those expected profits should be higher than those the provider expects by utilizing only

the posted price channel. If the provider offered his service only through the posted price

- 30 -

channel, his investment would amount to (1 )2

c− and his expected profits would be 2(1 )

4c− . A

comparison with (15) yields the result reported in Proposition 5.

PROPOSITION 5: The service provider will find it profitable to operate both channels of

distribution:

(1) If the degree of opacity of the NYOP channel is not too high, specifically, if ˆd d> ,

where d)

( ˆ0 1d< < ) is defined in (B.3) in Appendix 2.

(2) If the expected density of the NYOP channel is sufficiently high, and, in particular, larger

than the expected density of the posted price market. Specifically, ˆµ µ> where ˆ 1µ >

and defined in (B.4) in Appendix 2.20

PROOF: See Appendix 2.

The result stated in Proposition 5 is related, once again, to the cannibalization effect

discussed earlier. Selling through the NYOP channel implies transferring sales to a channel

where the service provider cedes some control to consumers as well as the intermediary who acts

as the NYOP retailer. This transfer of control is profitable only if this market is sufficiently

dense relative to the posted price channel (i.e., ˆ 1µ µ> > ), and if the willingness to pay of

consumers is not significantly reduced due to the opacity of the NYOP channel (i.e., ˆd d> .)

However, as the next proposition shows, the existence of some positive level of opacity is crucial

in order to sustain an equilibrium, where self selection by consumers between the two channels

yields the segments described in Figure 2 (Assumptions 1 and 2).

20 What this condition implies is that the NYOP channel has the capability to generate denser traffic than the posted price channel, possibly on account of network externalities. This condition would also obtain if the distribution of potential consumers (over reservation prices) was sufficiently skewed to be denser for lower reservation prices. For example, the business travel market (high reservation prices) might be thinner than the leisure travel market. (One can think of a family having one potential customer in the business travel market but the entire family in the leisure travel market – with a lower reservation price, at a different point in time.)

- 31 -

PROPOSITION 6: To guarantee that self selection by consumers yields the co-existence of both the

posted price and the NYOP channels, it is necessary that * 1 d d< < , where ∗d is given by (B.5)

in Appendix 2.

PROOF: See Appendix 2.

Figure 3 The Feasible Region of Opacity Levels Consistent with Dual Channel Distribution

In Figure 3, we describe the feasible range of d values that is consistent with the

existence of the dual channel distribution. Combining Propositions 5 and 6, this feasible range

becomes $ *d d d< < . The lower bound $d is necessary to guarantee the profitability of the dual

channel to the provider, and the upper bound *d is necessary to guarantee appropriate self

selection by consumers. In Appendix 2, we derive various values of the parameters µ and h that

yield a feasible range of values for the parameter d, satisfying the two conditions necessary to

sustain the dual channel when 0c = . For instance, when 1.5µ = and 0.4h = , * 0.35d = and

0

2(1 )4c−

d

Dualπ

Dual Channel

Zone

Self Selection Constraint for

Consumers

Profit Constraint for

Service Provider

- 32 -

$ 0.24d = , implying that any opacity parameter [0.24,0.35]d ∈ sustains the equilibrium with the

dual channel.

The upper bound of the feasible values of d is implied by the fact that consumers have

greater flexibility with regard to the price they pay in the NYOP channel in comparison to the

“take it or leave it” posted price they face when buying directly from the service provider.

Hence, unless there is some positive level of opacity imposed on them in the NYOP channel all

consumers would opt to obtain the service from the NYOP retailer. In order to induce higher-

valuation consumers to choose the posted-price channel, it is thus essential that a minimum level

of opacity be imposed on the NYOP channel (i.e. *d d< .) This result is consistent with the

casual observation that services featured on Priceline are made deliberately “opaque” by

withholding key information from consumers. Moreover, when Priceline deviated from it

original business practice in 2002, by selling tickets through eBay, with the site revealing

complete flight information, Northwest Airlines decided to stop its relationship with Priceline

(CNET News). The action by Northwest reflected its intent to better control the extent of

cannibalization of its posted price market.

