MANAGEMENT SCIENCE Informs ® Vol

Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis

Wilfred Amaldoss Fuqua School of Business, Duke University, Durham, North Carolina 27708, [email protected] Sanjay Jain Mays Business School, Texas A&M University, College Station, Texas 77843, [email protected]

n this paper, we study the name-your-own-price (NYOP) channel. We examine theoretically and empirically Iwhether asking consumers to place a joint bid for multiple items, rather than bid one item at a time as practiced today, can increase NYOP retailers’ profits. Relatedly, we also examine whether allowing consumers to self-select whether to place a joint bid or itemwise bids increases retailers’ profits and consumers’ surplus. We construct a dynamic model that incorporates both demand uncertainty and supply uncertainty to address these issues. Our theoretical analysis identifies the conditions under which joint bidding can increase both NYOP retailers’ profits and consumers’ surplus. We find that some consumers might bid more for the very same items when they place joint bids. The increase in bid amount is related to the fact that joint bidding reduces the chance of mismatch between NYOP retailers’ costs and consumer bids. We conducted a laboratory study to assess the descriptive validity of some of the model predictions, because there are no field data on joint bidding in the NYOP channel. The results of the study are directionally consistent with our theory. Key words: pricing; bidding; Internet; experimental economics History: Accepted by David E. Bell, decision analysis; received July 9, 2007. This paper was with the authors 1 month for 1 revision. Published online in Articles in Advance August 20, 2008.

1. Introduction The NYOP model is still evolving, and there is With the advent of the Internet, retailers have adopted no consensus on how best to structure the pricing several innovative pricing mechanisms. One such mechanism. For example, prominent NYOP retail- method is the name-your-own-price (NYOP) mecha- ers like Priceline and Expedia’s Price Matcher allow nism pioneered by Priceline. In this pricing method, consumers only to place a single bid for a given the NYOP retailer lists a set of perishable goods item. A German NYOP retailer, however, allows con- available for sale but does not post prices. These sumers to bid repeatedly for the very same item (see goods are also opaque in the sense that some impor- Hann and Terwiesch 2003). A recent theoretical anal- to this article and distributed this copy as a courtesy to the author(s). tant product information (e.g., flight time, number ysis shows that if it is prohibitively costly to prevent of stops, and identity of the service provider) is not surreptitious repeat bidding then the NYOP retailer revealed to consumers at the time of bidding. The might benefit by encouraging repeat bidding (Fay consumers, who arrive asynchronously to the mar- 2004). copyright ket, evaluate the opaque products and then place bids In practice, NYOP retailers often sell more than for them. The bid is visible to the NYOP retailer but one category of products. For example, Priceline and holds not to the service providers such as airlines or hotels. Expedia’s Price Matcher sell airline tickets, hotel The service providers frequently change the prices of rooms, and car rentals. This observation raises an goods according to their yield management policy, interesting question. In theory, would it be prof- but the price changes are not revealed to consumers. itable for NYOP retailers to ask consumers to place The spread between a consumer’s bid and the pre- INFORMS Additional information, including rights and permission policies, is available at http://journals.informs.org/. a joint bid for multiple items rather than bid sepa- vailing lowest price is retained by the NYOP retailer rately for each item? It seems that joint bidding might (Kannan and Kopalle 2001). The sales revenue of encourage consumers to place lower joint bids than Priceline, which is the leading NYOP retailer in the they would have if they were bidding individually United States, was more than $2 billion in 2005, and for each item. Therefore, a NYOP retailer’s profits it is expected to cross $4 billion in 2007, implying that could potentially decline if it allowed joint bidding. the NYOP mechanism is a viable business model.1 Intuitively, joint bidding might encourage consumers to bid less than what they would bid under item- 1 Priceline has also extended its business to international markets such as the United Kingdom, Hong Kong, and Taiwan (source: wise bidding. Indeed, consumers usually expect a priceline.com). discount when buying multiple items in a bundle

(Estelami 1999).2 However, one needs to recognize impact of joint bidding. In contrast to conventional that a consumer’s willingness to pay for some of the wisdom, the frictional costs involved in placing repeat individual items is sometimes inconsistent with the bids in a NYOP channel are substantial (Hann and seller’s corresponding reservation price. A joint bid Terwiesch 2003). The joint bidding option considered is more flexible in that it is more likely to cover the in our model will help to reduce frictional costs faced sum of the seller’s reservation prices. Furthermore, by consumers. Frictional costs, however, are not nec- the improved chances of getting both of the items essary to obtain our theoretical results. could increase a bidder’s willingness to place a higher As noted earlier, the goods sold through NYOP joint bid. This raises the possibility that joint bid- channels are opaque. For example, a consumer bidding could improve both consumer surplus and the ding for an air ticket may not know exact flight retailer’s profits. times, number of stops, or even the name of the airline. Because of the resulting uncertainty about prod- 1.1. Overview uct features, goods sold through NYOP retailers are The focus of this paper is to examine how NYOP ex ante very different from the goods that can be pur- retailers can augment the basic bidding mechanism chased from posted price markets such as the service to increase their profits. In particular, we examine provider’s direct channel and traditional retail outlets. the theoretical and managerial implications of three Consequently, the NYOP channel tends to attract low- different types of bidding strategies: itemwise bidding, valuation consumers. However, at the time of con- where consumers place a separate bid for each item; sumption (ex post) the products are similar. Thus, the joint bidding, in which consumers place a joint bid opacity of the goods may help the service provider to for several items; and mixed bidding, where consumers liquidate excess supply by attracting a different seg- can place itemwise or joint bids. Our theoretical anal- ment of consumers through the NYOP channel (Fay ysis suggests that often joint bidding, rather than and Xie 2008, Wang et al. 2005). Fay (2007) examined itemwise bidding, is more profitable for a NYOP the role of competition among firms selling opaque retailer. This is because, when consumers are asked goods. If firms are competing to sell opaque products to place joint bids, some consumers bid more for the with little brand loyalty, then opaque goods increase very same items. Thus, joint bidding can be more price competition and dampen firm profits. However, profitable than itemwise bidding even when we do if there is significant brand loyalty, opaque goods help not take into account the convenience of placing a soften competition and improve a firm’s profits (Fay single bid. Yet this increase in profits is not necessar- 2007). Our focus is on how to further improve the ily at the expense of the consumer—in fact, consumer profitability of the NYOP channel by allowing con- surplus can also be higher under the joint bidding sumers to place joint bids. strategy. Furthermore, joint bidding may also domi- Some researchers have investigated how consumers nate mixed bidding. behave in this channel. On studying the bids placed at Because there are no field data on these new a German NYOP retailer, Spann and Tellis (2006) note bidding mechanisms, we conducted a laboratory

