Bidding for Bidders? How the Format for Soliciting Supplier … · 2016-10-24 · Fay and Zeithammer: Format for Soliciting Supplier Participation in NYOP Auctions Impacts Channel

MANAGEMENT SCIENCEArticles in Advance, pp. 1–22ISSN 0025-1909 (print) � ISSN 1526-5501 (online) https://doi.org/10.1287/mnsc.2016.2556

© 2016 INFORMS

Bidding for Bidders? How the Format forSoliciting Supplier Participation in

NYOP Auctions Impacts Channel Profit

Scott FayMartin J. Whitman School of Management, Syracuse University, Syracuse, New York 13244, [email protected]

Robert ZeithammerUCLA Anderson School of Management, University of California, Los Angeles, Los Angeles, California 90095, [email protected]

In a name-your-own-price (NYOP) auction, consumers bid for a product or service. If a bid exceeds theconcealed threshold price, the consumer receives the product at her bid price. This paper examines how to

optimize the interactions between the NYOP retailer and service providers, while, at the same time, managingthe bid acceptance rates in order to induce the desired consumer bidding behavior. Channel profit is impactedby how the retailer decides whether or not a given consumer bid will be accepted and, if so, which serviceprovider is chosen to supply a unit of the product to the consumer. We devise a mechanism, the modifiedsecond-price auction, which maximizes channel profit.

Keywords : reverse auctions; name-your-own-price; bidding; channel coordinationHistory : Received July 26, 2013; accepted April 26, 2016, by J. Miguel Villas-Boas, marketing. Published online

in Articles in Advance October 17, 2016.

1. IntroductionThe name-your-own-price (NYOP) mechanism is acustomer-driven pricing strategy invented by Price-line.com to sell travel reservations on the Internet.Under NYOP, consumers bid for a product or ser-vice. If a bid exceeds the concealed threshold price,the consumer receives the product at her bid price.Other retailers use the NYOP system to sell both travelservices (e.g., Germanwings) and nontravel services(e.g., Chiching.com, which offers restaurant mealsand beauty/fitness services; eBay sellers who employeBay’s “Best Offer” feature; the Gap’s usage of its “GapMy Price” promotion) (Spann et al. 2010, Conlan 2011).

Many current NYOP retailers (e.g., Priceline.com,Chiching.com, Prisminister.dk) are intermediaries thatrely on service providers (such as airlines, hotels, andcar rental companies) to provide the service offerings.An NYOP intermediary has to make two interrelateddecisions: First, he must set the hidden threshold pricepolicy that will determine which consumer bids will beaccepted. The acceptance threshold policy influenceshow much consumers bid.1 Second, he must determinewhich service provider is selected to fulfill the demand

1 Although NYOP sellers do not reveal the threshold price thatis in effect at any given moment, they often communicate a bid-acceptance schedule to help consumers make more informed biddecisions. For example, Lufthansa accepts bids for upgrades undertheir “myOffer” program and shows a “strength meter” to indicate

from each consumer. These two decisions are interre-lated because the threshold prices typically depend onthe wholesale costs the intermediary is facing, whichare in turn driven by the mechanism used to select sup-pliers. While prior work in the literature has addressedthe first decision, i.e., how to set the threshold (e.g.,Fay 2009, Shapiro and Zillante 2009, Wang et al. 2009,Zeithammer 2015), this is the first paper, to our knowl-edge, to endogenize the second decision, i.e., how toprocure the good. Thus, we provide the first completemodel of a two-sided NYOP market.

We identify how to structure the NYOP channel inorder to maximize total channel profit. At first glance,an NYOP retailer’s role in an NYOP auction seemsdeceptively simple: the NYOP retailer creates a mar-ketplace, facilitating the communication of a consumerbid to sellers and letting the sellers decide whetheror not to accept a bid. We show, however, that sucha passive approach (which we term “demand collec-tion”) results in suboptimal profit because it inducesrelatively low bids from potential customers. Instead,to maximize channel profit, we show that the NYOP

how “strong” the amount of the offer is. Similarly, Greentoe.com,MeanBuy.com, and ScoreBig.com use a “PriceMeter,” “Chance”sliding scale, and color-coded “bid success potential,” respectively,to convey the approximate probability that a bid will be accepted.

1

mailto:[email protected]

mailto:[email protected]

Fay and Zeithammer: Format for Soliciting Supplier Participation in NYOP Auctions Impacts Channel Profit2 Management Science, Articles in Advance, pp. 1–22, © 2016 INFORMS

retailer must actively manage the acceptance rate asso-ciated with any particular bid submitted by a con-sumer while at the same time soliciting bids frompotential service providers in a way that their truecosts can be uncovered. We identify one such mech-anism that uncovers supplier costs while procuringtheir services only when there is an acceptable buyer;we call it the modified second-price (MSP) auction. Inthe MSP auction, service providers bid in a reversesecond-price, sealed-bid auction for the right to supplythe product. Our mechanism “modifies” the standardsecond-price, sealed-bid auction by making the reser-vation price depend on the level of the consumer’sbid in a particular way that maximizes overall channelprofit. The chosen procurer is thus the service providerwho submits the lowest bid, and the price this winningsupplier receives is the lesser of the next lowest bidsubmitted by a rival supplier and the reservation price.The reserve price is calibrated to replicate the opti-mal bid-acceptance strategy derived in Zeithammer(2015), and MSP generates the optimal channel profitbecause it both achieves the optimal number of tradesand ensures that the low-cost supplier is awardedthe sale. If side payments between the NYOP retailerand the service providers are feasible (e.g., participa-tion fees charged to suppliers who wish to be affili-ates in the NYOP system), then each supplier and theNYOP retailer prefer the MSP mechanism over anyalternative.

Alternative systems, such as one in which the NYOPretailer specifies a margin for each transaction, wouldsuppress competition since suppliers are chosen ran-domly rather than on the basis of who submittedthe lowest bid.2 Our results suggest that such a lackof competition does not necessarily benefit serviceproviders, however. In fact, service providers are moreprofitable if the NYOP retailer establishes a system inwhich service providers bid against each other for cus-tomers, provided that the NYOP retailer also takes anactive role in managing the acceptance rates of con-sumers’ bids.

The remainder of the paper is organized as follows:Section 2 reviews the related literature and discussesthe study’s contributions. We present the formal ana-lytical model in Section 3. Section 4 derives the opti-mal channel profit and constructs a mechanism (MSP)that can reach this optimum. In Section 5, we considerseveral alternative NYOP mechanisms. Section 6 con-siders the allocation of profit across channel members.In Section 7, we offer concluding remarks, includingmanagerial implications and areas for future research.

2 For instance, the conventional wisdom is expressed in Anderson(2009): Priceline’s mechanism “favors the property because 0 0 0 therandom nature of property selection does not require the propertiesto compete with each other on price; they only compete with thecustomer because a firm’s price relative to that of another firm doesnot impact its probability of being selected” (pp. 308–309).

2. Literature ReviewA stream of literature on NYOP channels is emerg-ing. The extant literature can be divided into stud-ies that focus predominantly on (1) how consumersrespond to the NYOP format and (2) how firms canutilize this format. This paper’s main contribution is tothe second stream of study. On the consumer-centricside, previous work has used bidding data to estimateconsumers’ bidding costs and/or their values for theunderlying product (e.g., Hann and Terwiesch 2003,Spann et al. 2004) and highlights the importance ofthe bid-elicitation format (Chernev 2003, 2006; Spannet al. 2012). Researchers have documented that con-sumer bidding behavior depends systematically onthe information about the threshold price distribu-tion (Hinz and Spann 2008, Wolk and Spann 2008,Wang et al. 2010), the expectations that the (hidden)threshold price may change over time (Fay and Laran2009), risk aversion (Abbas and Hann 2010), and theemotional components (such as potential frustrationor excitement) involved in bidding (Ding et al. 2005).In this study, we model consumers as being strate-gic risk-neutral agents who adopt bidding strategiesto maximize expected consumer surplus, taking intoaccount the expected probability a given bid will beaccepted. For tractability reasons, we utilize a staticmodel in which the consumer places at most onebid (as is done in many other analytical studies; see,e.g., Wilson and Zhang 2008, Fay 2009, Shapiro andZillante 2009, Wang et al. 2009, Spann et al. 2010).This assumption is also consistent with the busi-ness model utilized by Priceline, the most prominentNYOP practitioner, which restricts consumers to a sin-gle bid for a given product (where subsequent bidscan only be placed after a specified number of dayshave passed). Our model closely follows Zeithammer(2015) by taking into account that consumers havethe choice of whether to utilize the NYOP channelor to buy the item through a traditional posted-pricechannel.

The second strand of research on NYOP marketsfocuses on how firms can better utilize the NYOP for-mat. Note that the consumer-centric research discussedabove often examines the NYOP format in an environ-ment where consumers can place multiple bids for acertain product. Thus, an often-asked research ques-tion in the firm-focused literature is how a firm isimpacted if it allows consumers to rebid, rather thanrestricting them to a single bid (Fay 2004, Terwieschet al. 2005, Cai et al. 2009). An intuitive finding isthat the opportunity to rebid leads consumers to placelower initial bids. Other research questions addressedin the literature include how a firm might optimally setthe threshold price (Terwiesch et al. 2005, Wilson andZhang 2008) and whether or not charging consumers

Fay and Zeithammer: Format for Soliciting Supplier Participation in NYOP Auctions Impacts Channel ProfitManagement Science, Articles in Advance, pp. 1–22, © 2016 INFORMS 3

for the opportunity to bid might increase profit (Spannet al. 2010).

A key issue that arises in the extant literature is inter-action across channels. In particular, a service providermust determine how to utilize an NYOP channel inconjunction with a posted-price channel (Cai et al.2009, Shapiro and Zillante 2009, Wang et al. 2009).By contrast, the current study focuses on how ser-vice providers interact with the NYOP retailer withinthe NYOP channel. Several common assumptions thatappear in the literature include having a single ser-vice provider (Wang et al. 2009), taking the whole-sale price offered to the NYOP retailer as being givenexogenously (Wilson and Zhang 2008, Terwiesch et al.2005, Cai et al. 2009, Spann et al. 2010, Zeithammer2015), and having service providers offer their ownNYOP products without the use of an intermediary(Fay 2009). Our study enriches the extant literatureby developing a model that includes multiple serviceproviders and an NYOP retailer. This model enablesus to provide unique insights into NYOP markets bystudying the interactions of service providers bothwith each other (as they compete to be the supplier ofthe good) and with the NYOP retailer. These are impor-tant considerations because, as noted in the intro-duction, the most prominent NYOP channels employan intermediary that is not itself a producer of thecore service but instead relies on multiple suppliersto provide the services to its customers. Thus, howservice providers are selected for each particular trans-action and how payments to them are determinedcritically impact the profitability of the NYOP chan-nel (both as a whole and for each channel memberseparately).

Our study also relates to the vast literature on auc-tion design. It is well known that a second-price auc-tion induces competing agents to truthfully reveal theirprivate valuations (Vickrey 1961). For the NYOP chan-nel, however, setting threshold prices through suchan auction among service providers will not, in gen-eral, maximize total channel profit because the NYOPchannel also involves bidding by consumers and usinga second-price auction for procurement (without areserve) will not generate the maximum revenue fromconsumers. In particular, setting the threshold priceequal to the second-lowest cost realization inducesconsumers to place relatively low bids (to take advan-tage of the low threshold prices that occur when mul-tiple service providers have low costs).