Next, it is interesting to evaluate how the extent of informativeness of the signal observed

by the provider affects the provider’s expected profit. In Proposition 7, we summarize this

evaluation.

PROPOSITION 7:

* ˆ0 for

ˆ0 for ,Dual h hdE

dh h hπ > ≤

< >

where ˆ0 1h< < .

- 33 -

According to Proposition 7, the expected profit for the provider is not a monotone

function of the precision of the signal y. In fact, there exists an intermediate level of (0,1)h∈

that maximizes the profits of the provider. This result relates, once again, to the two

counteracting effects on the profitability of the NYOP channel. Larger values of h make this

channel more attractive, since pricing can be better aligned with the state of the demand when

the provider has a more precise signal of this state. However, larger values of h also imply the

transfer of sales from the posted price channel, where the provider has full control over pricing

and revenues, to another channel where control is shared with the NYOP retailer and consumers.

In our model, the precision of the signal is treated as a parameter. However, in reality,

the service provider has some control over the quality of the signal he observes at the time he

contracts with the NYOP retailer. If the provider chooses to wait longer before contracting with

the retailer he has more data on the extent of booking in the posted price channel, and as a result,

improved information about the uncertain state of the demand in this market. The results

reported in Proposition 7 imply that the provider may not necessarily want to wait too long

before committing to an agreement (specifying the minimum acceptable price) with the NYOP

retailer. In fact, there is an intermediate optimal time, prior to the date the service is actually

delivered, at which the service provider would want to set the terms of the agreement with the

NYOP retailer. This optimal time yields the intermediate precision level h described in the

proposition.

3.5. Expected Profit of the NYOP Retailer and Consumer Welfare

The expected profit of the retailer is calculated as the expected difference between the

bids of the consumers and the floor on acceptable bids that is dictated by the service provider.

Specifically,

- 34 -

2 2* ** * 2 2

0

1( ) [ ( ) ( )] [( (1 )] (1 )2 4 3

vL

NYOP iv

d hE B v P y dvdy K v vπ µµ

= − = − − + −

∫ ∫ .

(16)

The numerical simulations in Appendix 3 indicate that this payoff is increasing with d, h,

and µ . Hence, the NYOP retailer has incentives to reduce the extent of opacity confronting

consumers who decide to place bids. Moreover, the retailer benefits if the service provider has

greater incentives to transfer sales to the NYOP channel, which happens when the signal

observed by the provider is more informative (larger h) or when the relative size of this channel

increases (larger µ ).

The expected consumer surplus can also be calculated as follows:

1 2*

0

*2 2 * * 2

1( ) ( ) [ ( )]2

(3 2 )(1 ) (1 )[(1 )(1 ) ] .6 4

vH

dualvv

E CS v P dv dv B v dvdy

dh v hd h v Kh

µ

µµ µ

= − + −

− − += + − − −

∫ ∫ ∫ (17)

Surprisingly, the numerical simulations in Appendix 3 indicate that the expected surplus

of the consumer declines when the service provider has access to more precise information at the

time it transacts with the NYOP retailer. Moreover, reduced opacity does not necessarily

increase the welfare of consumers. For relatively small values of d in the feasible region

[ $ *,d d ], the expected consumer surplus may decline when d increases. A similar anomaly arises

also with respect to the size parameter µ . The reason why changes in the parameters may have

counterintuitive implications on the expected welfare of consumers is that those parameters

affect prices both in the NYOP and the posted-price channels. For instance, when the parameter

d increases, consumers who place bids in the NYOP channel are better off, but consumers who

- 35 -

buy the service directly from the provider face higher posted prices. A similar explanation

relates also to changes in the parameters h and µ .