to this article and distributed this copy as a courtesy to the author(s). that sometimes there is a drop in the sequence of bids investigation to examine whether the behavior of financially motivated agents conforms to the model made by individual customers, and they attribute this predictions. We ran a between-subject experiment drop to irrational consumer behavior. However, such with 100 subjects—50 subjects were allowed only a drop in bid sequence may be observed if consumers are allowed to bid repeatedly and if they expect a copyright itemwise bidding, and the other 50 subjects were given the additional option of bidding jointly. The service provider’s prices to vary over time because of experimental results are encouraging. As predicted, yield management policy. Unlike the German NYOP holds allowing for joint bidding increased NYOP retailer retailer, but consistent with Priceline, we do not allow profits and consumer surplus. Additionally, subjects repeated bidding in our model. However, we allow bid more for the very same items when they were for the possibility that a service provider’s costs could allowed to bid jointly. vary over time. In another study, Ding et al. (2005) INFORMS Additional information, including rights and permission policies, is available at http://journals.informs.org/. examine how emotions temper bidding behavior. Our 1.2. Related Literature experimental investigation examines how financially Our work is in the spirit of the initial efforts to refine motivated individuals may behave if given the option the NYOP mechanism (Hann and Terwiesch 2003, to place joint bids. Fay 2004, Terwiesch et al. 2005). They examined the Our work is also related to the literature on optimal theoretical implications of allowing for repeat bid- stopping theory, where researchers typically attempt ding, whereas we are interested in understanding the to answer the question: When should a decision maker optimally stop searching for new alternatives? 2 On surveying the prices of 480 product bundles, Estelami (1999) (e.g., Bertesekas 1987). For example, when should a reports that on average consumers save 8% by purchasing bundles. firm trying to sell an asset stop searching for new Amaldoss and Jain: Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis Management Science 54(10), pp. 1685–1699, © 2008 INFORMS 1687

offers? It is useful to note that offers are randomly and its yield management policy. Note that the ser- generated in these models, and hence offers are not vice provider’s selling price is the marginal cost for the outcome of a strategic process. In the NYOP the NYOP retailer. We capture the variation in the mechanism, on the contrary, consumers are strategic marginal costs of the NYOP retailer by assuming that

decision makers and hence make offers in response the marginal cost at time t for product j, namely cj t, to a ﬁrm’s equilibrium strategy. Thus, our work is is a random variable distributed according to a cumu-

more closely related to equilibrium search models in lative distribution j ct. The marginal costs can be which consumers search for prices and firms decide viewed as the minimum prices at which the NYOP on prices based on consumers’ equilibrium strategies retailer will be open to sell its goods (see Hann and (see for example, Reinganum 1979). However, this lit- Terwiesch 2003 and Fay 2004 for a similar assump- erature examines price search by consumers and does tion).4 An important feature of the NYOP channel is not focus on the issue of bidding for multiple items. that retailers often face an uncertain supply of goods. The product bundling literature uses a static model For example, Priceline is not certain that if it rejects to examine the advantages of selling multiple goods a consumer bid, the same airline ticket will be avail- (Adams and Yellen 1976, Schmalensee 1984, McAfee able for sale in the next period at the same cost. One et al. 1989, Bakos and Brynjolfsson 2000). Our work reason for this uncertainty is that Priceline gets an differs from the bundling literature because we con- opportunity to sell tickets at low prices only when sider a multi-period search model that involves sup- the airlines are not able to sell them at higher prices ply and demand uncertainties. through their direct channels of distribution. Because Finally, the literature on auctions is related to our the same tickets are being concurrently sold using work. There are several formats of auctions such multiple channels, Priceline cannot be sure that the as the English auction, the Dutch auction, the first- tickets will remain available at the same price in the price sealed-bid auction, and the second-price sealed- next period. This uncertainty is captured in our model bid auction (see McAfee and McMillan 1987 for a by letting the costs vary over time. For simplicity, we 3 review, Rothkopf 1991, Sinha and Greenleaf 2000). As assume that j ct = j c. In other words, the costs Rothkopf and Harstad (1994) showed, the results of are drawn from the same distribution in each period. single-item auctions may not apply to multi-item auc- Having outlined some important characteristics of the tions. Demange et al. (1986) study a multi-item auc- market, we proceed to discuss the behavior of con- tion where each item is auctioned independently in an sumers and retailers in our framework. English auction but all of the auctions open and close at the same time. The final price vector in this auction 2.1. NYOP Retailer Behavior can be close to the minimum competitive equilibrium In our formulation, the NYOP retailer first decides price vector. Mishra and Garg (2006) obtain similar whether it wants to (i) sell the items separately or results for the Dutch auction. In all of these one-sided (ii) sell them jointly or (iii) allow consumers to decide auctions, there are several buyers and one seller and whether to place a joint bid or itemwise bids. We consequently the buyers compete to win the object. label the first mechanism as itemwise bidding, the sec- to this article and distributed this copy as a courtesy to the author(s). In contrast, in the basic NYOP mechanism consumers ond as joint bidding, and the third as mixed bidding. arrive asynchronously and hence there is no direct The NYOP retailer’s decision about which mecha- competition among consumers. nism to use, of course, depends on which mechanism The remainder of this paper is organized as follows. will help the NYOP retailer earn more expected prof- copyright Section 2 introduces the theoretical model and ana- its. Note that the NYOP retailer is unaware of its lyzes its implications. Section 3 discusses a laboratory exact costs at the beginning of our game because of the yield management policy of the firm producing holds study. Finally, §4 concludes the paper by summa- rizing the findings and discussing their managerial the good. However, the retailer discovers the prevail- implications. ing marginal costs before it decides whether or not to accept a bid from a consumer. On comparing its marginal cost against the consumer bid amount and INFORMS Additional information, including rights and permission policies, is available at http://journals.informs.org/. 2. Model assessing the resulting expected profits, the NYOP Consider a NYOP retailer who sells perishable goods retailer decides whether to accept or reject a bid. such as airline tickets and hotel rooms. The service provider varies its price over time for these 2.2. Consumer Behavior i goods according to the prevailing demand condition We assume that consumer i places a value vj on item j. If the consumer bids for multiple items, then

