Competitive Reasons for the Name-Your-Own-Price Channel

Transcription

1 Compettve Reasons for the Name-Your-Own-Prce Channel Scott Fay* Department of Marketng Unversty of Florda P.O. ox 755 Ganesvlle, FL Phone: Fax: e-mal: (January 2008 (prl 2008 September 2008

2 2 Compettve Reasons for the Name-Your-Own-Prce Channel STRCT Ths paper shows that the Name-Your-Own-Prce (NYOP busness model can help soften competton. When consumers dffer n ther frctonal costs (.e., the shoppng hassle they experence when bddng at a NYOP retaler, the NYOP format can be a mechansm for dfferentatng a retaler from a posted-prce rval. eyond provdng a motvaton for usng a NYOP mechansm, competton also has mportant mplcatons for the optmal structure of the NYOP format. For example, ths paper shows that prohbtng re-bddng may beneft a NYOP frm by reducng prce rvalry. Keywords: Name-Your-Own-Prce, Reverse uctons, Prcng

3 uctons of many dfferent varants are sproutng up on the Internet and creatng opportuntes for researchers to analyze consumer and seller behavor n such envronments (Cheema et al The Name-Your-Own-Prce (NYOP format s one such new busness model that offers a non-tradtonal way of determnng prces and dstrbutve allocatons. Under the NYOP format, the seller sets a hdden threshold prce, consumers bd for unts of ts product, and any bd that exceeds ths threshold prce s accepted. Prcelne ( an onlne seller of travel servces, s the most promnent example of a NYOP frm. Unlke many of ts hyped e-busness peers that arose n the late 990 s, Prcelne survved the Internet bust and even flourshed. s a result, the NYOP mechansm has drawn the attenton of both the popular press and academcs (see Dolan and Moon 2000, Rust and Esenmann 2000, and the lterature cted below. spects of the NYOP model that have been studed prevously nclude: analyzng the optmalty of consumer bddng (Spann and Tells 2006; assessng the restrcton of bds to dscrete levels rather than from a contnuous nterval (Chernev 2003; examnng the role of emoton n bddng behavor (Dng et al. 2005; and measurng the wllngness-to-pay of bdders (Spann et al Somewhat surprsngly, lttle attenton has been pad to why a frm mght choose a NYOP format. Presumably, a frm would want to employ a NYOP format only f t s more proftable than alternate mechansms. Yet, much of the extant lterature ndcates that the NYOP format does not outperform posted prces. For nstance, Fay (2004 notes that posted prces weakly domnate NYOP n ths smple framework (p. 45. nd, usng data from a German NYOP retaler for three electronc products, Terwesch, Savn, and Hann (2005 fnd that the retaler s proft would have been hgher had the frm used posted prces (3.32 vs for DVD players, 8.6 vs for PD s, and 5.97 vs. 5.4 for CD rewrters. Furthermore, other papers n the lterature suggest several dsadvantages of the NYOP format relatve to posted prces. In partcular, due to uncertanty about the actual prce threshold,

4 2 consumers shade ther bds and thus place bds that are well below ther reservaton values (Spann, Skera, and Schafers 2004, Dng et al. 2005, Hann and Terwesch nd, Hann and Terwesch (2003 demonstrate that the frctonal costs assocated wth bddng are non-trval. Thus, the NYOP format reduces the wllngness-to-pay of consumers versus a posted-prce format n whch such frctonal costs would not be ncurred. It s mportant to develop a deeper understandng of why the NYOP format may be preferred to alternatve sellng mechansms n order to understand when and where such a busness model would be advantageous, and to structure the NYOP mechansm properly. In ths paper, I contrbute to deepenng ths understandng by explorng how competton wth a rval can affect the ncentve to adopt the NYOP format. In partcular, I demonstrate that ( the NYOP format may be superor to posted prces because t can soften competton wth a posted prce rval; and (2 accountng for the role of the NYOP channel n softenng competton has mportant mplcatons for how a NYOP frm should set ts rebddng polces. The ablty of the NYOP format to soften competton hnges on the fact that the frctonal costs consumers face when bddng vary across consumers due to dfferences n opportunty costs of tme, perceved dffculty of the task, experence, and other factors. Hann and Terwesch (2003 fnd strong emprcal evdence that frctonal costs substantally vary across users. In partcular, across the three products n ther data, the medan frctonal cost per bd s approxmately $4.7 wth a standard devaton of $4.74. The dfference n the mnmum and maxmum frctonal costs observed s $ Furthermore, these estmates are based on consumers who placed three or more bds for a partcular tem. The heterogenety n frctonal costs would lkely be even hgher among Hann and Terwesch (2003 estmate the frctonal costs (n EURO s for 3 products, PD s CD-RW drves, and MP3 players. The medan frctonal costs for bds on the three products are 6.08, 4.29, and 3.54, respectvely. Standard devatons of costs are 7.57, 4.42, and 3.8. The mnmum frctonal costs are.44,.26, and.44. The maxmum frctonal costs are 65.59, 32.06, The numbers n the text are averages across these three products converted nto dollars (at a rate of EURO =.90$, whch was the exchange rate when the orgnal data was collected.