4. Conclusions

4.1. Managerial Implications

Service providers now have a wider choice of channels to distribute their products with

the help of the Internet, among other technical innovations. One of the most salient innovations

is a pricing channel that generates demand from consumers via the NYOP process. While the

NYOP channel allows the service provider to adjust the price (after learning more about the

demand) to reach lower-valuation customers who otherwise are unlikely to buy at the posted

price, contracting with an NYOP retailer not only cannibalizes some of the high valued

customers from posted-price channel, but also allows this unconventional intermediary to share

their profits in the form of informational rents, derived from the NYOP retailer’s knowledge of

the individual bids – information not shared with the service provider or the population of

customers. Since the NYOP retailer has an asymmetric information advantage over both buyers

and sellers in this regard, the contribution of an additional NYOP channel to the overall profit of

the service provider depends on:

• how much differentiation there is between the product offered in the posted price channel and

the NYOP channel (in the form of “opacity”);

• how dense the potential demand in the NYOP market is likely to be; and

• how precise the signal from the posted price market is before the service provider contracts

with the NYOP retailer.

All three factors play different roles, and their respective effects on the service provider’s

profit are analyzed in §3.2. The service industry needs to find a fine balance between market

expansion and potential cannibalization. We find that incomplete product information

- 36 -

(“opacity”) at the NYOP channel – resulting is consumer uncertainty at the time of bidding – is

critical for the existence of the NYOP channel. In particular, we show that the participation of

both consumers and the service provider in the NYOP process depends on the consumer

uncertainty level associated with the “opacity” of the product featured on the NYOP channel.

We further find that both the density of the NYOP market and the quality of the demand signal

from the posted-price market in the first stage contribute to the conditions supporting the

existence of the dual pricing channel in the service industry.

The results of these analyses offer guidance on how a service provider can best manage

the NYOP channel with optimal pricing strategies, and on how a service provider can limit the

cannibalization by imposing a minimum level of consumer uncertainty (via product “opacity”) at

the NYOP channel. More specifically, there is a range of the opacity levels for which it is

profitable for the service provider to add the NYOP channel to the existing posted-price channel.

If the degree of opacity is too low, all (or at least too many) consumers will submit bids at the

NYOP channel. On the other hand, if the degree of opacity is too high, the consumers’

willingness to pay on the NYOP channel is reduced too much to make it profitable. In the range

of opacity in which it is profitable for the service provider to use an NYOP retailer, the service

provider’s profit increases as the degree of opacity decreases. Therefore, it is in the service

provider’s interest to make sure some opacity is present (to meet the consumer self-selection

constraint), but not too much, because that will reduce profits. The results of this Bayesian Nash

Equilibrium model are consistent with our observations of the marketplace.

An important contribution of this paper is that it enables us to evaluate the NYOP

channel from both the consumers’ and the service provider’s perspectives. Previous studies

attribute the existence of NYOP channel to consumers’ haggling cost of repeat bidding

(Terwiesch, Hann and Savin 2005). Our analysis adds new insights to the NYOP process as it

- 37 -

examines optimal strategies for both the service provider and the consumers, and provides an

alternate rationale for the existence of the NYOP channel without haggling cost, based on four

critical factors: (1) the presence of demand uncertainty, (2) 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. While channels selling

opaque products at a discount need not necessarily follow the NYOP model (e.g., Hotwire), the

appeal of the NYOP model is its greater pricing flexibility relative to posted-price options.

4.2. Limitations and Directions for Future Research

This paper represents a first step in studying the NYOP channel employing a game-

theoretic framework to derive a Bayesian Nash equilibrium. In this initial endeavor, we have

limited ourselves to focusing on the buyer-seller interaction assuming a monopolistic service

provider. It would be interesting to determine whether the primary results of the paper extend to

the case of competition. We can also accommodate competition between different types of

channel members – for example, considering one non-opaque channel (Expedia.com) and two

opaque channels (Priceline and. Hotwire) with different pricing mechanism (NYOP vs. posted-

price). The inclusion of Hotwire in the game will have an impact on both the traditional posted-

price channel and the NYOP channel, but to different degrees.