3 The ﬁrst-price sealed-bid auction and the Dutch auction are strate- 4 gically equivalent in some conditions, in that the bids are the same In the case of airline tickets, cj t ≥ 0 is the amount that a retailer in both auctions. Similarly, the English auction and the second-price like Priceline will be asked to pay the airlines for procuring the sealed-bid auction are strategically equivalent. ticket(s). Amaldoss and Jain: Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis 1688 Management Science 54(10), pp. 1685–1699, © 2008 INFORMS

we assume that the valuation of the two items is the e-companion)6 we show that the main insights of the sum of the two individual valuations, implying our analysis would apply in the case when the costs that the products are neither complements nor substi- are continuously distributed. In Online Appendix C, i we show that our main result would also hold in tutes. The valuation vj is distributed across the pop- cases where the valuations for the two products are ulation according to the pdf fj ·, which is common knowledge. In our formulation, the consumer is not different and not perfectly correlated. Furthermore, aware of the costs of the retailer but knows the cor- the analysis can accommodate situations in which the cost distributions for the two products are different. responding cumulative distribution j c. It is a standard practice in modeling games with asymmetric Thus, the main insights of our analysis would hold in information among players to assume that the cost more general models. distribution is common knowledge (e.g., Fudenberg In our formulation, the NYOP retailer’s decision and Tirole 1991). This is equivalent to assuming that problem seems to resemble the classical search prob- consumers have some belief about the distribution of lem where the retailer decides when to terminate its NYOP retailer’s threshold prices and that the belief is search and accept a bid. Because the consumer is not correct in equilibrium. Thus, the assumption of com- passive in our game, it adds a layer of complexity to mon knowledge of costs makes the presentation sim- the traditional search models. Indeed, the consumer ple but is not critical for our model formulation. can optimally react to the NYOP retailer’s equilib- Based on her knowledge of the NYOP retailer’s rium strategy. To analyze equilibrium behavior in this game, we study the stationary Markov perfect equi- cost distribution c and her own valuation for the j librium. Next we discuss equilibrium implications of items, the consumer decides on the bid amount x.On itemwise and joint bidding. observing the bid, the NYOP retailer decides whether Itemwise Bidding. Denote the NYOP retailer’s eq- or not to accept the bid. If the retailer accepts the bid, uilibrium strategy by xc, which gives the proba- then the game ends with the NYOP retailer earning I bility that a NYOP retailer with a cost c will accept a a profit of (x − c) and the consumer gaining a sur- consumer bid of x. Similarly, denote the consumer’s plus of (v −x), where v is the valuation of the product equilibrium strategy by xvi, which specifies the by the consumer. But if the NYOP retailer rejects the j amount x that consumer i with valuation vi would bid, then there is some probability that the retailer j bid for item j. Then let VI be the equilibrium value may get an opportunity to sell to another consumer in of the game for the NYOP retailer. This value could the following period. Because 0 ≤ <1, there is some be affected by the equilibrium behavior of both the probability that there will not be a new consumer in retailer and the consumer. The NYOP retailer’s deci- the next period. The parameter , therefore, reflects sion of whether or not to accept the bid x is given by the uncertainty in demand. Next we examine the theoretical implications of this parsimonious model. 1ifx ≥ c + VI x c = (1) I 0 otherwise 2.3. Analysis i i i This is consistent with the business practice of a to this article and distributed this copy as aConsider courtesy to the author(s). first the simplest case where vj = vk = v .In this case, because the valuations of both the products German NYOP retailer that Hann and Terwiesch are identical, we are ruling out traditional reasons for (2003) studied. Much like the German NYOP retailer, selling products together.5 In this polar case, is there Priceline typically accepts a bid if it exceeds a thresh- any incentive still to allow for joint or mixed bidding? old but rejects it otherwise (see Fay 2004). This thresh- copyright To appreciate the answer to this question, let the cost old may be greater than the NYOP retailer’s marginal cost, because V ≥ 0. Thus, the retailer will earn posi- distribution function be identical and binomial so that I holds p is the probability that the cost is c and (1 − p)is tive margins in all situations. This result makes intu- L itive sense. Note that if the retailer waits for the next the probability that the cost is c (c >c ). Though H H L period there is some chance that a high-valuation the cost distributions for the two items are identical, consumer may enter the market and bid b . Conse- the realized cost of each item could be different. In H quently, the low-cost retailer is more aggressive in its INFORMS Additional information, including rights and permission policies, is available at http://journals.informs.org/. Online Appendix B (all appendices are provided in bid acceptance strategy and consumers, in turn, are willing to bid a higher amount for low-cost items. 5 For example, it is argued that when the valuations of the The consumer, of course, does not observe the two products are negatively correlated then offering bundles can retailer’s costs and knows only the cost distribution.7 be attractive to the sellers (Adams and Yellen 1976; see also Schmalensee 1984 and McAfee et al. 1989 for a discussion of the 6 theoretical implications of bundling in contexts where consumer An electronic companion to this paper is available as part of reservation values follow a wider class of distributions). But when the online version that can be found at http://mansci.journal. the reservation prices are perfectly positively correlated, then there informs.org/. is no additional incentive for firms to bundle products. Hence, we 7 Alternatively, we could assume that the consumers are aware of

focus on this extreme case. the distribution of thresholds I ·. Amaldoss and Jain: Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis Management Science 54(10), pp. 1685–1699, © 2008 INFORMS 1689

Consequently, consumer i has to choose the optimal Similarly, the value of the game when the retailer has i bid xI vj , given the retailer’s equilibrium strategy. high costs is Therefore, we have W = b − c 1 − Fv + F v V (10) H H H 1 1 I i i i xI vj ∈ arg max vj − xj I xydj y (2) i i 0 Hence, the overall value of the itemwise bidding 0≤xj ≤vj game VI is implicity defined by the following Equations (1) and (2) define the conditions neces- equation: sary for determining the equilibrium Markov perfect VI = pWL + 1 − pWH (11) strategies, given the equilibrium value of the game. The value of the game in turn depends on the equi- Because bL and v1 are functions of VI , it is not pos- librium strategies of the players. Next we determine sible to give a closed-form solution for a general F·. the equilibrium value of the game. However, we can obtain a closed-form solution for Recall that the cost distribution is binominal. Fur- a uniform distribution of consumer valuations. For ther denote the NYOP retailer’s acceptable bid by other distributions, it is possible to numerically assess the value of the game. If f· is uniform with range I xcH = bH and I xcL = bL when the costs are high and low, respectively. In this case, it is easy to (0 1) and we focus on interior solutions, then the see that a consumer cannot benefit by bidding any value of the game is given by

amount other than 0bLbH . A consumer with valu- pcH − cLpcL + 1 − p − cH ation v therefore has to compare the expected payoffs VI = (12) 1 − p1 − + p cH − cL for bidding 0, bL, and bH and then bid the amount that maximizes her proﬁts. First note that, if v

v − b p = v − b (3) items. Also let J xjkcjk deﬁne the NYOP retailer’s 1 L 1 H bid acceptance strategy when it receives a joint bid Note that the cutoffs must satisfy xjk and its total cost is cjk. Note that the retailer will have different thresholds for the three possible total bL = cL + VI (4) costs for the two products: 2cL, cL +cH ,or2cH . Denote b = c + V (5) H H I the corresponding thresholds by bll, blh, and bhh. If the value of the joint game is V then we have Using these bids, we obtain J b − pb b = 2c + V (13) v = H L (6) ll L J to this article and distributed this copy as a courtesy to the author(s). 1 1 − p blh = cL + cH + VJ (14) c − pc + V 1 − p = H L I (7) b = 2c + V (15) 1 − p hh H J Given these bid acceptance thresholds, a consumer

copyright Note that as increases, the cutoff increases. This is will place a joint bid from the set 0b b b reasonable because an increase in increases the out- ll lh hh side option for the retailer and fewer consumers will depending on her total valuation for the two prod- holds ucts. As discussed earlier in itemwise bidding, we can be able to afford the resulting bH . It follows from this discussion that the optimal bidding strategy for the now compute the value of the game. If f· is uni- consumer is form, then we ﬁnd that (see Online Appendix A for  details) b if vi ≥ v  H j 1 INFORMS Additional information, including rights and permission policies, is available at http://journals.informs.org/.  pc −c "−p3 −3p2 +6pc +−5p2 +10p+p3 −8c +81−p2# i i V = H L L H xI vj = bL if vj ∈ bLv1 (8) J 41−p21− +p c −c  H L  (16) 0 otherwise With the aid of the preceding equation, we can com- The value of the itemwise bidding game for NYOP pute the equilibrium bid acceptance thresholds for retailer, when it knows that it has low costs in the NYOP retailer and optimal consumer bids. current period, is given by Mixed Bidding. Now consider the case where the consumer can decide whether to place a joint bid or W = b − c F v − Fb L L L 1 L several itemwise bids. As before, the retailer will have