The literature on two-sided auctions (e.g., McAfee1992, Friedman and Rust 1993) is more closely relatedto this study. Models of traditional two-sided auc-tions typically involve multiple buyers, assuming thatall of them have submitted their bids prior to anyallocation decisions being made (e.g., Myerson andSatterthwaite 1983, Wilson 1985). By contrast, the

NYOP retailer has to decide whether or not to accepta given bid prior to observing bids from other poten-tial customers. The literature on continuous doubleauctions, which allow for transactions to be com-pleted prior to all bids being submitted, is relativelyscant, and it primarily consists of studies involvingfield and laboratory experiments (Friedman and Rust1993). Theoretical analyses, such as Wilson (1987),rely on incomplete information approaches, whichare heavily dependent on strong assumptions regard-ing common knowledge. Such models assume thatconsumers collect an enormous amount of informa-tion and that they possess unrealistic computationalabilities (Friedman and Rust 1993). By contrast, inan NYOP market, consumers do not need to knowthe history of past bids or have a rational expecta-tion of future bids. Instead, knowledge of the bid-acceptance probabilities is sufficient for a consumerto determine her optimal bidding strategy. However,the NYOP retailer needs to play an active role bothin setting and in publicizing the acceptance rules forconsumer bids.

3. The Model3.1. Supply-Side AssumptionsWe posit two service providers (also interchangeablytermed “suppliers”). It is straightforward to extendthe analysis to allow for additional service providers,but this complicates the notation without qualitativelyaltering our results. We assume each service providerhas access to the traditional retail channel, which offersa unit of either product at a posted price R.3 We do notformally model how R is determined, which wouldpresumably be an outcome of competition in the tradi-tional retail channel. Instead, as is commonly assumedin the extant literature, and in line with the empiri-cal observation that NYOP sales tend to account fora relatively small portion of each service provider’stotal sales, we assume the posted price is given exoge-nously and does not depend upon the bid-acceptancepolicy of the NYOP retailer. A critical assumption ofour model is that neither service provider is guar-anteed the ability to sell all of its capacity at theposted price R. Instead, the probability of exhaust-ing inventory is �1 and �2 for service providers 1and 2, respectively. The two probabilities differ becausethe two suppliers experience idiosyncratic demandshocks (e.g., how many conventions and wedding par-ties have already booked rooms for a certain hotel

3 One way to justify the assumption that both suppliers sell at iden-tical posted prices in the traditional channel is if the two firms arenot vertically differentiated and the products appear undifferenti-ated to the NYOP consumers, who are placing NYOP bids withoutspecifying a particular supplier (i.e., the NYOP product is “opaque”in the nomenclature of Fay and Xie 2008).


on a specific weekend). This reflects the reality thatfixed capacity and demand uncertainty result in thepotential to have unutilized capacity in most serviceindustries.

Let �i = �i × R represent the opportunity cost of aunit of service to service provider i, i = 81129, whichwill, by construction, be less than or equal to R. Thismetric is analogous to the “shadow price” of capacitybecause selling through the NYOP channel is advan-tageous to service provider i only if its payment fromthe NYOP retailer exceeds �i. Thus, when participat-ing in an NYOP channel, a service provider choosesbetween selling a unit to the NYOP customer (at a pricethat will depend on the exact NYOP mechanism thatis being utilized) or retaining this unit for potentialsale through the posted-price channel (which wouldyield an expected profit of �i5. These opportunity costsare assumed to be private information to each serviceprovider, i.e., unobserved by the NYOP retailer, therival service provider, or the consumer. We assume�1 and �2 are drawn independently from a contin-uous distribution G with support on 6�1R7 (wherethe density function is denoted g).4 The study’s keyresults hold for general G. However, to illustrate thekey results and to derive additional insights, we alsoreport an analysis that assumes opportunity costs fol-low a uniform distribution. To reduce notation, we nor-malize the lower limit of the cost distribution to zero;i.e., �= 0.

An intermediary operates the NYOP channel. TheNYOP retailer is selling an opaque good since it doesnot specify to consumers which supplier the productwill be procured from (if the bid is, in fact, accepted)and customers cannot make their bids contingent uponwhich service provider is utilized. This NYOP retailerfaces a key decision: whether or not to accept a givenconsumer’s bid, b. The NYOP retailer must also decidewhich service provider to use whenever a bid isaccepted.

3.2. Demand-Side AssumptionsWe assume a risk-neutral consumer has a private valueV for a unit of the service (the value is private in thatneither the NYOP retailer nor the service providerscan observe V ). The consumer visits the NYOP web-site and places a bid, b, of her choosing. If the bid isaccepted, the consumer obtains a unit of the productand pays b, thus receiving a utility of V − b. If the bidis rejected, the consumer has the option to purchase aunit at the posted price R. The valuation V is drawn

4 The core results of the study continue to hold if costs are cor-related. However, the importance of our study, i.e., examininghow NYOP mechanisms determine which supplier to use to fulfilldemand, hinges upon there being potential differences in suppliers’costs. If costs are identical in every instance, the choice betweensuppliers becomes irrelevant.

from a continuous distribution F 4V 5 with density f 4v5and support on 6V 1 V 7, where V ≥ R. We assume thevirtual value ë4V 5≡V − 41 − F 4V 55/f 4V 5 is increasing;i.e., the distribution F is regular in the sense of Myerson(1981). The virtual value function is a central conceptin the theory of mechanism design, and it representsthe marginal revenue a seller can extract from a con-sumer of type V in a direct revelation mechanism (seeKrishna 2002 for more details).

3.3. Timing of the GameFigure 1 illustrates the timing of the game. First, theNYOP retailer announces its bid-acceptance schedule,A4b5. We assume that this announcement is credible;i.e., the announced bid-acceptance function reports thetrue probability that a bid of size b will be accepted.5

Whether or not there is a formal announcement, weassume that the consumer knows the bid-acceptancefunction before deciding on her bid (perhaps learn-ing it through experience or Internet word of mouth).6

The assumption that the bid-acceptance function isknown to consumers is commonly made in the liter-ature (e.g., Fay and Laran 2009, Almadoss and Jain2008, Wilson and Zhang 2008, Fay 2004, Shapiro 2011,Zeithammer 2015).

Next, the consumer submits a bid, with the bid levelchosen to maximize her expected net utility (takinginto account that she will have an opportunity to pur-chase at the posted price R if this bid is rejected). Then,the service providers observe their opportunity costs ofselling a unit through the NYOP channel (i.e., they geta signal of their �i). The NYOP retailer contacts the ser-vice providers to determine whether or not to acceptthe bid and, if so, which supplier to use. Thus, whethera bid is accepted depends on both the NYOP retailer’sprocurement policy and the service providers’ costrealizations. In subsequent sections, we discuss var-ious ways to structure the procurement mechanism,i.e., the interaction between the NYOP retailer and theservice providers. In equilibrium (with credible com-mitment), the bid-acceptance schedule announced toconsumers must equal the expected probability a par-ticular bid will result in a transaction, where expecta-tions are based on the supplier cost distribution andthe procurement mechanism.

5 As indicated previously, real-world NYOP sellers such as Luft-hansa, Greentoe.com, Meanbuy.com, and Scorebig.com activelycommunicate their bid-acceptance schedules. Through repeatedinteractions (and observation of these interactions, for example, viaposted user comments, chat rooms, and web forums), customers canobserve whether the posted schedules are being (approximately)followed, thus providing NYOP sellers with the opportunity todevelop a reputation for making credible announcements.6 For instance, to learn the probability associated with bids onPriceline, consumers could consult third-party sites (such asFlyerTalk.com, BetterBidding.com, and BiddingForTravel.com) onwhich users post their winning and losing bids.


Figure 1 Timing of the NYOP Model

Consumer submitsbid: b(V )

NYOP seller contactsservice provider(s) toprocure a unit of item

If bid is rejected, consumer can buyat outside market for R ; service

providers retain their items

NYOP seller announces (andcommits to) a bid-acceptance

policy: A(b) = Pr(b is accepted)

Each serviceprovider learns its

opportunity cost: �i

If bid is accepted, buyer pays b toNYOP seller and receives value V;

chosen service provider gets paymentfrom NYOP seller and incurs cost �i

4. Analysis4.1. Optimal Channel ProfitIn this subsection, we use a result of Zeithammer(2015) to derive the maximum channel profit thatcan be generated from the NYOP channel. The es-tablished theory of mechanism design (Riley andZeckhauser 1983) implies that the maximum profitthat would be obtainable in the channel, given ourassumptions about demand and costs, is the profitthat can be obtained by a monopolist who canfirst (somehow) obtain the service for min4�11�25

and then set the optimal take-it-or-leave-it monopolyprice. Zeithammer (2015) takes the retailer’s procure-ment cost as exogenously given and proves that anNYOP selling strategy can reach this theoretical max-imum. He constructs the optimal cost-contingent bid-acceptance policy, Pr4accept b � cost5, the expectation ofwhich then implies the consumer faces the bid accep-tance function A∗4b5= Ecost6Pr4accept b � cost57.

To apply Zeithammer’s (2015) analysis to our model,let M4�5 be the cumulative distribution function ofthe order statistic � = min4�11�25, and let m4�5 bethe associated density function. Consider a hypothet-ical NYOP seller who faces M4�5 as his cost distri-bution. One way to describe the motivation of thisseller is to imagine that our retailer and both serviceproviders are all integrated into a single firm. Sucha firm faces a procurement cost drawn from M4�5

and collects the entire channel profit by construction.The following lemma characterizes the cost-contingentbid-acceptance policy that maximizes channel profit,where this policy consists of an optimal bid accep-tance function, A∗4b5, which takes into account theconsumer’s best response, �4V 5, to this acceptancefunction.

Lemma 1. Let �−R = limV→R− �4V 5. The total channel

profit is maximized by the cost-contingent bid-acceptancepolicy of accepting bids below �−

R whenever b > �4ë−14�55

and accepting bids at or above �4R5 with certainty.

The implied ex ante optimal bid-acceptance function is

A∗4b5=

0 if b < �4�−140551M4�4�−14b555 if �4�−14055≤ b < �−

R1

less than∫ R

�−1405

M4�4z55

R− bdz

if �−R ≤ b < �4R51

1 if b ≥ �4R51

where

�4V 5=

∫ �4V 5

�=0�−14�5

m4�5

M4�4V 55d� if �−1405 < V <R1

R−

∫ R

�−1405M4�4z55 dz if V ≥R1

is the bidding function that best responds to A∗.

Lemma 1 is Proposition 2 of Zeithammer (2015) withM4 · 5 corresponding to the distribution of costs theretailer faces. The appendix contains a sketch of theproof of Lemma 1; see the proof of Proposition 2 ofZeithammer (2015) for more detail. To gain intuitionfor Lemma 1, suppose that the outside posted pricewere irrelevant to all consumers. (Note that this sit-uation corresponds to V = R under our notation andassumptions.) Then, ë−14�5 is the optimal monopolyposted price given a marginal cost of �, and thus b >

�4ë−14�55 is equivalent to accepting bids from con-sumers who would have been able to afford the opti-mal monopoly price. Lemma 1 effectively generalizesthis intuition to the case when V ≥ R, and thus theoptimal monopoly price is min4ë−14�51R5. We post-pone further discussion of the structure of the A∗ and �

functions until the full solution (i.e., both the demandand supply sides) has been presented (i.e., until afterProposition 1).