Finally, we assume a constant discount parameter associated with the degree of opacity of

the product across all consumers. In reality, this quality discount parameter d is likely to be

higher for low valued consumers and lower for high valued consumers (high-valuation

consumers are likely to be more sensitive to product opacity than low-valuation consumers).

- 38 -

Appendix 1 – Fixed Capacity

PROOF OF LEMMA 1:

Since the unconditional expected value of δ is 1 (i.e. E(δ) = 1), our specification of the conditional density function ( )f yδ implies that:

( ) (1 )1E y hy hδ = + − . (A1) Substituting (A1) back into (8) yields

( ) (1 )( 1 )v v K v hy hµ − = − − + − (A2) Plugging the value of v from (7) into (A2) and solving the equation yields

( ) (1 )(1 ) (1 )( )2 2 2 2

LL d v K d v h P d v hyP y µ

µ µ µ− − − −

= + + + . (A3)

From (A3) we can derive the lower and upper bound of the minimum acceptable price schedule as follows:

( ) (1 )(1 )(0)L L d v K d v hP P µµ µ

− − −= = + . (A4)

( ) (1 )(1 ) (1 )(2)L L d v K d v h d v hP P µµ µ µ

− − − −= = + + . (A5)

Therefore, by substituting the value of LP into (A3), we obtain the schedule of the minimum acceptable price as a function of the signal y that is observed by the service provider at the end of the first stage:

( ) (1 ) (1 ) (2 )( )2

L d v K d v d v h yP y µµ µ µ

− − − −= + − .

PROOF OF PROPOSITION 1:

(i) sgn vK

∂ ∂

= 21 3sgn 2 h hh

µ + −

−

Under the condition of this part the RHS is positive. As well, under the same condition 2 3

2 3

22 (1 ) (1 2 )13

2 24 (1 ) (1 2 )3

dh d h h hv dh d h h h

µ

µ

− + + − +> >

− + + − +.

(ii) Under the condition of this part, 0vK

∂<

∂. Moreover,

21 32h hh

+ − achieves its minimum

value when h = 1. Hence, if 32

µ < then 21 3

2h hh

µ + −< for all other values of h, thus implying

that 0vK

∂<

∂.

- 39 -

PROOF OF PROPOSITION 2:

(i) Differentiating (13) with respect to d yields: 2 3 2 2 3

2 3 2 3

1 2 1 1 22 (1 2 ) [ (3 1) 2 ] [ 4 (1 2 )]3 3

2 24 (1 ) (1 2 ) 4 (1 ) (1 2 )3 3

h h h h K h h h v h h h hv

d dd h d h h h h d h h h

µ µ µ

µ µ

− + + − + − − + − − + + − +∂

= −∂ − + + − + − + + − +

.

Rearranging terms yields,

2 3

2 (2 1)2[4 (1 ) (1 2 )]3

v h vdd d h d h h hµ

∂ −=

∂ − + + − +.

The result follows immediately from the above.

(ii) 2 2 3

2 2 3

2[(3 1) (1 2 )(1 )]3 02[4 (1 ) (1 2 )]

3

d h h K h h h vvdh d h h hµ µµ

− + − + − + −∂= >

∂ − + + − +.

The last inequality follows since 2 2 321 3 1 23

h h h h h+ − > + − + and 1K v> − to guarantee that

there is sufficient capacity to serve both the posted price and the NYOP channels.

(iii)

2

2 3

12(1 )(1 2 ) (2 2 2 )(1 ) (2 (3 2 ))

2[4 (1 ) (1 2 )]3

dd v h h v dK hv

dh h d h h h

µ µ

µ

− − + − + − + − −∂

=∂ − + + − +

.