5 3 all potental consumers,.e., consumers who place three or more bds, consumers who place less than three bds, and consumers who chose to purchase from an alternatve posted-prce retaler (and thus avoded presumably very hgh bddng costs. Ths substantal heterogenety n frctonal costs provdes an avenue for segmentng a market where there s both a NYOP and a posted-prce opton. n NYOP frm has an ncentve to target consumers wth low frctonal costs whle the posted-prce frm sells to consumers wth hgh frctonal costs. Thus, the NYOP format offers a mechansm for reducng prce competton and ncreasng mutual proft. 2 The analyss n ths paper s most applcable to settngs n whch a seller s prmary threat comes from a sngle compettor who offers a very close substtute, such as the competton between Hotwre (whch uses posted prces and Prcelne (whch uses a NYOP format n the U.S. travel market. lthough many onlne ntermedares (e.g., Orbtz, Expeda, Travelocty, offlne ntermedares (e.g., travel agents, and drect supplers (e.g. Delta rlnes, Marrott Hotels, Hertz Car Rental also sell travel servces, Hotwre and Prcelne, by offerng opaque travel goods, serve a dstnct market nche of the most prce-senstve and flexble travelers the mercenary traveler (McGee The goods are opaque because consumers are not told the exact flght tnerary (suppler, connecton cty, or departure tme or the hotel property pror to purchase. 3 ecause of ths opacty, even f the ex post product assgnment dffers across the two frms, ex ante Prcelne and Hotwre offer perfect substtutes, e.g., a flght between two ctes any tme on the specfed days. Thus, prce competton may be ferce f both frms offer posted prces. ut, by sellng through a NYOP format rather than through posted prces, Prcelne s able to reduce prce rvalry. Furthermore, snce Hotwre and Prcelne are the two domnant players n the opaque travel 2 Other non-posted prce mechansms may also be able to mtgate prce competton n ths context. However, t s beyond the scope of the current paper to compare the NYOP format to all possble prcng mechansms. 3 Fay (2008 and Fay and Xe (2008 provde addtonal dscusson of the role of opacty n market nteractons.

6 4 market (McGee 2003, t s mportant that Prcelne make ts decsons n antcpaton of Hotwre s response, and vce-versa. The NYOP format may be partcularly useful for retalers competng onlne. ecause they rely on the same manufacturers, retalers may fnd themselves sellng a product that s undfferentated from a rval s product. Ths dffculty s further compounded n onlne markets snce the lack of physcal locatons elmnates geographcally-based dfferentaton. In such settngs, the NYOP format may be a valuable tool for creatng dfferentaton and thus relaxng prce competton. Furthermore, the success of the NYOP format reles on ensurng that consumers beleve that the prce threshold s drawn from a dstrbuton,.e., that consumers do not know the actual prce threshold n effect at a gven tme. The onlne envronment may facltate such credblty. For example, an automated platform can be augmented to nclude a random component and can also ensure that the stated bddng restrctons are enforced (e.g., no re-bddng. 4 Furthermore, word-of-mouth, whch flows more easly onlne, can nform consumers about the dstrbuton of prce thresholds and also demonstrate the unpredctable nature of the acceptance decson. For nstance, numerous web forums, e.g., betterbddng.com, bddngfortravel.com, and flyertalk.com, now allow consumers to converse about ther experences n dealng wth Prcelne. Whle the current paper offers one ratonale for the NYOP format, namely to soften competton, I do not assert that ths s the only possble motvaton for usng the NYOP format. Indeed, another key objectve of ths paper s to encourage future research that dentfes alternatve explanatons. One such alternatve s provded n Terwesch et al. (2005 whch argues that the 4 There s some evdence that current NYOP sellers have ndeed commtted to such a decson structure. For example, Prcelne determnes whether a gven bd s accepted usng a complcated computer formula whch ncludes a random element (Segan 2005 and employs a randomzer program for decdng whether to accept a bd for a hotel room (Malhotra and Desra 2002, Haussman 200. In partcular, rather than settng the threshold prce equal to the lowest rate offered by the entre set of hotels that have rooms avalable, Prcelne only compares the bdder s offer to the rates set by two randomly-selected hotels. Such an acton s consstent wth the speculaton n Kannan and Kopalle (200 that Prcelne may delberately forgo a successful transacton n order to nfluence consumers expectatons,.e., persuade consumers to bd hgher n the future.

7 5 NYOP mechansm can facltate prce dscrmnaton. n llustratve example on p. 349 shows a potental beneft of the NYOP format. In ths example, there are two types of customers. The frst type has a reservaton value of 0, per-bd frctonal costs of.0, and beleves the threshold prce s drawn from U[0, 0]. The second has a reservaton value of 300, per-bd frctonal costs of 50, and beleves the threshold prce s drawn from U[0, 300]. The frst type wll place a sngle bd of , and the second wll bd 50. s long as the frst type suffcently outnumbers the second type, the NYOP format s more proftable than posted prces. ased on ths example, Terwesch et al. speculate that for the NYOP format to be advantageous to the seller, the followng s requred: (, substantal heterogenety n valuatons and (2, postve correlaton between valuatons and frctonal costs. It appears that ths example also reles on a thrd requrement a postve correlaton between valuatons and the expected threshold prce (so that the second type wll bd hgher. 5 In the current paper, I ntroduce an envronment n whch the NYOP format can be advantageous to sellers wthout meetng any of these three requrements. In partcular, n the current model, consumer valuatons are homogenous, there s no correlaton between valuatons and frctonal costs, and all consumers have the same expectatons about the threshold prce. Ths set-up ensures that the motvaton for a seller to use a NYOP format s dstnct from the motvaton dentfed n Terwesch et al. (2005. In the next secton, I present a duopoly model n order to explore the stuatons n whch a frm mght beneft from usng a NYOP format. In secton 3, I examne whether a NYOP frm should allow consumers to place multple bds, focusng on how ths choce depends upon a rval s response to the NYOP frm s bddng polcy. Secton 4 offers bref concludng comments, ncludng drectons for future research. 5 Notce that f the second type also beleved that the threshold prce was drawn from U[0,0], they would not bd 50, but nstead bd 0 or less.