+ bH − cL1 − Fv1 + F bLVI (9) threshold bid acceptance values for joint bidding as Amaldoss and Jain: Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis 1690 Management Science 54(10), pp. 1685–1699, © 2008 INFORMS

well as itemwise bidding. Note, however, that these Proposition 1. For any distribution f·, mixed bid- thresholds will be different from those for the con- ding is always dominated by joint bidding when = 0.If sumer who places only itemwise bids or only joint >0 and f· is uniform with range 0 1, then mixed bids. Let the value of this mixed game be denoted bidding is dominated by joint bidding.9 by V . The retailer will accept a joint bid x if M jk The proposition establishes that a NYOP retailer can benefit by adopting the joint bidding mechanism. x ≥ c + V (17) jk jk M In other words, mixed bidding is less profitable.10 We clarify the intuition for this result along with that Hence, the retailer’s cutoffs for joint bids are given by for the next proposition, where we compare the profitability of joint bidding mechanism against that of bm = 2c + V (18) ll L M itemwise bidding. On assuming that f· ∼ U0 1, bm = c + c + V (19) we obtain the following result: lh L H M √ m Proposition 2. (a) If p<5/2 − 17/2 ≈ 044 or p> bhh = 2cH + VM (20) 1 − cH /1 − cL, then joint bidding weakly dominates where the superscript m is used to denote mixed bid- itemwise bidding, and furthermore bll ≥ 2bL and bhh ≥ 2bH . ding. Similarly, if the consumer bids itemwise, we can (b) There exist parameter ranges for which mixed bidding determine the corresponding cutoffs. In this case, we dominates itemwise bidding. assume that if the retailer is left with only one item, The first part of the proposition identifies the condi- then the expected value of this item is VM /2. Note tions in which a NYOP retailer may find it profitable that, if the products are similar and the retailer has to ask consumers to place joint bids. Under these con- numerous products to offer, then the retailer can bun- ditions, a consumer places a higher total bid under dle the unsold item and offer it to another consumer the joint bidding mechanism than she would under and earn VM /2. Therefore, the cutoffs in this case are itemwise bidding. The second part of the proposition states that there exist conditions where it is prof- V m M itable for a NYOP retailer to let consumers self-select bL = cL + (21) 2 whether they want to place a joint bid or bid sepa- V rately for each item. In an attempt to clearly explain bm = c + M (22) H H 2 the intuition for Proposition 2, we first discuss the simple case when = 0 and then examine the case It is easy to see why the consumer will never place when >0. a joint bid bm when she can place itemwise bids ll Case where = 0. If = 0, the NYOP retailer will m m 8 (bL bL ). With the itemwise bids the consumer can accept any bid that is at or above its costs.11 To grasp get one product when the costs are (cLcH ) but gets the intuition for the key results, we need to under- m nothing with the joint bid bll . Also note that the con- stand the answers to the following questions:

to this article and distributed this copy as a courtesy to the author(s). m m m sumer is indifferent between bidding bhh and (bh bh ) 1. How does a consumer equilibrium bidding strat- because she gets both of the products in either case egy change as a NYOP retailer moves from itemwise and the total bid amount remains the same. There- bidding to joint bidding? m m m m fore, the consumer’s choice set is 0bL bL blhbhh. 2. How does a NYOP retailer’s proﬁts change as it copyright With this setup, we can study a consumer’s bid- moves from itemwise to joint bidding? ding strategy for a given valuation v and game value 3. How does consumer surplus change as a VM . Of course, VM is endogenous and needs to be NYOP retailer moves from itemwise bidding to joint holds determined. Using the approach discussed before, we bidding?

can now determine VM (see Online Appendix A for 4. How can mixed bidding lead to improved con- details). If f ∼ U0 1 then we obtain sumer surplus and retailers’ proﬁts? Consumer Bidding Strategy. Figure 1 shows con- INFORMS Additional information, including rights and permission policies, is available at http://journals.informs.org/. pc −c 4pc −3p2c +4−4c +4p2 −8p−p2c +4pc V = H L L L H H H sumer’s bidding strategy when the NYOP retailer M 2 21−p 1− + pcH −cL (23) 9 The proposition can also be shown to hold for a uniform distri-

2.3.1. Comparison of Bidding Mechanisms. On bution with range ab where cH 0 the NYOP retailer can pursue a more aggressive bid 8 This holds as long as there are no complementarities in the acceptance strategy, namely accept only bids above costs. This, in product. turn, will inﬂuence consumers’ bidding behavior. Amaldoss and Jain: Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis Management Science 54(10), pp. 1685–1699, © 2008 INFORMS 1691

Figure 1 Comparison of Bidding Under Itemwise and Joint Bidding allowed, then some consumers, who might have bid Mechanisms When = 0 (cLcL) under itemwise bidding, may place a higher Bid (c , c ) under itemwise joint bid (cL + cH ), because it increases the chance of Bid (c , c ) under itemwise H H L L bidding and switch down to getting both items. In essence, the joint bidding mecha- bidding and (c + c ) L L (c + c ) under joint bidding under joint bidding L H nism eliminates mismatch between costs and bids, which is possible under itemwise bidding.