Substituting for K in terms of v from (13) and rearranging terms, yields that: 2 3 2 3 4 2

2 2

4 1 2 1[2(1 ) (1 4 )](1 ) 2(1 2 )(1 ) (1 )3 3sgn sgn .1 1(3 1) 2 (3 1) 2

dh h h h h v v d hvh h h h h h h

µ µ µ

µ µ

+ − − − − + − − − + ∂ = + ∂ − + − − + −

The sign of the RHS is ambiguous. However, when 12

v < , we know from Proposition 1 that

21 (1 3 ) 2 0h h hµ

+ − − > , implying that the above derivative is positive.

Appendix 2 – Capacity Optimally Chosen

PROOF OF PROPOSITION 4:

(i) Differentiating *

v with respect to d yields: * *

*(8 5 )[12 6(1 )(2 1) (1 )]

,

hh v vvd

µµµ+

+ + − + −∂

=∂ ∆

- 40 -

where (8 5 )[12(1 4 ) (12(1 ) )]h hh dh h µµ+

∆ ≡ + − + + − .

Since*

0.5v > , the numerator of *

vd

∂∂

is positive as claimed.

Differentiating with respect to h and µ yields:

{ }* 2 2 3 4

2

6 4 [3 (3 4) 5 ] 16 (47 8 16 ) 10(4 ) 5

6 [2 2 3] . (B.1)

d dh h h d d h d h dhvh

c h

µ µ µ µ

µµ

+ − − + + − − + − −∂=

∂ ∆+ −

−∆

2* ** 2

(8 5 )12 (1 )12

dh hdhv vv chµµ

+− −

∂= −

∂ ∆ ∆. (B.2)

While the sign of the RHS of (B.1) and (B.2) cannot be determined in general, when c approaches zero it is positive under our assumption that 2µ < .

(ii)

* * * 2*

2

(8 5 )12 (1 ) [12(1 ) 6 4 ]2(1 4 )

h hh K K h K hK h cd d h

µµ µ

+− − − + + − +

∂ = +∂ ∆ +

.

The numerator of the first term of the above derivative is a strictly increasing function of *K . It is positive for *K values close to one and negative for values close to ½. Hence, there exists a certain threshold value of *K above which the derivative is positive and below which it is negative. The following table illustrates the results. For relatively large values of µ (yielding

large value of *K ) *

0Kd

∂>

∂, and for relatively small values of µ (yielding small value of *K )

*

0Kd

∂<

∂.

0c = *K

d∂∂

1µ = 2 3 4

2 3 2

6 (12 20 3 5 ) 0[12 24(2 ) 4 5 ]

h h h h hd h dh dh

− + + − −<

+ − − +

1.5µ = 2 3 4

2 3 2

9 (27 8 22 8 5 ) 0[12 24(2 ) 4 5 ]

h h h h hd h dh dh

− + − − −<

+ − − +

2µ = 2 3 4

2 3 2

12 (40 51 13 5 48) 0[24 (96 72 ) 16 5 ]

h h h h hd h dh dh

+ + + −>

+ − − + for 0.62h >

- 41 -

**

2

8 1012 (1 ) 18 6 12 (1 ) [48 (12(1 2 ) ]2

(1 4 )

hd d h dh d h KK ch d h

µ µµµ

+− + − − − − − + + +

∂= −

∂ ∆ +

For relatively small value of c in the neighborhood of zero, the expression indicates that the derivative is positive for relatively small values of h (close to ½) and negative for larger values of h. Numerical calculation illustrates this result in the following figure. For 1.5µ = , c = 0.

* 2 2 2

2

12 12 (8 5 ) 24 [2 (1 3 )] 2[12 ](1 4 ) (1 4 )

K dh K dh h K ch h h h hcdhh d h

µ µµ µ

∂ − + − − += + + − −

∂ ∆ ∆ ∆ + ∆ +.