8 6 2. Model 2. Specfcaton of the Duopoly Game Each of two retalers, and, obtan unts of a product from a manufacturer at the wholesale prce, whch I normalze to zero. The two frms play a two-stage game. In the frst stage, the two retalers sequentally select a market format ether a posted prce or a NYOP format. 6 In the second stage of the game, the frms choose ther posted prces (f the posted-prce format was selected n the frst stage. In the event that both frms use the posted-prce format, the prces (P and P are chosen smultaneously. Fnally, consumers decde whether to purchase and from whom. Under the NYOP format, a retaler s threshold prce, P NYOP, s not drectly observed by consumers. ny bd below ths threshold s rejected, whle any bd at or above P NYOP s accepted and results n that consumer payng hs/her bd. I assume that consumers expectatons of the threshold prce are confrmed on average. In partcular, the NYOP seller draws the threshold prce from a pre-announced dstrbuton and the consumers know ths s the process for determnng the threshold prce. To avod unnecessary notaton, I assume the dstrbuton functon s U[0, ]. I solve the game recursvely. Frst, I dentfy the proft that results from each possble format combnaton. Then, I dentfy the Sub-Game Perfect Nash Equlbrum n format choces for the full game. 2.2 Consumer Demand Each consumer has a reservaton value, R, for one unt of the product. 7 There are no frctonal costs of purchasng at the posted prce. However, consumers ncur bddng costs when 6 Sequental format choces are not requred for the core results of ths paper. However, wth smultaneously format decsons, multple equlbra may arse one n whch frm selects the NYOP format and frm selects posted prces, and one n whch frm selects the posted prce format whle frm selects the NYOP format. Thus, coordnaton ssues (.e., whch equlbra s played may arse n a smultaneous-choce settng. 7 Whle assumng a common reservaton value dramatcally smplfes the analyss, t s not essental for the paper s man qualtatve results. more subtle pont s that varaton n frctonal costs s essental for approprately segmentng consumers. The NYOP mechansm s an effectve means of targetng consumers wth low frctonal costs but not those wth low valuatons. Thus, to receve the prce dscrmnaton effect touted n the lterature (e.g., Hann and Terwesch 2003, varaton n frctonal costs s essental, but varaton n reservaton values s not.

9 nteractng wth a seller who uses a NYOP format. I assume that the cost to consumer of placng a bd through the NYOP channel, c, s drawn from U[0, c ]. I restrct attenton to c, whch 4 2 ensures that the range of bddng costs approxmately matches the emprcal estmates of these costs (whch were dscussed n the ntroducton. To allow each frm to have some market power, I use a loyal-swtcher model. Thus, consumers vary n ther proclvty to shop at a gven retaler. In partcular, a proporton λ of consumers are loyal to retaler. I assume another segment of sze λ s loyal to retaler. These consumers are only wllng to shop at ther favored retaler. The remanng ( 2 λ consumers are swtchers who wll vst ether (or both retalers. In the subsectons below, I consder the optmal purchase behavor under the three possble format permutatons. oth Frms Use Posted Prces The consumers who are loyal to retaler can ether purchase the product at a posted prce of P or forego consumng the product. Purchasng from s optmal f P. The consumers who are loyal to retaler can ether purchase the product at a posted prce of P or forego consumng the product. These consumers purchase from f P. The swtchers can purchase the product from ether retaler. They wll purchase from the retaler that charges the lowest prce, as long as ths prce does not exceed ther reservaton values. In partcular, the swtchers wll purchase from f P < P and P. The swtchers wll purchase 7 from f P < P and P. If both retaler charge the same prce (and ths prce does not exceed, then the swtchers wll be evenly dvded across the two retalers. One Frm Uses a Posted Prce; One Frm Uses a NYOP Format Wthout loss of generalty (due to symmetry, let retaler be the frm that uses a NYOP format, whle retaler uses a posted prce. Recall that consumers cannot observe the actual prce

10 8 threshold employed by the NYOP frm. Thus, consumers nstead rely on expectatons (.e., the belef that P NYOP ~ U[0, ] n order to decde what to bd. Here, I assume consumers are restrcted to a sngle bd. (s an extenson, n Secton 3, I allow consumers to bd agan f ther frst bd s rejected. Each consumer bds to maxmze her expected consumer surplus (gven the nformaton she possesses. The consumers who are loyal to retaler can ether purchase the product at a posted prce P or forego consumng the product. Such consumers wll purchase from f P. The consumers who are loyal to retaler can ether bd at s NYOP ste or forego bddng. Such a scenaro has prevously been analyzed by Spann et al. (2004 and Spann and Tells (2006. The optmal bddng strategy s: ( place a sngle bd of bˆ f c cˆ do not bd at all f c ˆ > c where b ˆ =, cˆ = 2 4 The swtchers have a more complcated decson. They must decde whether to a forego bddng and buy the product at the posted prce P ; b bd at s NYOP ste and then purchase at P f that bd s rejected; c bd at s NYOP ste and then not purchase at s posted prce f that bd s rejected; or d nether bd at s NYOP ste nor buy at s posted prce. s long as P, only the frst and second optons can be optmal. Ths condton, P, wll be satsfed n equlbrum snce retaler does not make any sales f ths condton s volated. I fnd that the optmal bddng strategy n such an envronment s: (2 bd at bˆ and then purchase at P f rejected f c cˆ purchase at P wthout bddng at all f c ˆ > c where ( 2 b ˆ = P P, cˆ = 2 4 oth Frms Use a NYOP Format s above, I assume consumers are restrcted to a sngle bd on each NYOP ste. The