Next consider the segment 2, namely v1

Bid (cH, cH) under itemwise However, the joint bid (cL + cH ) increases the chance Bid (cL, cL) under itemwise bidding and switch to of getting both of the items relative to itemwise bids bidding and switch up to (cH + cH) under joint bidding (c c )or(c c ). Consequently, consumers in this (c + c ) under joint bidding L H H L L H segment are willing to take their chances by reducing their total bid amount and placing a joint bid. allows itemwise bidding or joint bidding. The low- Finally, in region 3, namely v>v3, consumers bid valuation consumers lie on the left side of the (c c ) under itemwise bidding and b = c + c valuation line depicted in Figure 1. Consumers in seg- H H hh H H under joint bidding. Because the total bids as well ment , namely v

2 before, the joint bid increases the probability of the copyright Uc + c = 1 − 1 − p 2v − c − c (25) L H L H transaction going through by reducing the likelihood of a mismatch between bid and costs. This aspect It can be easily shown that for the consumer at v = v1, holds of joint bidding is helpful to consumers. We can UcL + cH >UcL + cL. Hence, this consumer will place a higher bid under joint bidding than under show that low-valuation consumers, namely con- itemwise bidding. Interestingly, we also ﬁnd that sumers with v ∈ v2v4 as shown in Figure 2, are worse off under joint bidding. But consumers with UcL + cH >UcLcL if v = v1. This implies that the valuations in the region (v v ) are actually better INFORMS Additional information, including rights and permission policies, is available at http://journals.informs.org/. consumer at v1 would switch to placing a higher joint 4 1 bid, even if she had the freedom to choose between item- off under joint bidding even though they are bid- wise bidding and joint bidding. Now to understand how ding higher amounts (the derivation of the cutoff v4 joint bidding can sometimes increase the chance of is in Online Appendix A and depicted in Figure 2). getting both of the items, consider the implications of Again, this improvement in consumer surplus is a consequence of joint bidding reducing the probability placing itemwise bids (cLcH ) against placing a joint bid of (cL + cH ). If the retailer’s costs were (cH cL), of mismatch and thereby increasing the possibility that then the joint bid would go through, but not the item- a consumer gets both items. Thus, the overall impact wise bids, because of the mismatch between costs of the change in bidding mechanism on consumer wel- and itemwise bids. Thus, if only joint bidding were fare is ambiguous. Amaldoss and Jain: Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis 1692 Management Science 54(10), pp. 1685–1699, © 2008 INFORMS

Figure 2 Comparison of Bidding Under Itemwise and Mixed Bidding The expected loss that the retailer incurs as a result of Mechanisms When = 0 consumers bidding a lower amount is given by Bid (c , c ) under itemwise v3 H H 2 bidding and switch down to 2 = cH − cL1 − 1 − p fvdv Bid (cL, cL) under itemwise v1 and mixed bidding (cL + cH) under mixed bidding = pcH − cL2 − p2 (27)

Thus, as the size of segment 2 increases, it reduces the proﬁtability of the joint bidding mechanism. v4 v1 v5 Product Finally note that in segment 3 the total bid amount valuation and the probability of the transaction going through are the same under both bidding mechanisms. Con- sequently, the size of does not affect the rela- Bid (cL, cL) under itemwise Bid (cH, cH) under itemwise 3 bidding and switch up to bidding and switch to tive proﬁtability of joint bidding. Hence, whether the (cL + cH) under mixed bidding (cL + cH) under mixed bidding NYOP retailer prefers joint bidding or itemwise bid-

Note. v4 >v2. ding will depend on the relative sizes of segments

1 and 2. The total impact on proﬁts, if the NYOP retailer switches from the itemwise to the joint bid- Turning attention to segment 2, we ﬁnd that con- ding mechanism, is given by sumers switch down to bidding blh = cL + cH . Note that these consumers always had the option of bid- = 1 + 2 = pcH − cLp1 − 2 − p2 (28)

ding bhh = 2cH , which is strategically equivalent to This implies that joint bidding is more proﬁtable iff (c c ) when = 0 case, implying that consumer H H 2 − p surplus improves with joint bidding in the segment. 1 > (29) Finally, consumer surplus remains unchanged for 2 p people in segment . Thus, whether the overall con- 3 If segment 1 is sufﬁciently large compared with 2, sumer surplus is higher or lower will depend on the then the retailer is better off under the joint bidding

size of the segment v4v1 ∪ 2 versus the size of the mechanism. segment (cLv4). It is also useful to examine how (28) changes with Impact on the NYOP Retailer’s Profits. When = 0, model parameters. First, consider the case when cH the NYOP retailer does not earn any profits from con- increases. We find that, as cost increases, the number of consumers who are able to make bids acceptable sumers in segment 0, because their bids just cover the product costs under both itemwise bidding and to the firm decreases. This implies that v1 increases as c increases. Also note that an increase in c joint bidding. However, consumers in segment 1 H H bid a higher amount under joint bidding as opposed increases the other cutoffs, namely v2 and v3. For to itemwise bidding. The higher bid amount also a uniform distribution with range (0 1), it turns to this article and distributed this copy as a courtesy to the author(s). out that as c increases both and increase. increases the chance that the NYOP retailer will H 1 2 Furthermore, we find that an increase in c increases be able to sell its products. The increased expected H the profitability of the joint bidding option as long as profits due to consumers switching to higher bids is √ p<5 − 17/2 ≈ 044.12 An increase in c has an given by L

copyright analogous but opposite effect on the profitability of the joint bidding mechanism. v2 2 2 1 = cH − cLp fvdv= cH − cLp 1 (26) Let us consider the impact of an increase in p on holds v1 the size of valuation segments 1 and 2. Note that, unlike changes in costs, a change in p not only affects where the first term (cH − cL) is the additional rev- the sizes of regions 1 and 2 but also the probabil- enue. Note that this additional revenue is realized ity of a transaction going through.13 For the uniform only when the retailer has low costs for both prod- INFORMS Additional information, including rights and permission policies, is available at http://journals.informs.org/. ucts, which happens with probability p2. Thus, as the 12 This is under the assumption that v < 1. If there is a corner size of segment increases, the NYOP retailer’s prof- 3 1 solution then joint bidding always becomes more attractive as cH its under the joint bidding mechanism increase com- increases. Also, note that if the distribution is skewed towards 0 pared with the profits under itemwise bidding. (such as the exponential distribution) the positive effect of a change in cH on 1 is likely to be higher than the negative effect of an In region 2, however, some consumers scale down increase in 2. Therefore, the result is likely to be stronger for the their bids. This downward transition dampens the exponential distribution. NYOP retailer’s profits because the total bid blh = 13 More specifically, we have cL + cH is lower than 2bH = 2cH , and furthermore it = c − c "p + − # + pc − c p 1 − 2 − p 2 reduces the chance of the transaction going through. p H L 1 2 2 H L p p Amaldoss and Jain: Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis Management Science 54(10), pp. 1685–1699, © 2008 INFORMS 1693

case with range (0 1), it turns out that the sizes of from placing itemwise bids (bH bH ) to placing a joint consumer segment 1 and 2 are increasing in p. Fur- bid blh. Note, however, that the opposite will hold thermore, if p<032 then joint bidding becomes more when joint bidding is less attractive. This implies that

attractive as p increases. If v3 = 1 (which happens for an increase in can exacerbate the difference between large values of p), an increase in p always increases the profitability of the two bidding mechanisms. 14 the profitability of the joint bidding. 2.3.2. Numerical Simulation. We now study the Impact of Mixed Bidding. Figure 2 draws a contrast case when the distribution of valuations is not uni- between mixed bidding and itemwise bidding. Our form. Specifically, we examine how model parameters previous discussion shows that both consumer sur- affect the profitability of the different bidding mecha- plus and the NYOP retailer’s profits increase in the nisms when >0. This allows us to explore the gen- region v4v1 ∩ 1 = v4v1. This raises the possi- eralizability of our results and also address issues that bility that both consumer welfare and retailer profits we could not study using the uniform distribution. could increase if the region (v4v1) grows in size. In We consider the case where the value distribution this case, a NYOP retailer could give consumers the is exponential. The exponential distribution, which is flexibility to place itemwise or joint bids. For = 0, used widely in the marketing literature, captures an a consumer cannot be worse off under mixed bid- important market reality (e.g., Xie and Sirbu 1994). ding because she will always choose the mechanism A large proportion of the consumers place low val- that gives her higher utility.15 However, if the region uation for goods, and the exponential distribution is