Evaluating the above at 0c = yields the result. PROOF OF PROPOSITION 5:

Calculating the difference between *DualEπ from (15) and

2(1 )4c− yields:

* * *[4 (3 2 ) 12 (1 ) (8 5 )] 1( ) ( ) [ (1 )]4 2 2Dual Posted

dh dh h h h h cE E c Kµ µ µπ πµ

+ − − + − +− = − − −

∆.

To guarantee that the dual channel yields higher profits, it follows, therefore, that: *

2

1( (1 ))12 (1 ) (8 5 ) 2 2 ˆ4 (3 2 ) (3 2 )

cc Kh h hd dh h dh h

µ µµ

− − ∆− + + +> + ≡

+ +. (B.3)

Note that the second term of (B.3) is positive since * 12

K > and 1c < . As well when 1µ = , the

first term of (B.3) is bigger than 1, implying that there are no feasible values of the parameter d that can satisfy (B.3). Hence, the density of the NYOP market should be sufficiently bigger than the posted price market. Specifically,

2 2 2 2(12 8 ) (12 8 ) 48(8 5 ) ˆ24

h h h hµ µ

− + − + +> = . (B.4)

0.2 0.4 0.6 0.8 1

0.59

0.61

0.62

h

*Kd = 0.1

0.2 0.4 0.6 0.8

0.585

0.59

0.595

d = 0.5

*K

h

- 42 -

PROOF OF PROPOSITION 6:

To guarantee that consumers self select into the different segments described in Figure 2, Assumptions 1 and 2 should be valid. The requirement that (0) 0R < is always satisfied

since2

(0) ( ) 04( )

LH

L L

PR PP P

= − + <−

. The requirement that (1) 0R > , yields that ** 1 d d< < .

For c = 0, 2 2 3 2 2 2 2 2 2

**2 2

6 (2 5) 3 (1 8 8 ) 9(4 8 8 10 ) 48 (1 4 )(2 15 3 6 ).

2 (2 15 3 6 )h h h h h h h h h h h h

dh h h

µ µ µ µ µ µ µµ µ µ

+ + + + + + + + + − + + + +=

+ + +

The requirement that '( ) 0R ⋅ > , yields that * 1 d d< < . For c = 0, 2 2 3 2 2 2 2 2 2

*2 2

3 (2 5) 3 (1 6 4 ) 9(2 6 10 ) 24 (1 4 )( 9 3 6 ).

2 ( 9 3 6 )h h h h h h h h h h h h

dh h h

µ µ µ µ µ µ µµ µ µ

+ + + + + + + + + − + + + +=

+ + +

(B.5)

The calculation in the table below indicates that * **d d< , implying that the constraint '( ) 0R ⋅ > is more demanding. Moreover, if this constraint is satisfied (i.e. *d d< ,) we are also guaranteed that

( ) HB v P< , 0HP > and 1v < , as illustrated by the calculations in the last three columns of the table. Hence, the bids submitted in the NYOP channel are always lower than the posted price. To summarize, to guarantee self selection of consumers *d d< .

c = 0

*d **d Max d ( ( ) HB v P< )

Max d ( 0HP > )

Max d ( 1v < )

h = 0.1 0.17 0.30 1.00 3.82 4.52

h = 0.5 0.58 0.76 1.01 1.57 1.71

1µ =

h = 1 0.76 0.84 0.95 1.18 1.25

h = 0.1 0.11 0.20 0.96 2.80 3.41

h = 0.5 0.41 0.56 0.90 1.21 1.33

1.5µ =

h = 1 0.58 0.66 0.82 0.94 1.00

h = 0.1 0.08 0.15 0.92 2.21 2.74

h = 0.5 0.32 0.44 0.80 0.98 1.09

2µ =

h = 1 0.47 0.54 0.72 0.78 0.83

When 0c = , the following table illustrates the existence of a feasible range of values for d that satisfy the requirements of both Propositions 5 and 6 (i.e. *d d< ). For instance, when 1.5µ = and 0.47h < , we are guaranteed that there are values of d such that the service provider prefers the dual channel over a single channel, and consumers self select between the two channels according to Figure 2. In particular, when 0.4h = , in this case, ˆ 0.24d = and * 0.35d = .