11 9 consumers who are loyal to retaler can ether bd at s NYOP ste or forego bddng. Ther optmal bddng strategy s gven by (. The consumers who are loyal to retaler face an somorphc decson. Thus, ther optmal bddng strategy s also gven by (, but for these consumers, retaler receves the bds. The swtchers have the followng optons: a to bd at s ste and then bd at s ste f that bd s rejected; b to bd at s ste and then bd at s ste f that bd s rejected; c to bd at s ste and then not bd agan f that bd s rejected; d to bd at s ste and then not bd agan f that bd s rejected; or e not to bd at ether ste. It turns out that the thrd and fourth optons are never optmal. Furthermore, due to symmetry, the frst two optons yeld equvalent expected surplus. The optmal bddng strategy n such an envronment s: (3 bd at bˆ and then bd at bˆ (on the other ste f rejected f c cˆ do not bd at ether ste f c ˆ > c where ˆb = 8 c 2.3 Prces and Proft for Each Sub-Game The ppendx contans the dervaton of the proft for each of the possble format confguratons. The text summarzes the results and provdes a bref ntuton. oth Frms Use Posted Prces To maxmze proft from sales to ts loyal customers, a retaler would prce at. ut, to maxmze proft from swtchers, a retaler would want to undercut ts compettor s prce by epslon. Due to ths dscontnuty n demand at P = P, no pure-strategy Nash Equlbrum n prces exsts when each retaler sells at a posted prce. Instead, there s a mxed-strategy equlbrum n prces. In ths equlbrum, both frms earn a proft of: (4 = = λ PP,PP PP,PP Notce that as store loyalty declnes, equlbrum profts also fall. Snce swtchers vew the two retalers products as perfect substtutes, as the magntude of the swtcher segment grows, the frms

12 0 have less market power and, as a result, prces (on average are drven closer to margnal cost. One Frm Uses a Posted Prce; One Frm Uses a NYOP Format gan, I focus on the case n whch retaler uses a NYOP format whle retaler uses a posted prce. Retaler randomly selects P NYOP from U[0, ]. The expected proft to the frm s: ĉ bˆ ĉ ˆ b bˆ f c d P dc 2 bˆ f c d P dc PP,NYOP (5 = λ ( + ( λ ( NYOP NYOP c = 0 PNYOP = 0 c = 0 PNYOP = 0 Retaler sells to ts loyal consumers (as long as P and to swtchers who do not have a bd accepted (ether due to not submttng a bd or due to havng ther bd rejected. Thus, frm earns a proft of: ˆ ĉ b P 2 f c d P dc PP,NYOP (6 = λ + ( λ ( NYOP c = 0 PNYOP = 0 Retaler chooses P to maxmze ths proft. oth Frms Use a NYOP Format Retalers and both randomly select P NYOP from U[0, ]. Sales to each retaler come from ther loyal consumers and from swtchers (some of whom have had a prevous bd rejected at the rval s ste. The expected proft to each NYOP seller s: (7 ( cˆ bˆ cˆ bˆ NYOP,NYOP NYOP,NYOP = = ˆ f ( d d ˆ b c PNYOP c + f ( d NYOP d 2 b c P c c = 0 PNYOP = 0 c = 0 PNYOP = 0 λ ĉ bˆ ( c = 0 PNYOP = 0 ˆ ˆ ( ( + b b f c d PNYOP dc Format Decson Now consder the frst stage of the duopoly game n whch each retaler selects ts market format. Wthout loss of generalty, assume retaler chooses ts format frst and then retaler chooses ts format. In the Subgame Perfect Nash Equlbrum, frm chooses the format that s the

13 best response to s format, and chooses the format that maxmzes ts proft gven frm s best response. Proposton descrbes the equlbrum format confguraton. Proposton : When there s suffcently lttle store loyalty n a market, n the Subgame Perfect Nash Equlbrum, one frm wll adopt the NYOP format whle the other wll use posted prces. Specfcally, f λ <, then n the unque Subgame 9 Perfect Nash Equlbrum, retaler selects a posted prce format and retaler select a NYOP format. To understand the ntuton behnd Proposton, consder how the sze of the loyal segment affects prces and proft when both frms use posted prces. Recall that n ths market confguraton there s a mxed equlbrum n prces. frm must balance settng hgh prces n order to maxmze revenue from loyal consumers wth settng low prces n order to woo swtchers away from a compettor. s the loyal segment grows, each frm puts less emphass on attractng swtchers. Specfcally, the lower end of the equlbrum prce dstrbuton ( ˆP depends on the degree of store loyalty: ˆ λ P =. s store loyalty ncreases, the lowest posted prce ncreases (and the frm λ chooses hgher prces wth hgher probablty. t the extreme case where all consumers are loyal ( λ =.5, each seller always prces at. However, at the other extreme n whch all consumers are swtchers ( λ = 0, the model converges to the standard ertrand competton wth perfect substtutes n whch both frms prce at margnal cost. Ths suggests that when there s lttle store loyalty, frms would lke to fnd a mechansm for softenng prce competton. The NYOP format can serve as such a mechansm. Notce that even though the swtchers vew the two seller s products as beng undfferentated, the swtchers vary n ther wllngness to bd on a NYOP ste snce they dffer n ther frctonal costs of bddng. Thus, when one frm adopts the NYOP format, segmentaton on the bass of heterogeneous frctonal costs occurs. In partcular, consumers wth low frctonal costs are wllng to bd at the NYOP ste. On the