4.2. Procurement Auction forMaximizing Channel Profit

In the previous section, we identified the demand-sideconditions that optimize total channel profit. Namely,Lemma 1 specifies the bid-acceptance function thatenables the NYOP channel to reach the maximumprofit possible when consumer valuations are privatelyobserved. The analysis in the previous section assumedaway any procurement issues by effectively consider-ing service providers that are fully vertically integratedwith the NYOP retailer. However, the NYOP retailerwe model must procure the service from two indepen-dently managed service providers. Thus, to maximizechannel profit following Lemma 1, the NYOP retailermust implement the cost-contingent bid-acceptancepolicy specified in Lemma 1 even though he does notactually face the cost � = min4�11�25 ∼ M45 as hiscost of procurement from the duopolistic, independentsuppliers.

Suppose the retailer simply invites the suppliers tobid in a second-price sealed-bid reverse auction,7 forc-ing them to reveal their opportunity costs �i (becauseof that auction’s well-known dominant truth-revealingstrategy, first shown by Vickrey 1961). Such an auc-tion results in the NYOP retailer paying max4�11�25 tothe winning supplier. Setting a bid-acceptance rule ofaccepting a bid only if b > max4�11�25 will not inducethe allocation decision implied by Lemma 1. For exam-ple, if max4�11�25 > b > �4ë−14�55, this acceptancerule would lead to a rejected bid, even though sucha bid must be accepted to achieve optimality. On theother hand, if �4ë−14�55> b >max4�11�25, this accep-tance rule would lead to an accepted bid, even thoughsuch a bid must be rejected to achieve optimality. Toachieve Lemma 1’s allocation through competitive pro-curement, the NYOP retailer must use the consumer’sbid to appropriately set the reserve threshold of thereverse auction. Specifically, to achieve exactly the opti-mal cost-contingent allocation, the reserve price needsto be ë4�−14b55, because b > �4ë−14�55, if and onlyif �<ë4�−14b55.

We call the resulting mechanism (a second-price,sealed-bid reverse auction with the channel-optimalreserve price) the MSP auction. Under this mechanism,each supplier, after observing her own �i, submits abid of pi to the NYOP retailer. The following definitiondescribes how the MSP mechanism we propose usesthe suppliers’ bids to determine which (if any) supplieris selected and the transfer price paid by the NYOPretailer to the selected supplier.

7 In a “reverse” auction, the supplier with the lowest bid wins, andthe buyer pays him the second-lowest bid for supplying the good.

Definition (The MSP Auction). Let p1 < p2 denotethe supplier bid prices. Let

�∗4b5=

0 if b < �4�−140551�4�−4b55 if �4�−14055≤ b < �−

R1

less than M−1

(

∫ R

�−1405

M4�4z55

R− bdz

)

if �−R ≤ b < �4R51

R if b ≥ �4R50

After a consumer bids, the NYOP retailer compares thecost threshold �∗4b5 to the service providers’ prices inthe following fashion to determine whether a transac-tion will occur and at what transfer price:

1. If p2 ≤ �∗4b5, the consumer pays b to theNYOP retailer, and the NYOP retailer pays p2 to thelowest-priced supplier in return for providing a unit ofthe good to the consumer.

2. If p2 > �∗4b5 ≥ p1, the consumer pays b to theNYOP retailer, and the NYOP retailer pays �∗4b5 to thelowest-priced supplier in return for providing a unit ofthe good to the consumer.

3. If p1 >�∗4b5, no transaction occurs.

The “medium-bid” case, �−R ≤ b < �4R5, specifies the

channel-optimal reserve threshold only as an upperbound because of the analogous indeterminacy ofA∗4b5 in Lemma 1. Thus, a continuum of (sufficientlylow) reserve prices in this bid region will satisfy thecondition implied by Lemma 1. One value that keepsthe formula for �∗4b5 parsimonious and elegant is to let�∗4b5 = ë4R5 across this entire bid interval. We illus-trate the indeterminacy issue in more detail in Exam-ple 2 and provide a formal remark to show why profitmaximization implies only a bound on the reserveprice for medium bids. Proposition 1 reports the keyproperties of MSP.

Proposition 1 (Optimality of MSP). The modifiedsecond-price auction, described in the MSP definition, in-duces service providers to truthfully reveal their costs tothe NYOP retailer and also achieves the optimal channelprofit by generating the bid-acceptance function outlined inLemma 1.

As explained previously, simply running an uncon-strained second-price sealed-bid procurement auctionwill not enable the NYOP channel to reach its optimalprofit because the consumer’s probability of winningwould be different from that established in Lemma 1.Proposition 1 shows that one modification of a sim-ple second-price auction that does optimize channelprofit is the addition of a reserve �∗4b5, where thereserve price depends on the consumer’s bid level.This reserve is calibrated to induce the bid-acceptanceprobability given in Lemma 1.


Figure 2 (Color online) Examples of the Strategies Within MSP When F and G Are Uniform

Probability of bidacceptance

Valuation

Consumerbidding function

Bid-contingentreserve price

Bid0.500

0.5

0.9

0.8

0.7

0.6

0.5

A* (

b)

1.0

0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00�R

– �(R )

�R–

�(V

)

0.5

1.0

0.5

00.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Bid �R– �(R )

�(R )

V = 0

V = 1/2

�* (

b)

Notes. The thicker dotted (black) lines correspond to Example 1 4V = 05. The thinner solid (red) lines correspond to Example 2 4V = 1/25. The shaded(pink) areas indicate indeterminacy of A∗ and �∗ over the bid interval 6�−

R 1 �4R55 in Example 2. The arrow indicates how the acceptance strategy in thisindeterminate bid interval implies that no bids are submitted inside this interval (a jump discontinuity in the bidding function). The dashed line in the bottompanel indicates the 45-degree line.

Example 1 (F and G Uniform; Outside Price RNot Affordable to Any Consumers). To illustratethe main features of MSP, we begin with an example inwhich no consumer can afford the outside posted-priceoption. Let the consumer valuations and the providercosts both be uniformly distributed on the interval60117, and assume that R= 1. The implied distributionof � is M4�5 = �42 −�5. The virtual value function isë4V 5≡V − 41−F 4V 55/f 4V 5= 2V −1. Using Lemma 1,we find the optimal acceptance strategy A∗ and theconsumer bidding function � that best responds to it:

A∗4b5=

z44 − z5

4if b <

231

1 if b ≥231

where z= max63b−√

342 − b542 − 3b51071 (1)

�4V 5=

∫ 2V−1

0

�+ 12

m4�5

M42V − 15d�

=2 + 4V 41 −V 5

343 − 2V 50 (2)

The reserve price under MSP that induces this opti-mal acceptance strategy, as specified in the MSP defi-nition, is

�∗4b5=

z

2if b<

231

1 if b≥231

where z is defined in (1)0 (3)

These functions for bid acceptance, consumer bid-ding, and reserve price are illustrated by the thickdotted (black) lines in the three respective subplotsof Figure 2. Lemma 1 indicates that the optimal bid-acceptance function involves a minimum bid thresh-old, �4ë−14055, such that any bid below this threshold


will always be rejected. The minimum bid thresholdequals 1/2 in this particular example. Therefore, Fig-ure 2 considers only bids above 1/2, with the under-standing that A∗ = �∗ = 0 for all bids below that level.As a result, consumers with V ≤ 1/2 will not be ableto obtain the good at any bid at or below their val-uations. Rather than submitting a bid that will neverbe accepted, such low-valuation consumers could (andprobably would) simply refrain from bidding.

At the other extreme, any bid of �4R5 or more mustbe accepted with certainty. In this example, �415= 2/3.Thus, in the top panel of Figure 2, we see that the bid-acceptance probability will be 1 if b≥ 2/3. To guaranteeprocurement of a unit of service, the NYOP retailermust set the reserve price 4�∗4b55 to 1 (as illustrated inthe bottom panel of Figure 2 by the fact that �∗4b5 = 1for any b ≥ 2/35. For consumer bids that lie betweenthese two extremes, a bid will be accepted with a pos-itive probability that is increasing in the bid level (andthe reserve price is increasing in b in order to achievean increasing rate of bid acceptance).

An interesting characteristic of this channel-optimalsolution is that some transactions that would gener-ate ex post positive channel profit are foregone, whilesome transactions that generate ex post negative chan-nel profit take place. This can easily be observed inthe bottom panel of Figure 2 by comparing the reserveprice, �∗4b5, to the 45-degree line for which b = � (asindicated by the dashed line). Notice that, for low bidlevels, the 45-degree line is above �∗4b5, which indi-cates that cost realizations can occur such that b > �>�∗4b5. Here, no transaction would occur (since � >�∗4b55, even though the consumer bids more than thatit would cost a supplier to provide the product (sinceb > �5. Now consider higher bid levels for which the45-degree line is below �∗4b5, which indicates that costrealizations can occur such that �∗4b5 > � > b. Here, atransaction would occur (since �<�∗4b55, even thoughthe consumer pays less than that it costs a supplier toprovide the product (since b <�5.

This apparent inefficiency is analogous to the dead-weight losses that arise for a posted-price monopolythat has an incentive to price above marginal cost inorder to maximize profit. In the case of the NYOPmarket, the NYOP retailer does not set the reserveprice equal to marginal cost but instead configuresthe reserve price function to generate a bid acceptancefunction that motivates consumers to bid higher thanthey otherwise would.

Now consider how the MSP mechanism allocatesrevenue from the NYOP market across channel mem-bers. Note that the NYOP retailer does not retain allof the channel profit because he has to compensatethe winning supplier in the procurement auction thatthe MSP Definition characterizes. Whenever a con-sumer’s bid is accepted, the NYOP retailer pays either

max4�11�25 or �∗4b5 to the low-cost service provider.This payment can be quite sizeable and may evenresult in the NYOP retailer experiencing a negativerealized profit from a given transaction; i.e., whenthe payment to the winning supplier exceeds the rev-enue, the NYOP retailer receives from the consumer.For the numerical example, we have �415 = 2/3 and�∗42/35 = 1. Thus, the NYOP retailer receives a pay-ment of 2/3 from the consumer but will make a pay-ment to the service provider that can be as high as 1.Despite the potential of a negative realized profit, theNYOP retailer earns a positive profit in expectation. InExample 1, the optimal channel profit is 1/8.8 Underthe MSP mechanism, this profit is split evenly acrossthe channel members; i.e., each service provider earnsan expected profit of 1/24, and the NYOP retailer alsoearns an expected profit of 1/24.9

It is important to note that the MSP mechanism isdesigned to maximize total channel profit. An NYOPretailer who is optimizing his own profit given hisactual procurement cost would likely choose a differ-ent reserve and, as a result, would generate a lowertotal channel profit than that achieved under Lemma 1.In other words, the MSP mechanism avoids dou-ble marginalization problems that would arise if theretailer set his reserve price to maximize his own profitgiven each bid level. In the next section, we discussalternative NYOP mechanisms that an NYOP retailermay consider as a way to boost his profit.

As an extension to the base model, we consider amarket setting in which side payments between thechannel members are feasible. If transfer paymentscan be made such that each channel member’s shareof the profit is constant across procurement mecha-nisms, then the retailer prefers the MSP mechanism toall other alternatives. For instance, an NYOP retailer

8 A simple way to calculate total profit is to note that Zeithammer(2015) proves that the optimal channel profit is the same as theexpected profit (over cost realizations) of a monopolist who firstlearns his cost and then sets the optimal posted price contin-gent on it. For a given �, a posted-price monopolist would set aprice of 41 + �5/2. Thus, the expected profit is çMSP

Total = çOptimalTotal =

∫ 1�=0441 +�5/2 −�541 − 41 +�5/25241 −�5d�= 1/8.