(v4v1) is large enough and the region (v1v5)isnot skewed toward the lower end of valuation. The prob- too large, then the retailer’s proﬁts could also be ability density function for the exponential distribu-

higher. However, because the region v4v1 ∈ 1, the tion is given by NYOP retailer always finds joint bidding to be more exp−x if x>0 profitable than mixed bidding. Now we proceed to fx= (31) examine the case when >0. 0 otherwise Case where >0. We find that >0 creates scope for the NYOP retailer to entertain the possibility that The analysis of this case cannot be done using ana- in the next period it may get more favorable costs lytical methods, and, therefore, we employ simula- or demand conditions. Consequently, the retailer will tion methods. In particular, we draw different values not sell its products at cost in the current period. Let of model parameters and solve for the equilibrium bids and acceptance thresholds for the NYOP retailer. b and b denote the itemwise bids acceptable to the L H Using this we calculate the equilibrium expected prof- NYOP retailer when the costs are c and c , respec- L H its for the retailer under the joint and itemwise bid- tively, and the corresponding value of the game for ding mechanisms. We assume c = 0, p varies from 01 two items is 2V . Also let the acceptable joint bids be L I to 0.9, c varies from 0.1 to 0.9, varies from 0 to 1, b b b , when both items’ costs are low, one item’s H ll lh hh from 0.1 to 1, with the parameter values changing cost is low, and no item’s cost is low, respectively. in increments of 0.1. to this article and distributed this copy as aDenote courtesy to the author(s). the value of the joint bidding game by V .If J Although it is not possible to obtain a closed-form V > 2V , then from (4) and (13) we know that J I equilibrium solution for the exponential distribution b − 2b = V − 2V >0 (30) of valuations, we can still use the methodology ll L J I described earlier to numerically determine a con- copyright In other words, when joint bidding is more prof- sumer’s equilibrium bids and a retailer’s bid accep- itable than itemwise bidding, the NYOP retailer will tance thresholds for the three bidding mechanisms. For the itemwise bidding case, we have holds demand a joint bid b which is more than the total ll itemwise bid amount 2b . Thus, under joint bidding v1 L W = b − c exp−x dx + b − c all consumers place a higher total joint bid except L L L H L bL possibly those consumers who are transitioning down bL INFORMS Additional information, including rights and permission policies, is available at http://journals.informs.org/. · exp−xdx+ exp−xVI dx (32) v 0 Note that the first term captures the direct effect of change in p 1 on probability of transaction going through, and the second term W = b − c exp−x dx captures the effect of p due to changes in and . H H H 1 2 v1 14 Although regions 0 and 3 do not affect profits, for complete- v1 ness we also report how model parameters affect the sizes of + exp−xVI dx (33) these regions. In particular, we find that, for interior solutions, 0

0 increases in p and cH while 3 decreases in cH and p. The overall value of the itemwise bidding game 15 When >0, this observation does not necessarily hold must also satisfy the following equation: because the threshold values would differ across the two bidding mechanisms. VI = pWL + 1 − pWH (34) Amaldoss and Jain: Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis 1694 Management Science 54(10), pp. 1685–1699, © 2008 INFORMS

For given values of , p, , cH , and cL we can joint bidding scenario. Thus, as increases, joint bid- solve (6), (32), (33), and (34) simultaneously to deter- ding is more profitable.16 mine v , b , b , and V . Using a similar approach, 1 L H I 2.3.3. Discussion. In sum, our analysis of the we can calculate the cutoffs and value functions three bidding mechanisms shows that both joint bid- for the joint and mixed bidding cases (see Online ding and mixed bidding can help improve NYOP Appendix A for more details). retailers’ profits and consumer surplus compared to This additional analysis shows that joint bidding the itemwise bidding that is practiced today. The theo- always dominates the mixed bidding mechanism. retical analysis also suggests that mixed bidding may Thus, the finding reported in Proposition 1 is gener- dominate joint bidding if consumer valuations are alizable to an exponential distribution of valuations. uniformly distributed. The numerical analysis further Next we focus our attention on understanding how clarifies that the theoretical results are generalizable the model parameters affect a NYOP retailer’s deci- to an exponential distribution of valuations. sion about whether to use itemwise bidding or joint bidding. It is a standard practice in simulation studies to use 3. Empirical Investigation regression analysis to understand the effect of model Experimental economists have used the laboratory as parameters on the key decision variable (e.g., Souza a test bed for designing innovative market institu- et al. 2004). In our data we find that in 67.75% of the tions such as the Arizona Stock Exchange, the auction cases joint bidding is more profitable than itemwise mechanism for leasing offshore drilling rights by the bidding. U.S. Government, and spot auction markets for elec- Note that, for the exponential distribution, an tricity (e.g., Kagel et al. 1989, Rassenti et al. 2001). increase in leads to a decrease in the mean valuation A laboratory test is often a useful first step in test- and the variance of the distribution. A logit analysis ing theoretical models, though it does not reflect all of the complexities of a field setting. Note that, if a shows that joint bidding becomes less attractive for model performs poorly in a controlled laboratory set- a NYOP retailer when the mean of valuation distri- ting, then there is very little chance that it will survive bution increases (beta for = 392p < 0001). Note in the field. But if a model survives a laboratory test, that as increases the exponential distribution shifts then it would be worthwhile to test it under rigorous to the left and the variance also decreases. This leads field conditions and better understand the extent to to an increase in the proportion of consumers with which the model predictions are generalizable. moderate valuations who could switch from placing Because NYOP retailers do not currently offer joint itemwise bids (b b ) to placing joint bid b . Con- L L lh bidding or mixed bidding, it is not possible to test sequently, when grows in size the profitability of our model predictions with field data. However, we joint bidding increases. In other words, as the mean can assess these bidding mechanisms in a laboratory of the distribution increases then joint bidding is less setting. The goal of our experimental investigation attractive. to this article and distributed this copy as a courtesy to the author(s). is to examine whether giving consumers the option An increase in c , however, increases the attractive- H to place joint bids increases consumer surplus and ness of joint bidding for a NYOP retailer (beta for retailers’ profits as predicted by our model. Note that, cH = 755p < 0001). This is because an increase in if mixed bidding performs better than itemwise bid- cH raises v1. Therefore, the mass of consumers who ding, it follows that joint bidding will also perform copyright place itemwise bids (bLbL) grows as cH increases. Fur- better than itemwise bidding as pointed out in Propo- thermore, these consumers will switch to placing a sition 1. Thus, by comparing itemwise bidding with holds higher joint bid blh if given the option to place joint bids. The logit analysis also shows that joint bid- 16 ding becomes less attractive as p increases (beta for In regions where joint bidding is superior to itemwise bidding, the mean profits from joint bidding, itemwise bidding, and p =−2577p<0001). mixed bidding are 0.375 (std = 0268), 0.310 (std = 0222), and 0.303 In general, as increases, the retailer can be more (std = 0222), respectively. But in regions where itemwise bidding INFORMS Additional information, including rights and permission policies, is available at http://journals.informs.org/. patient, and this should increase the value of game is more profitable than joint bidding, we find that the mean profits (both V and V ). The logit analysis examines the from joint bidding, itemwise bidding, and mixed bidding are 0.307 I J (std = 0303), 0.329 (std = 0326), and 0.283 (std = 0280), respec- relative profitability of joint bidding and item- tively. Also note that itemwise bidding dominates mixed bidding wise bidding. We find that, as increases, joint on 79.59% of the occasions. We have also explored the issue of cor- bidding becomes more profitable (beta for = 06868 relation in values using a normal distribution. In general, we find that joint bidding is more profitable for items with positively cor- p<0001). This is because an increase in raises v1. Therefore, the mass of consumers who place itemwise related valuations. This makes intuitive sense, because an increase in correlation increases the standard deviation of the joint value bids (bLbL) grows as increases. These consumers distribution, which improves the profitability of the joint bidding will switch to placing a higher joint bid blh under the option. Amaldoss and Jain: Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis Management Science 54(10), pp. 1685–1699, © 2008 INFORMS 1695