14 2 other hand, consumers wth hgh frctonal costs or those whose bds the NYOP ste rejected, wll purchase at the posted-prce channel. Interestngly, such segmentaton occurs (and s benefcal to both retalers even though the posted-prce frm can nfluence how many consumers wll bd at the NYOP ste. In partcular, at a lower posted prce, fewer consumers (.e., only those wth suffcently low frctonal costs wll bd at the NYOP ste. Thus, lower posted prces lead to hgher sales for the posted-prce frm, but at the same tme reduces margns. In balancng these trade-offs, the posted-prce frm may compete for the swtchers (.e., by choosng a prce less than one. Even so, the heterogenety n frctonal costs means that competton s not as ferce as t would have been f both frms had used posted prces. Ths s because a posted prce frm does not have the ncentve to lower ts prce so much as to persuade swtchers wth low bddng costs to forego bddng at the NYOP ste. Thus, even though a retaler realzes that f t mplements a NYOP format, ts posted-prce rval wll poach some of the swtchers, the NYOP format s stll advantageous (versus the alternatve of facng the ferce competton under posted prces. Fnally, t s nterestng to explore how the magntude of frctonal costs affects the proft of the NYOP frm. For nstance, one mght expect that as costs get larger, the NYOP format becomes less proftable (snce bddng on a NYOP ste becomes less attractve to consumers. Fgure llustrates the NYOP frm s proft as a functon of the range of frctonal costs (usng λ =.. Interestngly, profts do not monotoncally decrease n frctonal costs. When 4 c, 4 9, the NYOP frm s proft actually ncreases n c. Ths result occurs because, n ths range, an ncrease n c nduces the posted-prce rval to prce less aggressvely. Interestngly, ths fndng mples that the NYOP frm may beneft f the average frctonal cost of placng bds on ts ste rses. Greater nconvenence for some consumers makes segmentaton on frctonal costs easer and thus ncreases

15 the proft of both the NYOP frm and ts posted-prce rval. However, f frctonal costs become too 3 large c 4 > 9, the NYOP frm s proft decreases n c. Here, the posted-prce retaler s already prcng at each consumer s reservaton prce and thus prce competton cannot be any lower. In ths case, a larger c smply mples that fewer customers are wllng to bd at the NYOP ste. Fgure Proft for the NYOP Frm When Its Rval Uses Posted Prces ( λ =. 0.4 Proft by NYOP Frm Maxmum Frctonal Cost ( c 3. Incentve to llow Re-bds The precedng secton ntroduced a new motvaton for why a frm mght employ a NYOP format namely to reduce prce rvalry. In ths secton, I explore how ths new ratonale affects the optmal way to structure the NYOP format. I focus on a desgn aspect that has been a focal pont of much past research whether a NYOP frm should allow rejected bdders to re-bd. Focusng on a monopoly context, the extant lterature suggests that allowng re-bds usually mproves the proftablty of the NYOP channel. For example, Spann et al. (2004 assert that restrctng consumers to a sngle bd may reduce the seller s revenues. Hann and Terwesch (2003, n a techncal appendx (p. 0, propose a ratonale for ths result: heterogenety n frctonal costs allows a NYOP frm to prce-dscrmnate between customers and thus ncrease proft. y allowng

16 4 consumers to re-bd, the NYOP seller can ncrease total sales (.e., capture some sales from consumers whose frst bd was rejected and also prce-dscrmnate (.e., charge, on average, a hgher prce to consumers wth hgh frctonal costs snce such customers ncrease ther bds n larger ncrements. ddtonally, Fay (2004 argues that restrctng consumers to a sngle bd s lkely to be undesrable n lght of the fact that sophstcated bdders crcumvent ths restrcton whle many other bdders cannot. In ths secton, I consder the mpact of allowng re-bds when the NYOP frm faces a posted-prce rval. In the text, I report the man results of my analyss and ntuton, relegatng the techncal detals to the ppendx. Frst, I fnd that n the current model, n the absence of any strategc effect, a NYOP frm never benefts from restrctng consumers to a sngle bd. In partcular, f the rval frm s posted prce s the same when consumers are allowed to re-bd at the NYOP ste as when they are restrcted to a sngle bd, then the NYOP frm benefts from allowng consumers to re-bd. Ths fndng s consstent wth the lterature descrbed above. Second, I fnd that restrctng bdders to a sngle bd can have the strategc beneft of reducng competton. Ths result s summarzed by Proposton 2. Proposton 2: When facng competton from a posted-prce rval, a NYOP frm may beneft from restrctng consumers to a sngle bd. For example, when λ =.05, restrctng consumers to a sngle bd s more proftable than allowng them to re-bd f 9 c < Ths potental advantage from prohbtng re-bds occurs because re-bddng polces may mpact the prcng strategy of a rval. In partcular, the posted-prce rval may choose a lower prce f consumers can re-bd than f they are restrcted to a sngle bd. llowng re-bds ncreases the appeal of the NYOP channel to consumers, especally those wth relatvely low frctonal costs. In order to prevent consumers from re-bddng and nstead buy at the posted prce, the posted prce