9 The expected surplus earned by the service providers is çMSPsuppliers =

∫ 1V=1/2

∫ 2V−1�=0

[∫ 2V−1h=�

4h − �/1 − �5dh + 42 − 2V /1 − �542V − 1 − �5]

·

241 −�5d�dV , where h = max4�11�25, and the distribution of hconditional on � is clearly uniform 6�117 because there are exactlytwo suppliers. The first term in the bracket captures the situa-tion when h < �∗4x5, and the second term captures the situationwhen the reserve is binding. Thus, the bracketed term gives theexpected surplus of the winning supplier given V and �. Theouter two integrals merely average over the valuations and low-est costs whenever there is a trade according to the underlyingdirect revelation mechanism. Evaluating this double integral, wefind çMSP

suppliers = 1/12. Since each service provider is equally likely tobe the low-cost supplier, each firm earns an expected profit of 1/24,and the remainder of the channel profit is retained by the NYOPretailer: çMSP

retailer =çMSPTotal −çMSP

suppliers = 1/8 − 1/12 = 1/24.


who uses two-part tariffs and makes take-it-or-leave-itoffers to the service providers could capture all chan-nel profit by utilizing MSP to set the marginal trans-fer prices and using fixed fees to extract the serviceproviders’ entire surplus.

Although the formulas in Lemma 1 and the MSPdefinition are rather complex, implementation of theMSP mechanism is relatively simple. Using the pre-ceding numerical example, the NYOP retailer shouldnever accept a consumer bid that is less than or equal to1/2. This could be incorporated into the bid interfacefor consumers by specifying that only bids in excessof 1/2 are allowable or by automatically generatinga bid rejection message (before searching for supplieravailability) for bids that are “too low.” Furthermore,the MSP mechanism specifies that any bid that is 2/3or larger should be accepted with a probability of 1.This could be incorporated into the bid interface byusing a “buy-it-now price.” Thus, the bid interfacewould allow consumers to bid between 1/2 and 2/3.A table or figure could be displayed indicating to con-sumers how likely it is for a given bid to be acceptedin this intermediate region (see Figure 5 for an exam-ple of such a display from Greentoe.com). On the sup-ply side, the NYOP retailer would set a reserve priceaccording to �∗ 4b5 after receiving a consumer bid of b.The service providers would submit their price bids (orhave them held in a database that could be updated asfrequently as desired). These price bids would dependon the cost realizations, and the price bids (in conjunc-tion with the reserve price) would determine whetheror not a given bid is accepted. While such a mecha-nism is clearly logistically feasible, issues of credibilitycould be very important. In particular, a consumer mayworry that the NYOP retailer will deviate from theseposted acceptance rates. Indeed, this potential lack ofcommitment is a main rationale for why we consideralternative NYOP mechanisms in the next section. Wediscuss the issue of credibility in more detail in theconcluding section of the paper.

Example 2 (F and G Uniform, and Outside PriceRAffordable to Some Consumers). Before turning toalternative NYOP mechanisms, we must examine oneaspect of the MSP mechanism left out of the previousexample. Example 1 assumes that no consumer wouldbe willing to buy at the posted price. This examplehelps one understand the central driving factors of theMSP mechanism and captures market environments inwhich the NYOP channel fully segments consumers,i.e., enables service providers to reach only the cus-tomers who would not purchase through traditionalchannels. However, in practice, segmentation may notbe perfect, and some consumers who use the NYOPchannel may be willing to purchase through the tradi-tional channel. To explore such market situations, we

keep the assumptions about the supply side the sameas in Example 1, but we shift the distribution of val-uations up by V to become V ∼ U6V 1V + 17, whereV ∈ 60117 (so Example 1 is a special case with V = 05.10

Under these assumptions, F 4V 5 = V − V , so the vir-tual value function becomes ë4V 5 = 2V −V − 1. Theconsumer’s bidding function under MSP, as given inLemma 1, is thus

�4V 5=

16

(

2+4V +V −2

3−2V +V

)

if V <11

4−V 3 +3V6

if V ≥11

(4)

with an inverse of

�−14b5=4 + 6b+V −

√

344 +V − 2b544 + 3V − 6b58

for b < �−

1 = limV→R−

�4V 5= 1 +V

6−

1341 +V 5

0

The corresponding bid-acceptance policy is

A∗4b5=

0 if b < 41 +V 5/2142�−14b5−V − 1543 − 2�−14b5+V 5

if 41 +V 5/2 ≤ b < �−1 1

less than2 − 3V +V 3

641 − b5if �−1

1 ≤ b < 44 −V 3 + 3V 5/611 if b ≥ 44V 3 + 3V 5/60

(5)

The optimal reserve is

�∗4b5=

0 if b<41+V 5/2124�−14b55−1−V

if 41+V 5/2≤b<�−1 1

less than 1−

√

1−2−3V +V 3

641−b5

if �−11 ≤v<44−V 3 +3V 5/61

1 if b≥ 44−V 3 +3V 5/60

(6)

Figure 2 illustrates this example for V = 1/2, usingthe thinner solid (red) lines. The graphs for Example 2share many of the same characteristics as those forExample 1. In particular, a lower threshold of bid levelexists, below which all bids are rejected and a higherthreshold exists, above which all bids will be accepted.Because of the higher valuations, these thresholds arehigher than in Example 1 (increasing from 1/2 to 3/4for the lower threshold and from 2/3 to 43/48 ≈ 00896for the higher threshold). A notable difference from

10 Under these assumptions, the expected channel profit is çMSPTotal =

43 −V 541 +V 53/24.


Example 1 is that all consumers whose valuationsexceed the posted price in the non-NYOP channel (i.e.,V ≥ R = 1) bid the same amount, effectively mimick-ing the consumer with V =R, because they have a realoption to buy in the outside market should their NYOPbid be rejected. The NYOP retailer wants to inducehigher bids from this high-value segment as its sizeincreases, but to do so, it must reduce the probabilityof accepting low bids (sacrificing sales from low-valuecustomers to generate more revenue from high-valueones).

The top and bottom panels of Figure 2 contain ashaded region, which corresponds to the third line ofthe equation for A∗4b5 in Lemma 1, for which optimal-ity implies only an upper bound when bids are withinthe 6�−

R1�4R550 interval. Thus, any value in the shadedregion is equally profitable. The reason for the inde-terminacy is that for all the possible values of A∗4b5in the shaded region, no consumer has an incentive tosubmit a bid in the 6�−

R1�4R550 interval; this jump dis-continuity is indicated by the arrow pointing from thetop panel to the middle panel of Figure 2. We formal-ize this result in the following remark in regard to thereserve price.

Remark. The bid-contingent reserve price �∗4b5 thatobtains the optimal channel profit is not unique.

While this remark indicates the presence of multipleequilibria, it is important to recognize that all equilibriainduce the same bidding behavior and allocation deci-sions, and thus result in the same total channel profit.

5. Other Common or HypothesizedPricing Mechanisms

Adoption of the MSP mechanism hinges upon theretailer and the supplier firms’ ability to coordinateon an NYOP contract structure that maximizes totalchannel profit. A necessary component of the optimalselling strategy is the retailer’s credibility in establish-ing the optimal bid-acceptance function. Because suchconditions may be challenging to achieve in practice,we draw both on practice and on the existing literatureto identify three alternative ways one could structureNYOP pricing mechanisms, and we analyze how thesealternative mechanisms perform relative to the opti-mal profit available in the NYOP channel. This analysisprovides insight into factors that can undermine theprofitability of the NYOP channel.

5.1. Demand CollectionAt its core, an NYOP mechanism collects offers tobuy from individual customers and communicates thisdemand directly to participating sellers. We begin ouranalysis of alternative NYOP mechanisms by con-sidering an NYOP channel that operates merely as

a collection platform to facilitate the transference ofconsumer bids to potential suppliers. Consider thefollowing model of such an interaction, in which a con-sumer’s bid is presented to suppliers in a sequentialfashion:

1. A consumer bids b for a unit of the product.2. The NYOP retailer randomly selects a service

provider and queries it to see whether it is willing tosell a unit of its product at the price b. If it agrees, thenthe bid is accepted, and the service provider receives apayment of b.

3. If the first supplier rejects the bid, the NYOP re-tailer queries the other service provider to see whetherit is willing to sell at the price b.

We refer to this NYOP mechanism as demand col-lection (DC) since the NYOP retailer does not receivea payment for each transaction. This is consistent witha market structure in which the service providers paya fixed fee to have access to the consumers, or if theNYOP channel is jointly owned by the suppliers (sim-ilar to the way in which Orbitz.com developed as apartnership of several airline companies in the non-NYOP hospitality market).

We analyze the above three-stage game via back-ward induction. In the third stage (if it occurs), serviceprovider j has two choices: accept the bid (and thusreceive a net payoff of b − �j5 or reject the bid (andreceive a payoff of zero). Clearly, the service providershould accept the bid only if �j ≤ b. Similarly, in thesecond stage, provider i can accept the bid (for a payoffof b−�i) or reject the bid (for payoff of zero). Thus, ser-vice provider i will accept the bid only if �i ≤ b. Nowturn to the first stage. Anticipating the responses bythe service provider, the consumer knows her bid willbe accepted (by one of two service providers) if andonly if b >�= min4�11�25 Recall that we denote M4�5as the cumulative distribution function of the orderstatistic �. Thus, the consumer will choose b to maxi-mize CS = 4V − b5M4b5 if V <R or CS = 4R− b5M4b5 ifV ≥R.11 Let bDC4V 5 be the bid level that maximizes thesurplus for a consumer with valuation V . For example,suppose R = 1 and �i ∼ U60117 as in Example 1. Forthese parameters, M4�5 = �42 − �5, and the resultingconsumer’s optimal bid function is

bDC4V 5=

2+V−√V 2 − 2V + 4

3if V < 11

3 −√

33

≈ 0042265 if V ≥ 10

(7)

11 The high-valuation consumers with V ≥ R mimic the consumerwith V =R as in the main model. The outside option price R gener-ates the expected surplus M4b54V − b5+ 61−M4b574V −R5= 4V −R5+ 4R− b5M4b5.


The expected profit to supplier 1 (who is symmetricwith supplier 2) is

çDCS1 =F 4R5EV<R

[(

1−G4bDC4V 55

2

)

G4bDC4V 55

·E�1 ��1<bDC 4V 54bDC4V 5−�15

]

+61−F 4R57

(

1−G4bDC4R55

2

)

G4bDC4R55

·E�1 ��1<bDC 4R54bDC4R5−�150 (8)

The first term of Equation (8) gives the profit whenthe consumer’s valuation is below R, and either onlysupplier 1 is willing to sell for the consumer’s bid(probability 41−G4b55G4b55 or both suppliers’ costs arebelow R, and the mechanism thus splits their profitsin half, resulting in supplier 1 winning with proba-bility G24b5/2. The second term of Equation (8) thenanalogously captures the profit when the consumer’svaluation is above R. The total profit created underDC is çDC

Total =2çDCS1 , since each service provider earns

an expected profit of çDCS1 and the NYOP retailer earns

zero profit.Let V =min4V 1R5 be the effective consumer valua-

tion the NYOP retailer faces. Total channel profit is

çDC=EV 6M4bDC4V 55E�1 ��1<bDC 4V 54b

DC4V 5−�1570 (9)

In other words, a consumer with effective valuationV will have his bid accepted with the probability ofM4bDC4V 55 and delivers a profit equal to an expecteddifference between his bid and all possible costs of asingle supplier that fall below the bid.