- 43 -

Max h with feasible range of d ( d < *d when h < h )

h d *d

1.2µ = 0.14h = 0.13 0.06 0.18

1.3µ = 0.23h = 0.20 0.07 0.24

1.4µ = 0.34h = 0.30 0.19 0.31

1.5µ = 0.47h = 0.40 0.24 0.35

1.6µ = 0.64h = 0.50 0.26 0.39

1.7µ = 0.85h = 0.60 0.27 0.41

1.8µ = 1h = 0.60 0.13 0.39

1.9µ = 1h = 0.70 0.15 0.41

2µ = 1h = 0.70 0.03 0.39

PROOF OF PROPOSITION 7:

To evaluate the effect of changes in the parameter h on the expected profits of the service provider, derive the total derivative of (12) with respect to h. Note that by the envelope theorem, this total derivative coincides with the partial derivative

** *2*

2 2 2

**2 2** 22

( ) 1 1 (1 ) 1(1 )( ) (1 )4 4 3 4 2

1 1 (1 ) [ (1 )] (1 ) [ ]4 4 3

DualE h K K vvh h h h

K h vK vh

π∂ −= − + − + − +

∂

−= − − + − +

The calculations in the figure below indicate that the above expression is positive for small values of h and negative for large values of h. Hence, *( )DualE π is single peaked as asserted in the proposition.

0.2 0.4 0.6 0.8 1

0.252

0.254

0.256

0.258

0.26

0.262

2µ = 0.4d =

h0.1 0.2 0.3 0.40.2498

0.2502

0.2504

0.2506

1.5µ = 0.1d =

h

- 44 -

Appendix 3 – Expected Payoffs of the NYOP Retailer and Consumers NYOP Retailer’s Profit as a function of h ( 1.5µ = )

NYOP Retailer’s Profit as a function of d ( 1.5µ = )

NYOP Retailer’s Profit as a function of µ (h = 0.5)

0.2 0.4 0.6 0.8 1

0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014

d = 0.1

0.2 0.4 0.6 0.8 1

0.002

0.004

0.006

0.008d = 0.5

h

0.2 0.4 0.6 0.8 1

0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014

h = 0.1

0.2 0.4 0.6 0.8 1

0.00020.00040.00060.00080.0010.00120.0014

h = 0.5

d

1.2 1.4 1.6 1.8 2

0.004

0.005

0.006

0.007

d = 0.5

1.2 1.4 1.6 1.8 20.00055

0.00065 0.0007 0.00075 0.0008 0.00085

d = 0.1

d

h

µ µ

- 45 -

Consumer Surplus from Dual Channels as a function of h ( 1.5µ = )

Consumer Surplus from Dual Channels as a function of d

Consumer Surplus from Dual Channels as a function of µ

1.2 1.4 1.6 1.80.1238

0.1242

0.1244

0.1246

0.3h = 0.2d = 0.1240

µ1.2 1.4 1.6 1.8 2

0.1010.1020.1030.1040.1050.106

1h = 0.4d =

0.2 0.4 0.6 0.8 1

0.122

0.123

0.124

0.125

d = 0.1

0.2 0.4 0.6 0.8 10.1075

0.11250.1150.11750.12

0.12250.125

d = 0.5

h

0.2 0.4 0.6 0.8 1

0.1150.120.1250.130.1350.14

2µ = 1h =

Feasible d (0.33 < d < 0.47)

d0.2 0.4 0.6 0.8 1

0.121

0.122

0.123

0.124

0.125

1.5µ = 0.3h =

Feasible d (0.02 < d < 0.3)

µ

d

h

- 46 -

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