17 5 frm must lower ts prce. ut, a lower prce n the posted-prce channel negatvely mpacts the NYOP seller s proftablty. Fgure 2 llustrates the profts for both frms when re-bddng s or s not allowed (assumng λ =.05 and 9 c. Under these parameters, store loyalty s suffcently small so that n the 9 Subgame Perfect Nash Equlbrum retaler uses the NYOP format, and under the sngle-bd structure, retaler would set ts posted- prce equal to. Thus, n ths stuaton, the NYOP format s very effectve at mtgatng prce competton when consumers can bd only once at the NYOP retaler s ste. However, f the NYOP frm allows re-bds, the NYOP frm s more appealng to consumers. Thus, the posted-prce retaler s proft falls. Furthermore, facng ths greater compettve threat, the posted-prce retaler would lower ts prce. Ths, n turn, dmnshes the level of bds placed on the NYOP ste. Thus, the advantages of allowng re-bds dentfed above (hgher sales and better prce dscrmnaton are counterbalanced by lower bds. When heterogenety n frctonal costs s small, the negatve effect from lower bds s szable because the posted-prce rval prces aggressvely. Thus, f heterogenety n frctonal costs s suffcently small ( c <.476, then the NYOP retaler s proft s hgher f t restrcts consumers to a sngle bd. However, as heterogenety grows, the posted-prce rval has less ncentve to try to poach the low frctonal-cost consumers (snce consumers wth hgh frctonal costs are wllng to pay a hgh posted prce rather than make a costly bd. Thus, f heterogenety n frctonal costs s suffcently large ( c >.476, the NYOP retaler fnds t advantageous to allow re-bds.

18 6 Fgure 2 Comparson of Proft wth and wthout Re-bddng ( λ =.05 NYOP Retaler Posted-Prce Retaler Sngle d 0.24 Two ds Sngle d 0.68 Two ds Maxmum Frctonal Cost ( c Maxmum Frctonal Cost ( c Interestngly, these results offer an explanaton for an apparent conflct between theory and practce. s noted earler, much of the past theory suggests that a NYOP retaler would earn hgher profts f t allowed consumers to re-bd. Yet, Prcelne the most promnent retaler that employs a NYOP format does n fact restrct consumers to a sngle bd. The above results suggest that restrctng bdders to a sngle bd may have the strategc beneft of reducng competton. Thus, Prcelne may beneft from mposng a sngle-bd restrcton n order to mtgate prce rvalry wth Hotwre. However, t s mportant to note that other factors can affect the desrablty of allowng rebds. In partcular, allowng re-bds can ncrease sales,.e., rejected bdders contnue bddng, but the nformaton rent of the NYOP seller falls f re-bds are allowed snce consumers can start ther bd sequences at a lower level and rase ther bds n smaller ncrements (Fay The key nsght from Proposton 2 s that the mpact on rvals prcng s another mportant factor a NYOP frm should consder before allowng re-bds. 4. Concludng Remarks Ths paper takes an mportant step towards modelng the effect of competton on a retaler s choce of whether or not to use a NYOP format. In dong so, t provdes one explanaton for why a

19 7 frm would employ a NYOP mechansm rather than posted prces,.e., the NYOP format provdes a mechansm for reducng prce competton. Many ssues reman for future research. It would be valuable to extend the theoretcal model and to test t emprcally n order to assess the robustness of the deas ntroduced n ths paper. One partcularly restrctve assumpton n the current paper s that the NYOP retaler s assumed to randomly draw t prce threshold from an exogenously determned dstrbuton, namely U[0,]. Presumably, f a NYOP retaler had the opton to commt to any dstrbuton, then the NYOP format would be even more benefcal to a frm. Future research should consder what dstrbuton would be optmal for a NYOP retaler to adopt. nd, t would be nterestng to explore how a retaler mght credbly commt to such a dstrbuton (rather than settng the prce threshold whch maxmzes ex post profts. It would also be useful to explore addtonal ratonales for the NYOP format. Lastly, whle the current paper focuses on the polcy decson of whether to allow consumers re-bd, future research should explore other desgn aspects of the NYOP mechansm (e.g., non-unform prce threshold dstrbutons, nformaton to reveal about ths dstrbuton, frequency wth whch to change the actual prce threshold, or havng consumers select rather than name a prce wth an eye toward understandng how these desgn ssues mpact the ablty of the NYOP format to fulfll ts purpose. References Cheema, mar, Peter T. L. Popkowsk Leszczyc, Rajesh agch, Rchard P. agozz, James C. Cox, Utpal M. Dholaka, Erc. Greenleaf, mt Pazgal, Mchael H. Rothkopf, Mchael Shen, Shyam Sunder and Robert Zethammer. (2005. Economcs, Psychology, and Socal Dynamcs of Consumer ddng n uctons. Marketng Letters 6 ( Chernev, lexander (2003. Reverse Prcng and Onlne Prce Elctaton Strateges n Consumer Choce. Journal of Consumer Psychology 3 (/