5.2. Percentage Margin CommissionIn contrast to DC’s essentially benevolent NYOP re-tailer who does not distort the communication betweenthe consumer and the suppliers, the NYOP retailercould seek to capture profit from each transaction.A simple way to do so would be to transfer only aportion, rather than all, of the consumer’s bid to theselected service provider. Here, we assume the NYOPretailer specifies its required margin (or commission)in percentage terms. Specifically, under the percentagemargin (PM) mechanism, the NYOP retailer retains afraction � of the bid value for itself. Thus, a sale occursonly if a service provider is willing to provide the goodto the consumer for 41−�5 times the bid value. Anexample of a percentage margin used in the NYOPchannel is described by Malhotra and Desira (2002),who assert that Priceline seeks to find a hotel thatallows it to receive a 7% margin by using a randomizerprogram to choose among the hotels that are willingto accept this offer. Furthermore, Elkind (1999) reportsthat Priceline’s negotiation with Delta Airlines speci-fied that the latter retained “any gross profits over 12%on the Delta seats.” This PM setup is also consistent

with the NYOP model utilized by Chiching.com, inwhich the NYOP retailer solicits bids from consumers,passes them along to participating merchants, and col-lects a 15% commission only when a merchant acceptsan offer.

Let � be the percentage commission retained by theretailer. Under PM, having received a bid of b, theNYOP retailer randomly selects a service provider andqueries it to see whether it is willing to sell a unit of itsproduct at the price 41−�5b. If it agrees, then the bidis accepted, and the NYOP retailer makes a paymentof 41−�5b to that service provider. If it does not agree,the NYOP retailer queries the other service provider tosee whether it is willing to sell at the price 41−�5b. Ser-vice provider i is willing to accept the NYOP retailer’soffer as long as �i ≤ 41−�5b. Note that the previouslyconsidered demand collection system is a special caseof the percentage margin mechanism in which �=0.

Observing the structure of the game, the consumeranticipates that her bid will be accepted if and only if�≤ 41−�5b. We assume that the NYOP retailer chooses� to maximize its own profit, and since � is publiclyannounced, the consumer knows its value when shedecides on her bid. Thus, the consumer will choose bto maximize CS= 4V −b5M441−�5b5 if V <R or CS=

4R−b5M441−�5b5 if V ≥R. Let bPM 4V 1�5 be the bidlevel that maximizes the surplus of a consumer withvaluation V , when the commission rate is �. For exam-ple, the consumer’s optimal bid function under uni-form G and R=1 is

bPM 4V 1�5

=

2+41−�5V −√

4−V 41−�542−V 41−�55

341−�5if V <11

3−�−√

4−41−�543−�5

341−�5if V ≥10

(10)

The NYOP retailer recognizes that its choice of �will impact the consumer’s optimal bid. Thus, theNYOP retailer chooses � to maximize (“I” stands for“intermediary”):

çPMI =

∫ R

y=V

∫ 41−�5bPM 4y1�5

x=0�bPM 4y1�5m4x5f 4y5dxdy

+

∫ V

y=R

∫ 41−�5bPM 4R1�5

x=0�bPM 4R1�5m4x5f 4y5dxdy0

(11)

Let �∗ be the value of � that maximizes the profitgiven in (11).12 For instance, numerical calculations for

12 One could envision market settings in which � chosen to max-imize an objective function other than the NYOP retailer’s profit.However, all the analytical results that follow depend only on �being positive.


the example with uniform distributions show that �∗

ranges from 0.54 to 0.58 as V goes from 0 to 1.Let V =min4V 1R5 be the effective consumer valua-

tion the NYOP retailer faces. The expected profit to ser-vice provider 1 (who is symmetric with supplier 2) is

çPMS =EV 6M4b4V 1�∗55E�1 ��1<b4V 1�∗54b4V 1�∗5−�1571 (12)

where b4V 1�∗5= 41−�∗5bPM 4V 1�∗5 is the effective bidreceived by the suppliers. Note that Equation (12) isderived from Equation (8) by replacing bDC4V 5 withb4V 1�∗5.

5.3. First-Price, Sealed-Bid Supplier AuctionAnother way the NYOP retailer could extract profitfrom the NYOP channel would be to keep the spreadbetween the consumer’s and the seller’s bid for itself.Indeed, this is how Ding et al. (2005) describe Price-line’s system: “Priceline takes a bid from a consumerand then000searches its price database, which containsthe lowest acceptable prices by various airlines part-ners at that time. If the bid price is higher than thelowest fare available to Priceline, it will accept the bidand retain the spread (bid − lowest fare) as its profit”(p. 352). Similar descriptions of Priceline’s businessmodel are provided in Terwiesch et al. (2005), Hannand Terwiesch (2003), Wang et al. (2009), and Wanget al. (2010). In such a system, service providers areencouraged to compete for the opportunity to be thechosen supplier for a given consumer. We assume theservice providers’ bids are kept secret from each otherand refer to this mechanism as a first-price, sealed-bid(SB) mechanism.

Consider the following game setup:I. Having experienced a privately observed, real-

ized cost of �i, each service provider simultaneouslysubmits a bid price Pj , j=81129. These prices are notobserved by the consumer.

II. The consumer submits a bid b.III. The NYOP retailer compares b to the lowest sub-

mitted price by the suppliers. If b≥min6P11P27, the con-sumer pays b to the NYOP retailer, and the NYOPretailer pays min6P11P27 to the supplier with the lowestbid in return for providing a unit to the consumer. Ifb<min6P11P27, no transaction occurs.

A supplier’s optimal bid price will depend on itsown realized cost, the expected bid price of the rivalservice provider, and the expected bid level of the con-sumer. In particular, service provider 1 observes �1,conjectures that service provider 2 follows a biddingrule P24�25, and anticipates that the consumer bid isdrawn from the distribution D4x5 with support onthe interval 6b1b7. Let �4P5 be the inverse function ofP24w25. For a given �1, supplier 1’s expected profit is

çSBS14P15=

∫ R

�2=�4P15

∫ b

b=P1

4P1 −�15d4b5g4�25dbd�20 (13)

Supplier 1 chooses P1 to maximize (13). In equilibrium,a supplier’s expectation of the other’s bidding rulecoincides with the actual bidding rule the other fol-lows, and as a result of symmetry, the suppliers havethe same bidding function, which we denote as P SB4�i5.Thus, the lower-cost supplier will win the auction.

Now consider the consumer’s optimal bid (whichwill determine D4x55. The consumer knows a bid ofb will be accepted only if P SB4min6�11�275≤b. Thus,the consumer chooses b to maximize CS= 4min6V 1R7−b5Prob6b≥P SB4min6�11�2757. Let bSB4V 5 be the bidlevel that maximizes the consumer surplus of a con-sumer with valuation V .

A Nash equilibrium, characterized by the orderedpair 4bSB4V 51P SB4�55, exists when the consumer is bestresponding to the service providers’ bid price function,P SB4�5, and the service providers are best respondingto each other, with the consumer’s bid drawn fromD4x5, whereD4x5 is cumulative distribution that resultswhen the consumer uses the bidding rule bSB4V 5. Inthis equilibrium, the NYOP retailer earns an expectedprofit of çSB

I =∫ R

�=0

∫ b

b=P SB4�54b−P SB4�55d4b5m4�5dbd�,

and the total profit for the NYOP channel is çSBTotal =

∫ R

�=0

∫ b

b=PSB4�54b−�5d4b5m4�5dbd�. Figure 3 illustrates

this profit for the example of R=1, �i ∼U60117 and V ∼

U6V , V +17, where 0 ≤V ≤1. The equilibrium is calcu-lated numerically via repeated iterations until the bidfunction of consumers and the service providers con-verge to a stable solution in which all agents are bestresponding to each other.

5.4. Suboptimality of Alternative SellingMechanisms

Proposition 2 compares the profit under the threealternative NYOP mechanisms to the optimal channelprofit.

Proposition 2 (Suboptimality of Common Pric-ing Mechanisms). The NYOP pricing mechanisms de-mand collection, percentage margin, and sealed bid yieldstrictly less total channel profit than the optimal channelprofit, çOptimal

Total .

Proposition 2 shows that none of the three alter-native mechanisms achieves the maximum channelprofit. The logic behind this result is straightforward:none of these alternative procurement mechanismswill generate the optimal bid-acceptance function. Oneeasy way to see this is to note from Lemma 1 that, toreach the optimal NYOP channel profit, one necessarycondition is that all consumers with V ≥R must receivea unit of the product regardless of the cost realization.However, under DC, PM, and SB, the bid submitted bysuch a high-value consumer will be strictly less thanR; i.e., each consumer will shade her bid downward inorder to maximize her expected surplus. Under eachof these three mechanisms, such a bid will be accepted


Figure 3 (Color online) Profit Comparisons of the NYOP Mechanisms

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1.0

Cha

nnel

pro

fit (

Π)

Minimum customer valuation (V )

% margin

Demand collection

Optimal = MSP

Sealed bid

with a probability of less than 1 (since it is possible for�1 =�2 =R5.

While it may not be surprising that (unlike MSP)DC, PM, and SB do not reach the optimal NYOP chan-nel profit, it is more interesting to examine the magni-tude of these shortfalls. For instance, intuition drawnfrom the preceding paragraph might suggest the short-fall is small (or even trivial) since the identified “lost”transactions (that occur when both service providershave high cost realizations) would yield relativelysmall returns (or even be negative). It is obvious thatthe exact magnitude of the shortfall in channel prof-its will depend on the underlying parameters and thecost/value distributions. However, to provide insightregarding the relative performance of these variousNYOP mechanisms, we present results using numer-ical examples. In particular, Figure 3 illustrates thechannel profit for these mechanisms as V varies from 0to 1, under the assumptions that R=1, �i ∼U60117, andV ∼U6V , V +17. Examples 1 and 2 are special cases ofthis family of assumptions.

Figure 3 demonstrates that the optimal NYOP chan-nel profit that can be reached via MSP is substantiallylarger than that under the other NYOP mechanisms.At V =0, DC obtains only 28.4% of the profit possibleunder MSP. For PM and SB, the percentages of opti-mal profit obtained are 33.8% and 82.2%, respectively.For V =1, the sacrificed profit is even more significant,with PM, DC, and SB obtaining only 20.1%, 21.1%, and56.5% of the optimal profit, respectively. Note that theprofit under SB is substantially larger than that underPM and DC. This advantage of the sealed-bid formatarises from the increased efficiency of the SB mecha-nism: unlike PM and DC, SB always selects the lowest-cost supplier by forcing them to compete for the bidder.

A key factor that explains the large magnitude of theprofit shortfalls relative to MSP is that consumers bid

much lower when they face the PM, DC, or SB versionsof the NYOP mechanism. Lower bids occur becausePM, DC, and SB lead to higher bid-acceptance rates forlow bid levels (relative to MSP). Figure 4 shows thebid-acceptance probabilities across the various mech-anisms for two cases, V =0 and V =1. First, considerthe case of V =1. With this distribution of consumervaluations, any consumer is willing to purchase in theposted-price market if her bid at the NYOP channelis rejected. As a result, the optimal bid level does notdepend on the value realization. To maximize NYOPchannel profit through the MSP mechanism, the NYOPseller would establish an acceptance rule that any bidat or above 1 will be accepted, while any bid below thisthreshold will be rejected. In response, a consumer willbid 1. By contrast, under DC, the consumer knows herbid will be accepted whenever b≥min6�11�27 (a valuethat is very likely to be significantly less than 1). Takinginto account the distribution of min6�11�2] (as shownin Figure 4(b)), the consumer maximizes her expectedsurplus by bidding 0.423 (i.e., less than half of what shewould have bid under MSP). Instituting a commissionfee via PM makes low bids less likely to be accepted,as shown in Figure 4. Such a downward shift in theacceptance rate schedule slightly increases the bid aconsumer would place (to 0.47). But PM also leads toother demand-side inefficiencies because it creates asituation in which transactions occur only if there isa substantial gap between a consumer’s bid and theprocurement cost, thus eliminating all transactions thatwould generate only moderate or small profit margins.Thus, as Figure 3 shows, both DC and PM generatemuch less channel profit than the optimal NYOP mech-anism. The SB mechanism creates an incentive for ser-vice providers to shade their bid prices upward (since,under this first-price auction, payment will equal thesubmitted bid price). This shading behavior has anespecially large effect when a service provider realizesa very low cost (and thus anticipates that the other sup-plier is likely to have significantly higher costs). Takinginto account this shift in bid prices, the consumer willbid at 0.701, which is significantly higher than underPM or DC, but still much lower than under MSP.