mixed bidding, we seek answers for the following the NYOP retailer’s profit should improve to $5.15 empirical questions: for both items. The predicted mean bid for the two 1. Will consumers bid more when mixed bidding is items and consumer surplus were $55.35 and $72.86, allowed? respectively. 2. Will consumer surplus increase when mixed bidding is permitted? 3.2. Subjects 3. Will NYOP retailers’ profits improve if mixed The subjects were undergraduate and graduate stu- bidding is allowed? dents who volunteered to participate in a bidding It is quite unlikely that our subjects solve for opti- experiment for a monetary reward contingent on their mal behavior and accordingly bid for different items. performance in the experiment. In addition to their It is possible that their bidding decisions are guided earnings, the subjects were promised a show-up fee of by some heuristics. For example, subjects could bid $5.00. For this experimental study, we considered two less when they have the option of placing joint bids. treatments: itemwise bidding only, and mixed bidding After all, they are used to getting discounts when where subjects were offered the option of placing joint products are purchased in bulk. If all subjects sys- bids. In each treatment, 50 subjects participated in 160 tematically engage in such discounting, then retailers trials. Thus, a total of 100 subjects participated in this are unlikely to realize more profits by allowing joint study. bidding. It is definitely convenient to place a single bid for multiple items rather than a separate bid for 3.3. Procedure each item. However, it is cognitively more demand- This study was conducted on the Web, with the server ing to figure what that joint bid should be. Thus, to playing the role of seller and subjects playing the role save cognitive effort and also avoid the potential risk of buyers. See Online Appendix D for instructions. of making financially imprudent decisions, some sub- Below we discuss the roles of the seller and buyer, jects might choose to bid one item at a time, even rules of the bidding game, and information provided when offered the option of placing joint bids. Fur- to subjects. thermore, some subjects, while making itemwise bids, Seller. The seller had two different products, namely might bid different amounts even if the items are the item 1 and item 2. It was not certain whether the same. Such a behavior could potentially hurt con- seller’s cost of these items would be high or low. sumer surplus, as well as retailers’ profits. Thus, it is The seller would accept an offer as long as it cov- not clear whether, on average, subjects will bid more ered her cost. There was a 70% chance that the cost without hurting their surplus, and whether retail- of item 1 was $20 for the seller and a 30% chance ers will make more profit as implied by our model. that it was $40. The cost distribution was the same Hence, we test our model in the laboratory. for item 2. As noted earlier, the actual realized costs of items 1 and 2 could be different. On each trial, 3.1. Parameters whether the cost of each item was high or low was

to this article and distributed this copy as aIn courtesy to our the author(s). experimental study, we focused attention on determined by drawing a random number between 0 the case where = 0, the probability of cost c being and 1 separately for each item. If the random number $20 is p = 07, and the probability of its being $40 drawn for item 1 was less than or equal to 0.7, then is 1 − p = 03. Though the two items have identical item 1’s realized cost was $20, else the cost was $40. cost distributions, the realized cost of the items could Similarly, another random number was drawn for copyright be different. The valuations for the two items were item 2. If this random number was less than or equal identical and were drawn from the exponential dis- to 0.7, then item 2’s realized cost was $20, otherwise holds tribution with mean 20. All subjects were exposed to the cost was $40. The computer played the role of the same set of valuations for items 1 and 2 over the seller, and subjects were aware of this fact. This the 160 trials so that their bidding behavior could experimental design helped us to eliminate potential be compared. It is important to note that the valu- noise in the decisions of sellers and to more closely INFORMS Additional information, including rights and permission policies, is available at http://journals.informs.org/. ations of the items changed from trial to trial and investigate the bidding behavior of buyers. that the costs were different in each trial depending Buyer. Subjects played the role of buyers. We on the draws from the binomial distribution. Conse- induced the desired valuations for items 1 and 2 by quently, the decision faced by the subjects was not promising resale values for these items. Specifically, a trivial one. Furthermore, it is not easy to learn if subjects happened to win an item, then the differ- in such a noisy environment. The predicted mean ence between the resale value and their bid would be profit for both items was $4.57 if only itemwise bid- their profit. In each trial of the experiment, the sub- ding was allowed. The corresponding predicted mean jects had to bid depending on the treatment and the bid and consumer surplus were $46.5 and $69.99, resale values of the items. If only itemwise bidding respectively. On the other hand, under mixed bidding was allowed, then they made separate bids for item 1 Amaldoss and Jain: Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis 1696 Management Science 54(10), pp. 1685–1699, © 2008 INFORMS

and item 2. On the other hand, if both types of bid- null hypothesis that these mean bids were the same

ding were allowed, then they first decided whether to (F1 98 = 13314p<0001). bid itemwise or jointly, and then the bid amounts. Our theory also makes specific predictions about Bidding Rules. In itemwise bidding, the seller made how itemwise bids should change with consumer val- independent decisions on whether or not to accept uations of items. Specifically, consumers should bid

the bid for each item depending on the realized cost (bLbL) if valuations were low (namely, 20 = bL v1 realized cost of items 1 and 2. (t = 347p<001). Furthermore, in theory, mixed bid- Information Provided to Subjects. At the commence- ding should motivate consumers with intermediate ment of each trial, subjects were informed of the valuations (v = 6333 8667. Amaldoss and Jain: Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis Management Science 54(10), pp. 1685–1699, © 2008 INFORMS 1697

was encouraging to note that the mean consumer sur- Table 2 Mixed Bidding plus was $72.34 under mixed bidding. In contrast, Valuation region Bidding strategy Predicted bid Actual bid the consumer surplus when only itemwise bidding 20