20 8 Dng, Mn, Jehoshua Elashberg, Joel Huber, and Rtesh San (2005. Emotonal dders n nalytcal and Expermental Examnaton of Consumers ehavor n a Prcelne-Lke Reverse ucton. Management Scence 5 ( Dolan, Robert J, and Youngme Moon (2000. Prcng and market makng on the Internet. Harvard usness School Study , Harvard Unversty, Cambrdge, M. Fay, Scott (2004. Partal-Repeat-ddng n the Name-Your-Own-Prce Channel. Marketng Scence 23 ( Fay, Scott (2008. Sellng an Opaque Product Through an Intermedary: The Case of Dsgusng One s Product. Journal of Retalng 84. (Sprng Fay, Scott and Jnhong Xe (2008. Probablstc Goods: Creatve Way of Sellng Products and Servces. Marketng Scence 27.4 (July/ugust Hann, Il-Horn and Chrstan Terwesch (2003. Measurng the Frctonal Costs of Onlne Transactons: The Case of a Name-Your-Own-Prce Channel. Management Scence. 49 ( Haussman, Glenn (200. Prcelne Urges Property Partcpaton. Hotel Interactve May 30 Kannan, P.K. and Praveen K. Kopalle (200, Dynamc Prcng on the Internet: Importance and Implcatons for Consumer ehavor, Internatonal Journal of Electronc Commerce, 5(3, Malhotra, Namt and Chrstan Desra (2002. Hotel Internet Dstrbuton Channels. HVS Technology Strateges Hosptalty Report February McGee, Wllam J. (2003. ookng and ddng Sght Unseen: Consumer s Gude to Opaque Travel Web Stes. Consumer WebWatch Research Report. Dec. 8. Rust, Jon K. and Thomas Esenmann (2000. Prcelne Webhouse Club. Harvard usness School Case, , Harvard Unversty, Cambrdge, M. Segan, Sascha (2005. Prcelne.com for Dummes. Wley Publshng, Inc., Hoboken, N. J. Spann, Martn, ernd Skera, and jorn Schafers (2004. Measurng Indvdual Frctonal Costs and

21 Wllngness-To-Pay Va Name-Your-Own-Prce Mechansms. Journal of Interactve Marketng 8 ( Spann, Martn and Gerard J. Tells (2006. Does the Internet Promote etter Consumer Decsons? The Case of Name-Your-Own-Prce uctons. Journal of Marketng 70 (January Terwesch, Chrstan, Serge Savn, and Il-Horn Hann (2005. Onlne Hagglng at a Name-Your-Own-Prce Retaler: Theory and pplcaton. Management Scence 5 ( Varan, Hal R.. (980. Model of Sales. mercan Economc Revew 70 ( Wlcox, Ronald T. (2000. Experts and mateurs: The Role of Experence n Internet uctons. Marketng Letters ( ppendx Dervaton of consumers optmal bds when Retaler uses a NYOP Format Retaler s loyal consumers can ether bd at s NYOP ste or they can forego bddng. bd of b s accepted wth a probablty of b, n whch case the consumer gets a net surplus of (-b. Thus, the consumer s expected value from bddng b s: ( EVL ( b = ( b b c EVL ( b The FOC of ths maxmzaton problem s: = 2b 0. Ths FOC s satsfed when b = bˆ and EVL ( b ˆ s b 2 non-negatve (so as to nduce bddng rather than abstanng ff c ˆ c. 4 Suppose retaler sells at a posted prce of P. swtcher who purchases at the posted prce earns a surplus of (- P. swtcher can bd at s NYOP ste f she so chooses. The expected value from placng a bd of b and then purchasng at the posted prce f that bd s rejected s: EV ( b = b b c + b P (2 ( ( ( S Usng the FOC, ths expected value s maxmzed when b = b ˆ and weakly exceeds the surplus from buyng at the posted prce wthout bddng ff c c ˆ, where ˆb and ĉ are defned n (2. Now suppose retaler also uses a NYOP format. If a swtcher were to not bd on ether ste, she would earn a surplus of zero. nother alternatve bddng strategy would be to place a bd of b at one of the two stes and then not bd at the other ste f ths bd were rejected. Ths strategy generates an expected value gven by (, whch s maxmzed when b = b ˆ, yeldng an expected value of 4 c. Fnally, a swtcher could place a bd of b at one of the two stes and then place a bd of b 2 at the other ste f the frst bd s rejected. Ths strategy yelds an expected value of: (3 EVS2 ( b,b 2 = ( b b c + ( ( 2 b b b2 c Usng the resultng FOC s, the consumer s expected value s maxmzed when b ˆ = b and b = ˆ 2 b where ˆb and ˆb are defned n Equatons (3 and (, respectvely. Ths dual-bddng strategy yelds a hgher expected surplus than the sngle bddng strategy c c ˆ. Ths dual-bddng strategy s weakly superor to not bddng at all ff c c ˆ. 9

22 20 Dervaton of Equlbrum Prces and Proft for Each Sub-Game In accordance wth Proposton, the remander of the dervatons n the ppendx proceed under the assumptons c and λ < oth Frms Use Posted Prces The loyal-swtcher model whereby both frms sell at a posted prce s a slghtly smplfed verson of a model whch has prevously been analyzed by Varan (980 (usng the terms nformed and unnformed to descrbe the two segments. Rather than replcatng that entre analyss, below, I smply report the results. There s not a pure-strategy equlbrum to ths game. Instead, there s a mxed-strategy equlbrum n prces n whch each retaler charges prce P wth a probablty f(p. f(p = 0 f P < P ˆ λ or P >, where ˆP =. On the nterval λ ˆP,, f ( λ P = P. Each frm s expected proft s PP,PP PP,PP = = λ. ( 2 Frm Uses Posted Prces; Frm Uses a NYOP Format Retaler chooses ts posted prce n order to maxmze the expected proft gven n Equaton (6 (wth the proft functon for retaler, PP,NYOP, gven by Equaton (5. t the nteror soluton of ( ( ( 3 -λ c -λ PP,NYOP( IS Frm (who uses a posted prce s 3 =. The proft for Frm s ( λ ( λ λ - c - 6c PP,NYOP( IS CS = + 3. There s also a potental corner soluton at 4 IS P ( λ 2c - = 3, proft for the - P =. Here, frm s proft s PP,NYOP( CS - PP,NYOP( CS λ = λ and frm s proft s =. Frm chooses the posted prce that yelds the 8c 6c hghest proft: (4 ( λ ( λ λ 3 f c 2 4( - 2( -λ 3 - c - 2 PP,NYOP PP,NYOP( IS PP,NYOP( CS = Max, = - λ f c > 8c 2( -λ oth Frms Use a NYOP Format When both retalers use a NYOP format, proft s gven by Equaton (7. Takng these ntegrals, NYOP,NYOP NYOP,NYOP 2 λ (5 = = 48c Dervaton of the Optmal Market Format Proposton For (PP, NYOP to be a Subgame-Perfect Nash Equlbrum, then Frm must earn greater proft by choosng the NYOP format rather than the posted prce format. One can calculate the dfference n proft under these two formats as: (6 PP,NYOP c ( -λ λ 3 λ + f c 4 PP,PP 4 4( - 6c 2( -λ = - λ - λ f c > 6c 2( -λ