Now consider the case of V =0, where the bid accep-tance function for this example is given in Figure 4(a).Under MSP, the NYOP retailer rejects all bids below1/2 and any bid at or above 2/3 will be accepted forsure. As a result, a consumer with V <1/2 will not bid,and consumers with valuations between 1/2 and 1 willplace a bid between 1/2 and 2/3, with higher valu-ations leading to higher bids. By contrast, the largestbid induced under PM, SB, and DC is 0.469, 0.61, and0.423, respectively. Furthermore, whereas MSP wouldinduce a consumer with V =1/2 to bid her true val-uation (namely, 1/2), a consumer with V =1/2 will


Figure 4 (Color online) Probability of Bid Acceptance

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only bid 0.243, 0.404, and 0.232 under PM, SB, and DC,respectively.

These examples help illustrate the potential short-comings of various NYOP mechanisms. Specifically,the analysis suggests that the format used to solicitservice providers’ participation in the NYOP channelcan significantly impact consumer bidding behavior.If a consumer anticipates a substantial possibility thata low bid will be accepted, she will significantly shadeher bid downward. This bid-shading effect is espe-cially large when the NYOP retailer simply collectsdemand and transfers the bids, in full, to the par-ticipating suppliers. To counteract such bid shadingby consumers, the NYOP retailer can take an activerole in trying to reduce the probability that low bidswill be accepted. There are several means of doing so,including implementing minimum margins that mustbe achieved on each transaction, setting minimum lev-els at which consumers must bid to use the NYOPsystem, and having the service providers bid to bethe chosen supplier (since they will have an incen-tive to place bids in excess of their true costs). How-ever, such shifts in the acceptance rate under thesealternative mechanisms cannot replicate the optimalbid-acceptance function and thus fall short of maxi-mizing channel profit. To achieve the optimal bidderincentives, the NYOP retailer must actively managethe acceptance rate, which will involve strategicallyaccepting some bids that are below realized costs andrejecting some bids that are above them. Our identifiedMSP mechanism is capable of generating this optimumbid-acceptance function.

Furthermore, one must carefully consider whetheror not a mechanism achieves supply-side efficiency.The NYOP retailer must ensure that the mechanism is

providing an incentive for service providers to truth-fully reveal their costs and that this cost information isbeing used to fulfill demand in the most cost-efficientmanner possible. Margin-based strategies, such as PM,do not always identify the lower-cost service provider,e.g., when both service providers can provide theproduct at the requested margin. In such cases, thehigher-cost service provider may be the chosen sup-plier, thus leading to a smaller total channel profit.

6. Allocation of Profit AcrossChannel Members

In this section, we discuss the allocation of channelprofit among channel members. This is an importanttopic since channel members are primarily concernedwith their own profit.

Let çMSi 4T 5, ç

MI 4T 5, and çM

Total be, respectively, theexpected profit for each supplier, for the NYOP retailer(i.e., “Intermediary”), and for the entire channel underselling mechanism M , where çM

Total =2çMSi +çM

I and Tis a lump-sum transfer payment from a supplier to theretailer. Specifically, the NYOP retailer charges eachservice provider a fixed fee 4T 5 for the right to be aparticipating supplier. Note that T can be negative, inwhich case the NYOP retailer pays the suppliers to jointhe NYOP channel. Suppose that channel profit is allo-cated so that each service provider receives a share SSof the total channel profit; i.e., çM

Si 4T 5=SS ×çMTotal and

çMI 4T 5= 41−2SS5×çM

Total. For instance, SS could reflectthe outcome of a Nash bargaining solution, which isa common way of modeling noncooperative negoti-ation (Binmore et al. 1986). For example, Draganskaet al. (2010) model a setting with multiple retailers andmanufacturers by analyzing one manufacturer–retailerdyad at a time. Dukes and Gal-Or (2003) find that the


Nash bargaining solution involves each pair splittingthe gain from the market evenly. For the setting inthe current study, bargaining power, represented by SS ,determines what level of T results from the negotia-tions between channel members. Note that the criticalassumption is that SS is not a function of the sellingmechanism M . For example, this assumption holds ifthe channel members are engaged in Nash bargain-ing and the value of the outside options are zero. Inour model, it is reasonable to assume that the outsideoptions (also known as disagreement payoffs shouldnegotiations fail) are zero, since the NYOP retailer willhave no products to sell if the suppliers do not partic-ipate in the NYOP channel, and the opportunity coststo the suppliers of selling a good through the NYOPchannel are subsumed into the costs �i.

The choice of selling mechanism is modeled as athree-stage game. In the first stage, the NYOP retailerchooses M , where M equals MSP, DC, SB, or PM.In the second stage, the fixed fee T is determined,e.g., via bilateral negotiations. In the third stage, aconsumer arrives at the NYOP channel and places abid. Contingent on the chosen mechanism, the analy-sis from Sections 4 and 5 gives the consumer’s opti-mal bid, whether or not this bid is accepted, and thesize of the payment made to each respective channelmember. Allowing a service provider to choose M inthe first stage would not alter the results that follow.Furthermore, allowing for additional mechanisms willnot impact the equilibrium profit, since Proposition 1shows that no mechanism can yield more channelprofit than MSP. Proposition 3 summarizes the resultsof this game.

Proposition 3 (Channel Member Profit). In equi-librium, the NYOP retailer chooses the modified second-price auction. Each supplier earns an expected profit of SS ×ç

OptimalTotal , and the NYOP retailer earns an expected profit

of 41−2SS5×çOptimalTotal . A supplier participation fee is set at

T =çMSPS1 −SSç

OptimalTotal .

Since the channel members will share channel profitaccording to a predetermined percentage, they havean incentive to utilize the mechanism that generatesthe highest total channel profit. MSP is a mechanismthat achieves this optimal level. Transfer payments areused to ensure that each channel member receives itsappropriate share of the surplus.

An important implication of Proposition 3 is that,when fixed transfer payments between channel mem-bers are feasible, switching to MSP from another cur-rently used NYOP procurement mechanism can bestructured in a way to generate a win-win-win out-come. To illustrate this result, consider an NYOP chan-nel that currently yields an expected profit of çI forthe NYOP retailer and çS for each of the two serviceproviders. Define çTotal =çI +2çS and SS =çS/çTotal.

Now, suppose the firms switch to the MSP mecha-nism and agree to transfer payments from each ser-vice provider to the NYOP retailer such that T =

çMSPS1 −SS ×çMSP

Total. Under this new system, each serviceprovider earns a net profit of SS ×çMSP

Total, whereas eachearned a profit of SS ×çTotal under the previous format.The retailer now earns a net profit of 41−2SS5×çMSP

Total,whereas it previously earned a profit of 41−2SS5×çTotal. Define ã=çMSP

Total −çTotal. From Proposition 3, weknow ã≥0. Thus, this switch to MSP would increaseeach service provider’s expected profit by SS ×ã andwould increase the NYOP retailer’s expected profitby 41−2SS5×ã. In other words, each channel memberbenefits, independently, from switching to MSP, withthe magnitude of each member’s benefit depending ontheir bargaining power.

7. Concluding CommentsThe results of this study show that the specific mecha-nism used by an NYOP retailer to identify a supplier tomeet consumer demand can significantly impact howmuch profit is generated by the NYOP channel. Dif-ferent mechanisms influence the channel profit bothdirectly by selecting different suppliers and indirectlyby affecting consumer bidding strategies. We constructa mechanism we call the modified second-price auctionthat maximizes channel profit by simultaneously iden-tifying the lowest-cost supplier and inducing con-sumers to bid at the maximum level possible given thata consumer’s valuation is private information.

Our second main finding is that several NYOPmechanisms used in the industry and commonly dis-cussed in the extant literature do not maximize chan-nel profit. However, before wholeheartedly advocatingthat NYOP firms adopt MSP, it is important to considerpotential impediments that might be encountered dur-ing implementation. For an NYOP retailer to imple-ment the optimal NYOP strategy, consumers have tobelieve that the acceptance probability associated witha particular bid is given by the bid acceptance func-tion the retailer announces. Similar issues of crediblecommitment arise for other marketing strategies, suchas advance selling, i.e., committing to a future postedprice (Xie and Shugan 2001) and committing not tohaggle with customers (Desai and Purohit 2004). How-ever, in these cases, a breach (e.g., a posted price thatdiffers from what was promised or a price concessionfrom haggling) is verifiable. In our setting, the NYOPseller must commit to a bid-acceptance policy, wherethe bid-acceptance probability is not verifiable unlessconsumers can observe a large sample of bid outcomes.Thus, the credibility issue our NYOP retailer faces ismore similar to the commitment problems that arisefor stochastic auditing, where a tax collector commitsto an auditing probability (Border and Sobel 1987) and


Figure 5 (Color online) Bid-Acceptance Information at Greentoe.com

Source. https://www.greentoe.com/product/Sigma_18-35mm_f-1-8_DC_HSM_Lens_for_Canon_210-101?keyword=Sigma+18-35. Used with permissionfrom Greentoe.

probabilistic selling, i.e., committing to random prod-uct assignments (Fay and Xie 2008).

As discussed in Section 4.2, lower and upper boundsfor the bid-acceptance function can be established viasimple modifications to the bidding interface, e.g., byonly allowing consumers to enter bids within a cer-tain range. While it may be more difficult to estab-lish the probability of acceptance for intermediate bidvalues (Zeithammer 2015), as mentioned in the intro-duction, several online retailers already convey theapproximate probability that a bid will be accepted.For example, Figure 5 presents several screenshotsfrom Greentoe.com.13 These screenshots indicate that avery low bid ($100 on a lens that has an online priceof $799) has a very low success rate. By contrast, a bid

13 Note that a customer is not restricted to the three particularbid levels shown in Figure 5. By adjusting one’s proposed bid,a customer can explore the entire spectrum of possible bids anddetermine the corresponding acceptance rate of each.

of $500 has a moderate chance of success, and a bid of$700 is very likely to be accepted. It would be straight-forward for an NYOP seller to modify these graphsto convey the probability of acceptance that occursunder MSP.