$81.35 under mixed bidding (F1 98 = 5012p<0001). mechanism. Table 2 shows the theoretical predictions Retailer’s Proﬁt. The model predicts that allowing for and corresponding observed outcomes when subjects mixed bidding should increase the NYOP retailer’s use the appropriate bidding mechanism. In theory,

proﬁt. The mean retailer’s proﬁt when only item- subjects should place joint bid blh = $60 in the inter- wise bidding was allowed was $5.10, whereas the mediate valuation region 6333

ding (F1 98 = 4692p <00001). Note that consumer ity, the average joint bids in these regions were $58.09 surplus increased for intermediate valuations of v and $58.23, respectively, which are close to the equilibrium prediction (p>010). Next subjects should bid (namely, v4 055). ical prediction (t = 161p>011). Though the overall The results were similar when subjects were given the behavior is consistent with the equilibrium prediction, option of placing joint bids (actual earning = 7234, we observe deviations from the equilibrium predic- prediction = 7286, t = 016p>087). tions at the level of consumer valuation segments. copyright Retailer’s Profit. The model provides point predic- Table 1 details the predicted and actual outcomes. tions on bids that subjects should place for different For example, subjects actually bid $46.25 instead of valuations of items. Using the predicted bid and the holds the predicted $40.0 when vv1, they bid per theory. If only itemwise bidding were allowed, only $52.58 (t = 23p<0001). the mean profit should be $4.57 for items 1 and 2. Under mixed bidding, subjects bid $55.25 on aver- The actual mean profit was $5.10. We could not reject INFORMS Additional information, including rights and permission policies, is available at http://journals.informs.org/. age, which is significantly more than the theoret- the null hypothesis that these profits were the same ical prediction of $48.75 (t = 1305p < 001). This (t = 161p>011). On the other hand, under mixed excessive bidding could be a consequence of either bidding the predicted mean profit for both items should be $5.15, but the actual mean profit was $8.37. Thus, mixed bidding produced more than the pre- Table 1 Itemwise Bidding dicted increase in profit (t = 947p<001). Valuation region Predicted bid Actual bid 3.5. Discussion 20 8667 80 5258 the aggregate behavior of subjects is qualitatively Amaldoss and Jain: Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis 1698 Management Science 54(10), pp. 1685–1699, © 2008 INFORMS

consistent with many predictions of our model. On equilibrium strategies of service providers and NYOP average, retailers made more profits and subjects retailers in such settings. It would also be interest- increased their bids without reducing their earnings ing to study the implications of competition among when provided the option to bid jointly. Though the NYOP retailers (see also Fay 2007). Finally, in the cur- overall behavior is directionally consistent with the rent research we subjected the model to a laboratory model, we observe deviations at the level of valuation test, and future research can confront the model with segments and subjects tend to use joint bidding more field data when such data become available. often than predicted. 5. Electronic Companion 4. Conclusion An electronic companion to this paper is available as The NYOP channel has drawn a lot of attention part of the online version that can be found at http:// from the public and the press for its innovativeness. mansci.journal.informs.org/. The focus of our research was to explore whether the existing market institution can be further aug- Acknowledgments mented. Toward this end, we developed a dynamic Both authors contributed equally to the paper. The authors thank Teck Ho, Amnon Rapoport, Ambar Rao, the anony- model of a NYOP retailer who faces both demand mous reviewers, the associate editor, and the department and supply uncertainty and examined the retailer’s editor for helpful comments. equilibrium bid acceptance strategy in the presence of strategic bidders. Our analysis focused on evalu- ating the profit and consumer surplus implications References of three different bidding mechanisms: itemwise bid- Adams, W., J. Yellen. 1976. Commodity bundling and the burden ding, joint bidding, and mixed bidding. We find that of monopoly. Quart. J. Econom. 90 475–498. in the presence of joint bidding some consumers may Bakos, Y., E. Brynjolfsson. 2000. Bundling and competition on the bid a higher amount than they would bid if they were Internet. Marketing Sci. 19(1) 63–82. placing itemwise bids. This increase in bid amount Berteskas, D. 1987. Dynamic Programming Deterministic and Stochas- tic Models. Prentice Hall, Englewood Cliffs, NJ. is related to the fact that joint bidding reduces the Demange, G., D. Gale, M. Sotomayor. 1986. Multi-item auctions. chance of a mismatch between the NYOP retailer’s J. Political Econom. 94(4) 863–872. realized costs and consumer bids. Interestingly, the Ding, M., J. Eliashberg, J. Huber, R. Saini. 2005. Emotional bidders— improved NYOP retailer’s profit need not come at An analytical and experimental examination of consumers’ the cost of consumers, because joint bidding can also behavior in a Priceline-like reverse auction. Management Sci. 51(3) 352–364. improve consumer surplus. Even if the NYOP retailer Estelami, H. 1999. Consumer savings in complementary product offers mixed bidding, where consumers can self-select bundles. J. Marketing Theory Practice 7(3) 107–114. whether they want to place itemwise or joint bids, we Fay, S. 2004. Partial repeat bidding in the name-your-own-price can observe improved profits and consumer surplus. channel. Marketing Sci. 23(3) 407–418. In our framework, we also observe that joint bidding Fay, S. 2007. Selling an opaque product through an interme- to this article and distributed this copy as a courtesy to the author(s). dominates mixed bidding. We conducted an experi- diary: The case of disguising one’s product. J. Retailing. Forthcoming. mental test of our model predictions. The test lends Fay, S., J. Xie. 2008. Probabilistic goods: A creative way of selling support to many qualitative predictions of our model. products and services. Marketing Sci., ePub ahead of print In particular, offering the option of joint bidding sig- March 31, http://mktsci.journal.informs.org/cgi/content/ copyright nificantly improved consumer surplus and retailers’ abstract/mksc.1070.0318v1. profits. Fudenberg, D., J. Tirole. 1991. Game Theory. MIT Press, Cambridge, MA. holds There are several avenues for further research. Hann, I.-H., C. Terwiesch. 2003. Measuring the frictional costs of Although we investigated how NYOP retailers can online transactions: The case of a name-your-own-price chan- augment their pricing mechanisms, we did not study nel. Management Sci. 49(11) 1563–1579. the conditions under which service providers should Kagel, J., D. Levin, R. Battalio, D. Meyer. 1989. 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