23 Ths dfference n the bottom term s postve as long as λ ( 6c met when λ < (snce 9 PP,NYOP PP,PP the dfference n proft ( PP,NYOP = PP,PP > + or λ <. Note that ths condton wll be + 6c c <. Furthermore, the top term s decreasng n c. Thus, on the range, 2 2 ( λ ( 5λ 2 2( s mnmzed at c =. When c =, 2 -λ 2 -λ, whch s postve for all retaler to prefer the NYOP format over a posted prce format. ( ( c,, 4 2( -λ λ <. Therefore, λ < s a suffcent condton for 5 9 In addton, for (PP, NYOP to be a Subgame-Perfect Nash Equlbrum, Frm must earn greater proft by choosng the posted prce format rather than the NYOP format. The precedng analyss shows that f frm chooses the posted prce format, then frm wll select the NYOP format. To determne frm s proft from selectng the NYOP format nstead, one needs to antcpate whether frm would best respond by selectng the posted prce format or the NYOP format. Specfcally, one can calculate: ( λ ( λ λ λ 3 f c 2 4( - 48c 2( -λ 3 - c NYOP,PP NYOP,NYOP (7 == 8-3λ λ f c > 48c 2( -λ Numercal calculatons verfy that ths dfference s postve over the entre relevant parameter range. Therefore, frm wll choose the posted prce format f frm has chosen the NYOP format. For (PP, NYOP to be a Subgame-Perfect Nash Equlbrum, we must have (8 PP,NYOP NYOP,PP PP,NYOP. We can show NYOP,PP 3 ( ( 3 0c -λ 2c λ f c 3 6c 2 2( - = λ λ 3-5λ λ f c > 6c 2 - For both the upper and lower expressons of (8, the dfference, mnma over the two ranges are reached at dfference, PP,NYOP are postve for all λ <. 9 Incentve to llow Re-ds NYOP,PP, are c = and ( ( ( λ 5 -λ 4 λ 4λ PP,NYOP NYOP,PP ( λ, s ncreasng n c. Thus, the c =, respectvely. t these mnmzng ponts, the 2 - λ ( λ ( 5 λ and 8(, respectvely. These values Customers who are loyal to retaler (who uses the NYOP format can place up to two bds. The optmal bddng strategy s: 2 bd b2, then bd b22 f b2 s rejected f 0 c c2 (0 place a sngle bd of bˆ f c2 < c cˆ do not bd at all f c > ˆ c For the swtchers, the optmal bddng strategy s: + 2c 2 + c 2 3 b =, b =, c = where

24 22 ( bd bˆ 2, then bd bˆ 22 f bˆ 2 s rejected; purchase at P f bˆ 2 s rejected f 0 c cˆ 2 place a sngle bd of ˆ ; purchase at f ˆ b P b s rejected f cˆ < c cˆ purchase at P wthout bddng at all f c c 2 > ˆ where ˆ P c ˆ 2P + c P P b ˆ 2 =, b 22 =, c2 = The followng analyss proceeds under the assumpton that c and λ. These restrctons ensure that 2 λ 9 ( when retaler (.e., the NYOP frm restrcts consumers to a sngle bd, retaler selects a posted prce P =. The equlbrum expected proft for each frm s: PP,NYOP( bd (2 = λ 8c PP,NYOP( bd λ (3 = 6c If retaler allows consumers to re-bd f ther ntal bd s rejected, then the profts for the two frms are gven by: ˆ ˆ ˆ2 22 ˆ c b c b PP,NYOP( 2 bds (4 = P λ ( f ( c d PNYOP dc + f ( c d PNYOP dc c = 0 PNYOP = 0 c = cˆ 2 PNYOP = 0 ˆ c2 b2 b 22 ĉ b PP,NYOP( 2 bds = λ 2f ( d 22f ( d d ˆ b c PNYOP + b c PNYOP c + bf ( c dpnyop dc c = 0P NYOP = 0 PNYOP = b2 c = c2 PNYOP = 0 (5 bˆ ˆ 2 b ˆ cˆ 2 22 cˆ b + ( bˆ 2f ( c dp ˆ NYOP + b22f ( c dp NYOP dc + ˆb f ( c dpnyop dc c = 0 PNYOP = 0 P ˆ NYOP = b2 c = cˆ 2 PNYOP = 0 Retaler chooses P to maxmze (4. The closed form soluton s extremely complex. ut, Fgure 2 provdes an PP,NYOP( bd PP,NYOP( 2 bds example that verfes the clam n Proposton 2. In partcular, when λ =.05, > for 9 c, Furthermore, one can verfy that n the absence of ths strategc effect on prces (.e., that P s lower when re-bddng s allowed, the NYOP frm s always more proftable when rebddng s allowed. In partcular, (6 PP,NYOP( 2 bds PP,NYOP( bd ( P ( λ = ( P = = > 0 692c 692c