The more challenging issue for the seller is howto induce customers to believe these acceptance ratesreflect the actual bid acceptance policy. It may bepossible for a seller to obtain such credibility viareputation building, e.g., through transparent obser-vation of previous responses to consumers’ bids. Theseller can establish such a reputation if consumersare able to observe prior acceptance/rejection deci-sions. The Internet has facilitated the spread of wordof mouth, thus enabling users to learn more eas-ily about other users’ experience with NYOP retail-ers. For instance, BiddingForTravel.com, which hasexperienced over 100 million visits, is a forum inwhich Priceline users report which bids have beeneither accepted or rejected (Fay and Xie 2008). By

https://www.greentoe.com/product/Sigma_18-35mm_f-1-8_DC_HSM_Lens_for_Canon_210-101?keyword=Sigma+18-35


Figure 6 (Color online) Channel Member Profit in the Absence of Transfer Payments

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viewing the listings that are most closely related toone’s current purchase decision, a consumer can esti-mate the probability of winning with a particular bid.Or, if an NYOP retailer were to announce a certainbid-acceptance function, a consumer could determinewhether or not actual bid acceptance rates differ sig-nificantly from the announced rates. Such observa-tions could facilitate development of a reputation fortruthful announcements. Sellers could accelerate thisprocess by financially backing the development andpromotion of such consumer forums. Furthermore, anNYOP retailer might introduce an automated report-ing system in which the bid rejections and acceptancesare verified by a third party and automatically postedto that third party’s website. Such an automated proce-dure would increase both the amount and the accuracyof information available to potential buyers.

It is important to note that developing a reputa-tion for following the announced bid acceptance pol-icy requires consumers or a third-party auditor to beable to observe a large sample of bid outcomes. Thus,implementation of MSP would be very difficult, if notimpossible, in thin markets in which transactions occurinfrequently. However, repeated transactions of thesame product are not required since the reputation con-cerns the relationship between the stated and actualprobability of acceptance by the same retailer, not nec-essarily for the same product (Zeithammer 2015). Sincereputations take time to build, this NYOP mechanismwould only be applicable for sellers who are suffi-ciently focused on long-run profits rather than short-term gains.

An NYOP retailer’s lack of necessary informationcan also impede implementation of the optimal NYOPselling mechanism. In particular, to establish the opti-mal acceptance-rate schedule, the NYOP retailer must

know the distributions of customer valuations and ofthe suppliers’ opportunity costs. Absence of such infor-mation would also impede the ability to set appro-priate transfer payments between the NYOP retailerand its service providers. Without such transfer pay-ments, each channel participant’s profit may not bemaximized by utilizing the MSP selling mechanism.In Figure 6, we show the expected profit of the ser-vice providers and the NYOP retailer, respectively,under the assumption of a uniform cost distributionon 60117 and a uniform value distribution on 6V 1V +17.Notice from Figure 6(a), in the absence of any participa-tion fees, a service provider’s expected profit is higherunder our proposed MSP mechanism than under anyof the other alternative NYOP mechanisms discussedin the paper (with the percentage margin strategyyielding the lowest profit for the service providers).However, from Figure 6(b), we see that MSP yieldsthe highest profit for the NYOP retailer only if con-sumer valuations are sufficiently high. Otherwise, thesealed-bid mechanism and percentage margin strate-gies are more profitable for the NYOP retailer. Thus,if the NYOP retailer is unable to charge fixed fees tothe service providers and very few customers value theproduct in excess of the posted price, he will not havean incentive to adopt the MSP mechanism. However,notice that the service providers still would prefer theMSP mechanism over other ones. Thus, they may bewilling to pay the NYOP retailer to switch to MSP.

This study suggests that participation fees may be auseful means for allocating profit across channel mem-bers and thus ensuring an incentive to adopt the mech-anism that maximizes total channel profit. This resultcomplements the finding in Spann et al. (2010) that itcan be beneficial for an NYOP retailer to charge a feeto consumers for the right to bid. Here, we show that


an NYOP retailer may also benefit from charging itssuppliers for the right to sell to these consumers.

One limitation of the current study is that suppliers’costs are assumed to be uncorrelated, while in practice,they can be correlated. In the appendix, we consideran extension to our model in which costs are perfectlycorrelated and find that all of the core results of thestudy continue to hold in this case. Specifically, whilethe choice between suppliers becomes irrelevant whencosts are perfectly correlated, the procurement mech-anism still has a large impact on the bid-acceptancefunction, which, in turn, affects customer bidding deci-sions. The MSP auction still obtains the maximumchannel profit, while the alternative NYOP mecha-nisms fall short of this optimum. These results suggestthat (imperfect) correlation of costs would reduce thepotential inefficiency losses from choosing the wrongsupplier but would increase the relative importance ofdesigning the procurement mechanism so as to man-age consumer bidding behavior appropriately.

Several important areas remain for future researchto address. One potential extension would be to modelhow bargaining power is obtained. Cross-channeleffects could be important since service providerswith more profitable non-NYOP channels would havegreater outside options and thus higher bargainingpower. It would also be of interest to consider theimpact of having more than two service providers.One would expect that greater competition amongsuppliers would shift profit from service providersto the NYOP retailer. Furthermore, adding more ser-vice providers to the NYOP channel could signifi-cantly impact the total channel profit obtained underthe various selling mechanisms. Although all the coreresults of the study should continue to hold qualita-tively when additional suppliers are added, one wouldexpect more competitive bidding under auction for-mats, such as the SB mechanism, and that the NYOPretailer would set higher margins under margin-basedstrategies such as the PM mechanism. Another poten-tial area for future research is to consider issues thatarise in a dynamic setting. For instance, suppliersmight be concerned if repeated interactions throughthe NYOP channel reveal private information abouttheir costs to their rivals. Thus, they may prefer NYOPmechanisms that allow their costs to remain opaque. Inaddition, past interactions in the NYOP channel mayimpact how service providers are treated by the NYOPretailer in the future; e.g., Priceline rewards supplierswho have made successful offers in the past by direct-ing a greater share of future demand to such suppliers(Anderson 2009). Furthermore, in a dynamic setting,consumers face the decision of when to bid. Bid timingcould have important implications for capacity alloca-tion both within and across channels.

AcknowledgmentsThe authors thank J. Miguel Villas-Boas, Preyas Desai, theparticipants of the 13th Annual Pricing Conference (SyracuseUniversity), and several anonymous reviewers for theirhelpful comments and suggestions. The first author wouldlike to thank the Earl V. Snyder Innovation ManagementCenter for providing generous financial support for thisresearch project.

Appendix

Sketch of a Proof of Lemma 1Lemma 1 is equivalent to Proposition 2 of Zeithammer(2015), using slightly different notation. We provide only asketch of the proof here. See Zeithammer (2015) for furtherdetails.

The retailer is effectively a monopolist facing buyers withprivate valuations drawn from F censored above at R (con-sumers with V >R all mimic the consumer with V =R5.When such a monopolist learns his production cost � beforehaving to accept a consumer’s bid, the optimal direct rev-elation mechanism (DRM) allocates the object to the con-sumer whenever a posted-price monopolist facing the samedemand would. Specifically, the optimal DRM allocates thegood to the consumer whenever V <R and �<�4V 5 perstandard monopoly pricing, and when V ≥R because theproduction cost is below R by construction.

The main contribution of Zeithammer (2015) is showinghow this allocation rule can be implemented in NYOP sellingwhen consumers shade their bids below their valuations (inother words, NYOP is not a DRM). The constructive proofuses revenue equivalence, i.e., the fact that all mechanismsthat allocate the good with the same probability q4V 5 forevery V generate the same revenue. The optimal DRM ruleimplies a unique q4V 5=Pr4�<�4V 55=M4�4V 55 for everyV <R and q4R5=1. Moreover, the DRM also determines theexpected utility of every consumer type V <R to be U4V 5=∫ V

�−1405M4�4z55dz. Under the NYOP mechanism, the expectedutility to a consumer of type V <R is U4V 5=q4V 54V −�4V 55.Thus, the optimal NYOP mechanism must deliver the sameexpected utility as the optimal DRM. By setting these twoutilities equal, one can solve for the unique bidding func-tion �4V 5 for V <R. To ensure that q4R5=1, the bid of thehigh bidders �4R5 must be strictly above limV→R−�4V 5 toprohibit low-value bidders bidding slightly more and secur-ing certain acceptance. Since the bidding function has a stepdiscontinuity (as long as V >R5, the optimal bid-acceptancefunction must involve an interval of intermediate bid levels4limV→R−�4V 51�4R55 for which the acceptance probability4A5 of those bid levels is low enough that nobody submitsthem. Lemma 1 gives the upper bound on A on that intervalsuch that no consumer submits a bid in that interval.

Proof of Proposition 1We begin by showing that each service provider’s optimalstrategy is to submit a price equal to its true cost, i.e., pi =�i.Note that the size of the payment made by the NYOP retailerto the winning supplier does not depend on the price sub-mitted by that service provider; the payment either equalsthe price submitted by the rival service provider (under con-dition 1) or is a function of the consumer’s bid, i.e., �∗4b5


(under condition 2). Thus, the bid price of a service providerwill only impact whether or not its bid will be accepted.Assume service provider 2 has bid its true cost 4p2 =�25, andsuppose service provider 1 considers placing a bid higherthan its true cost, i.e., p1>�1. Compared with bidding itstrue cost, the service provider will lose sales in the followingtwo cases: (1) if �∗4b5≥p2 and p1 >p2>�1 or (2) if �∗4b5<p2 and �1 ≤�∗4b5<p1.14 Sales under both of these scenarioswould be profitable for service provider 1, either yieldinga net profit of p2−�1>0 in the first case or a net profit of�∗4b5−�1 ≥0 in the second case. Thus, bidding above costlowers one’s profit. Now consider the effect of bidding lowerthan one’s true cost, i.e., p1 <�1. Compared with bidding atone’s true cost, the service provider will gain sales in thefollowing two cases: (1) if �∗4b5≥p2 and p1<p2 <�1 or (2) if�∗4b5<p2 and �1 >�∗4b5≥ p1. Sales under both of these caseswould yield negative profit for service provider 1 (eitherp2 −�1<0 in the first case or �∗4b5−�1<0 in the secondcase). Thus, bidding less than one’s opportunity cost lowersone’s profit. Therefore, service provider 1’s optimal strategyis to submit a bid price equal to its true realized opportu-nity cost. The same line of reasoning verifies that serviceprovider 2’s optimal strategy is to bid truthfully.

We now show that the MSP generates the optimal allo-cation, as identified in Lemma 1. Given that both serviceproviders are submitting bid prices equal to their true costs(as shown in the preceding paragraph), the MSP mechanismexplicitly specifies that the lower-cost supplier be chosen andthat a transaction will occur only if min6�11�27≤�∗4b5. Notethat, directly by the definition of �∗4b5, this condition reachesthe same allocation as the cost-contingent bid-acceptancepolicy of Lemma 1.

Proof of RemarkNote from the definition of MSP, the third line includes thecondition “less than,” thus indicating that the optimal costthreshold is not unique; i.e., a continuum of thresholds inthis particular interval would yield the same profit. FromLemma 1, channel profits are maximized such that no con-sumer would find it optimal to place a bid in the interval(�−

R1�4R55. By definition, at the upper bound of MSP givenin the third line, a consumer with a valuation of R wouldbe indifferent between bidding �4R5 and placing a bid inthe interior of this interval. Thus, setting a cost threshold atany level below this lower bound will make it suboptimalto place a bid in the interval (�−

R1�4R55. (Such a bid nowhas a lower probability of acceptance and the same payoffif the bid is accepted, thus decreasing the expected payoffof placing a bid in this interval. A cost threshold decreasein this interval does not change the expected payoff of bid-ding �4R5. Therefore, placing a bid of �4R5 is now a strictlysuperior option to bidding in the interval (�−

R1�4R555.

Proof of Proposition 2To prove that the alternative mechanisms yield channelprofit strictly below the optimum, we demonstrate that eachalternative violates a necessary condition that defines theoptimal solution. In particular, as we note in our proof of

14 Under all other situations, bidding p1 yields the same outcomefor service provider 1 as bidding �1.

Lemma 1, Zeithammer (2015) proves that, to obtain the opti-mal channel profit, a mechanism must allocate the object tothe consumer whenever a posted-price monopolist facingthe same demand would do so. One characteristic of theoptimal allocation is that all consumers with valuations ator above R receive the good with probability one. Thus, toprove that DC, PM, and SB yield suboptimal profit, it is suf-ficient to simply demonstrate that, for each of these NYOPmechanisms, high-value consumers receive the product witha probability of less than 1; i.e., A4b4R55<1.

First, we show that under any NYOP mechanism, includ-ing MSP, a bid of a consumer whose true valuation is Rmust be strictly less than R. Such a consumer earns anexpected surplus of CS= 4R−b5A4b5 and chooses b to maxi-mize CS. Any bid such that b>R yields a negative expectedsurplus. A bid of b=R yields zero surplus regardless ofthe acceptance-rate function. As long as A4b5>0 for at leastsome b<R, then the consumer can earn a strictly posi-tive expected surplus by placing some bid less than R. Toprove that the optimal consumer bid, b4R5, is strictly lessthan R, we only need to show that the acceptance rate of abid R−� is strictly greater than zero (for each of the threealternative mechanisms), where � is arbitrarily small butstrictly greater than zero. Under DC, A4b5=M4b5. Since �i iscontinuously distributed from 601R7, we have M4R−�5>0;thus, A4R−�5>0. Similarly, under PM, the acceptance rateis A4b5=M641−�5b7. Since �i is continuously distributedfrom 601R7 and 0<�<1 (which we will show in the nextparagraph), we have A4R−�5=M641−�54R−�57>0. Finally,for SB, consider a service provider who realizes a cost of 0.Let P SB405 be the price bid of such a firm in equilibrium.We should note that it must be the case that P SB405<R. IfP SB405>R, the service provider will earn zero profit fromthe NYOP channel since no consumer will ever bid in excessof R. If P SB405=R, there are two cases to consider: (a) if therival submits a price bid less than R, then the focal serviceprovider will earn zero profit since the product will be pro-cured from his rival; or (b) the rival submits a price bid equalto R, then, if the consumer’s bid is also R, the focal serviceprovider will make a sale half of the time. Clearly, one couldearn a higher profit by submitting a price bid of less than R.In the first case, profit will remain at zero if he does not winthe auction and be positive if he does win. In the second case,a price bid of R−� would double the probability of makinga sale and have only an infinitely small impact 4�5 on hismargin. Thus, under SB, P SB405<R, and thus A4R−�5>0.

Second, to complete the proof, we show that, under eachof these three mechanisms, A4R−�5<1. Under DC, A4b5=M4b5. Since �i is continuously distributed from 601R7, wehave A4R−�5=M4R−�5<1. Under PM, the NYOP retailerchooses � to maximize its own profit. If �<0, the retailer’sexpected profit is negative (since all sales produce nega-tive margins. If �=0, the NYOP retailer earns zero profitregardless of whether or not a sale occurs. If �≥1, the NYOPretailer also earns zero profit, since there is no cost real-ization for which a service provider would be willing toaccept the price offer. Thus, any optimal � must satisfy thecondition 0<�<1; i.e., any successful transaction generatespositive profit for both the NYOP retailer and the chosen ser-vice provider. Since the acceptance rate under PM is A4b5=


M641−�5b7, where 0<�<1, and �i is continuously distri-buted from 601R7, we have A4R−�5=M641−�54R−�57<1.Finally, for SB (which is a first-price auction), each serviceprovider submits an offer price of Pi>�i. (If Pi =�i, the ser-vice provider would earn zero profit regardless of whetheror not his bid is accepted; if Pi<�i, the service providerwould earn zero profit if his bid is rejected and negativeprofit if his bid is accepted). Since it is possible for �1 =

�2 =1, we have A4R−�5<1.In summary, we have shown that consumers have an

incentive to shade their bids—namely, that one’s surplus-maximizing bid, b4R5, is strictly less than R. Furthermore,under each of the alternative mechanisms, the biddingthreshold can be as high as the upper bound of the costrealizations, i.e., equal to R. Thus, DC, PM, and SB willbe characterized by an equilibrium bid acceptance rate ofA4b4R55<1. Since the optimal allocation requires A4b4R55=1,none of these alternative mechanisms is able to reach theoptimal channel profit.

Proof of Proposition 3We solve the three-stage game using backward induction.In stage 3, each mechanism 4M5 yields the allocation out-come and total profit 4çM

Total5 given in Sections 4 and 5. (Notethat the value of T will not impact any of the pricing orbid acceptance decisions in the third stage since it is a fixedcost/benefit.) In stage 2, bilateral negotiations determinethe value of T . Specifically, for each selling mechanism, M ,T is set so that çM

Si 4T 5=çMS1 −T ≡SS ×çM

Total ⇒T =çMS1 −SS ×

çMTotal, where çM

Total =2çMSi +çM

I .We now turn to the first stage of the game. The NYOP

retailer chooses the M that yields the highest profit foritself: argmaxM=8MSP1DC1SB1PM9ç

MI = 41−2SS5×çM

Total. Since SSis constant across M , the NYOP retailer’s profit is maximizedby choosing the M with the highest çM

Total. Propositions 1and 2 establish that MSP is the mechanism that yields thehighest total channel profit and that no other mechanism cando strictly better.

Perfectly Correlated CostsIn the base model, we assumed �1 and �2 were drawn inde-pendently from a continuous distribution G with supporton 6�1R7. If costs are perfectly correlated, we have �1 =�2 ≡

�, where � is drawn from G. The derivation of Lemma 1proceeds exactly the same as in the original model, exceptthe minimum cost realization is distributed according to Grather than according to M . Thus, Lemma 1 becomes thefollowing.

Lemma 1(a). The total channel profit is maximized by the fol-lowing bid-acceptance function:

A∗4b5=

0 if b<�4ë−140551G4ë4�−14b555 if �4ë−14055≤b< limV→R−�4V 51

less than∫ R

ë−1405

G4ë4z55

R−bdz

if limV→R−�4V 5≤b<�4R51

1 if b≥�4R51

where �4V 5 is the bidding function that best responds to A∗:

�4V 5=

∫ ë4V 5

�=0ë−14�5

g4�5

G4ë4V 55d� if ë−1405<V <R1

R−

∫ R

ë−1405G4ë4z55dz if V ≥R0

All three of the propositions are unaffected by this modelingchange. Thus, allowing for correlated costs does not alter the factthat MSP can reach the optimal channel profit or that the alterna-tive NYOP mechanisms fall short of this optimal.

However, allowing for correlated costs will impact theexact profit earned under each NYOP mechanism. To seethis, return to the numerical example in which R=1, �i ∼

U60117, and V ∼U6V 1V +17. Figure 3 shows the profit (whencosts are independent) for the four NYOP mechanisms con-sidered in this paper, as V varies from zero to one. Now, letus suppose that the costs are perfectly correlated; i.e., eachfirm realizes the same cost. Substituting the fact that G4x5=xand g4x5=1, the consumer’s bidding function under MSP,as given in Lemma 1(a), is

�4V 5=

∫ 2V−V−1

�=0

1+�+V

21

42V −V −15d�

=1441+2V +V 5 if V <11

1−

∫ 1

z=41+V 5/242z−V −15dz=

43−V 541+V 5

4if V ≥10

(14)

The corresponding optimal acceptance function is

A∗4b5=

0 if b<1+V

21

242b−V −15 if1+V

2≤b<

3+V

41

less than41−V 52

441−b5

if3+V

4≤b<

43−V 541+V 5

41

1 if b≥43−V 541+V 5

40

(15)

To induce this acceptance rate, the following thresholdunder MSP is needed:

�∗4b5=

0 if b<1+V

21

242b−V −15 if1+V

2≤b<

3+V

41

less than41−V 52

441−b5

if3+V

4≤b<

43−V 541+V 5

41

1 if b≥43−V 541+V 5

40

(16)

The resulting profit is

çMSPTotal =

1+3V 41+V 5

120 (17)

Under the demand collection mechanism, the consumerknows her bid will be accepted (by one of two service


providers) if and only if min6�11�27≤b. For correlated costs,min6�11�27 is distributed according to G4x5=x. Thus, theconsumer will choose b to maximize CS= 4V −b5G4b5 if V <R or CS= 4R−b5G4b5 if V ≥R:

bDC4V 5=

V

2if V <1

12

if V ≥10

(18)

The expected profit to service provider 1 (who is symmet-ric with supplier 2) is

çDCS1 = F 4R5EV<R

[

G4bDC4V 55

2E�1 ��1<bDC 4V 54b

DC4V 5−�15

]

+61−F 4R57G4bDC4V 55

2E�1 ��1<bDC 4R54b

DC4R5−�150 (19)

Note that Equation (19) is simpler than Equation (8) because,with identical realized costs, either both firms are willing tosell at the consumer’s bid price or neither firm is willing todo so.

The total profit created under DC is çDCTotal =2çDC

S1 = 41+

3V −V 35/24 (since each service provider earns an expectedprofit of çDC

S1 and the NYOP retailer earns zero profit).Under the percentage margin mechanism, the consumer

anticipates her bid will be accepted if and only if �≤ 41−�5b.Taking � as given, the consumer chooses b to maximize CS=

4V −b5G441−�5b5 if V <R, or CS= 4R−b5G441−�5b5 if V ≥R:

bPM 4V 5=

V

2if V <11

12

if V ≥10

(20)

The NYOP retailer chooses � to maximize its profit:

çPMI =

∫ 1

y=V

∫ 41−�5y/2

x=0�y

2g4x5f 4y5dxdy

+

∫ V+1

y=1

∫ 41−�5 12

x=0�

12g4x5f 4y5dxdy0 (21)

Taking the derivative of (22) with respect to �, we find thatthe NYOP retailer maximizes its profit with �=1/2, whichyields a profit of çPM

I = 41+3V −V 35/48. The expected profitto each service provider is

çPMS1 =

12

∫ 1

y=V

∫ y/4

�=0

[

y

4−�

]

f 4y5g4�5d�dy

+12

∫ 1/4

y=1

∫ y/4

�=0

[

14

−�

]

f 4y5g4�5d�dy

=1+3V −V 3

1920 (22)

The total channel profit is çPMTotal =çPM

I +2çPMS1 = 41+3V −

V 35/32.Finally, we consider the sealed-bid mechanism. With iden-

tical costs, each service provider knows the other firm’s cost,which results in Bertrand competition: P1 =P2 =�. Thus, theconsumer knows her bid will be accepted if and only if �≤b.Since this is the same decision choice one would face underDC, the optimal bid strategy is given by (18). With consumer

Figure A.1 (Color online) Profit Comparisons of the NYOPMechanisms (Perfectly Correlated Costs)

0.2 0.4 0.6 0.8 1.0

0.1

0.2

0.3

0.4

0.5

Cha

nnel

pro

fit (

Π)


MSP

PM

DC = SB

bids being the same as under DC, transactions occurringunder exactly the same conditions as DC, and the serviceproviders earning zero profit, total channel profit must bethe same as DC: çSB

Total = 41+3V −V 35/24, where all the profitis retained by the NYOP retailer.

In sum, profits are lowest under PM. DC and SB yield thesame profit, which is strictly less than MSP. The profits ofthese NYOP mechanisms are given in Figure A.1.

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