Horizontal Product Differentiation in Auctions and Multilateral Negotiations *

Transcription

1 Horzontal Product Dfferentaton n Auctons and Multlateral Negotatons * Charles J. Thomas Bart J. Wlson John E. Walker Department of Economcs Economc Scence Insttute Clemson Unversty Chapman Unversty 222 Srrne Hall One Unversty Drve Clemson, SC Orange, CA E-mal: cjt@clemson.edu E-mal: bartwlson@gmal.com August, 2011 Abstract: We expermentally compare frst-prce auctons and multlateral negotatons after ntroducng horzontal product dfferentaton nto a standard procurement settng. Both nsttutons yeld dentcal surplus for the buyer, a dfference from pror fndngs wth homogeneous products that results from dfferentaton s nfluence on sellers prcng behavor. The data are consstent wth ths fndng beng drven by concessons from low-cost sellers n response to dfferentaton reducng ther lkelhood of beng the buyer s surplus-maxmzng tradng partner. Further analyss shows that ntroducng product dfferentaton ncreases or leaves unchanged the ntensty of prce competton among sellers, whch contrasts wth the conventonal wsdom that product dfferentaton softens competton. * We thank the Internatonal Foundaton for Research n Expermental Economcs for provdng fnancal support, and Jeffrey Krchner for wrtng the software. The data and nstructons are avalable upon request. Ovdu Lasca, Mke Maloney, Curts Smon, Ange Starrett, Patrck Warren, and semnar partcpants at Clemson Unversty and the Unversty of South Carolna provded helpful comments and advce. JEL: C78, D44, C9, L14 Keywords: voluntary exchange, multlateral negotatons, auctons, product dfferentaton

2 1. Introducton Understandng the varety of ways n whch voluntary exchange s conducted s a fundamental goal of economcs, n part to enable an nformed choce amongst exchange methods by usng metrcs such as proftablty or effcency. For example, n dfferent settngs barganng, auctons, and posted prces all are used to arrange for the trade of goods and servces. Varants emerge that blur the lnes between what prevously appeared to be dstnct types of exchange methods. 1 In fact, some of these new methods themselves become goods and servces, wth ther desgners applyng for patent protecton and beng hred to organze markets. 2 Prevous research suggests that a tradng mechansm s performance depends on characterstcs of the strategc envronment n whch t s used. For example, Klemperer [2002] argues that one sze does not ft all n aucton desgn, wth factors such as the number of potental bdders, ther relatve sze or mportance, and the lkelhood of colluson mertng careful consderaton. Smlarly, theoretcal arguments show that t matters who makes offers n blateral barganng when there s one-sded prvate nformaton. 3 Wth the precedng ponts n mnd, n ths paper we use the expermental method to evaluate how ntroducng horzontal product dfferentaton nto a standard procurement settng affects the outcomes of two commonly used means of exchange, auctons and multlateral negotatons. Auctons are used n procurement and to allocate products such as electrc power, polluton rghts, art, and government securtes. 4 Multlateral negotatons combne features of auctons and blateral barganng, although they have receved much less academc attenton than 1 Consder the Anglo-Dutch aucton descrbed n Klemperer [2002], the smultaneous ascendng aucton, used to sell U.S. rado spectrum, descrbed n Mlgrom [2000], or the Buy It Now feature n auctons on E-Bay. 2 Companes such as MercExchange, Inc. and Ozro, Inc. have obtaned patents coverng onlne auctons and electronc negotatons, respectvely. Economsts such as Paul Mlgrom and Larry Ausubel also hold patents on dfferent aucton desgns. 3 Kennan and Wlson [1993] provde an excellent overvew of barganng wth prvate nformaton. 4 See Wolfram [1998], Cason [1995], Mlgrom and Weber [1982], and McAfee and McMllan [1987]. 1

3 have those two exchange methods. 5 In them, a buyer solcts offers from multple sellers, and then plays the sellers off one another to receve addtonal concessons. They are used n settngs such as procurement, hgh-end job markets, and the purchase of contractors servces and automobles. Gven that auctons and multlateral negotatons often are used n smlar settngs, even by apparently smlar buyers n narrowly defned markets, our prmary reason for nvestgatng them s to see f they yeld equvalent outcomes. One reason we consder product dfferentaton s that analyses of auctons and multlateral negotatons typcally assume that bdders are homogeneous from the auctoneer s perspectve, 6 but frequently n procurement the buyer has preferences over non-prce attrbutes of the sellers products. For example, when Arbus and Boeng competed for a szeable contract from Ibera Arlnes n 2003, both sellers had to deal wth Ibera s prvately known preferences. 7 These stemmed from Ibera s evaluaton of dfferences n the sellers product characterstcs, and of how ts fleet composton would affect mantenance costs and future procurement epsodes. Smlar stores abound from companes lke Hewlett-Packard, IBM, Kaser Permanente, Nssan, Pfzer, and Sun Mcrosystems. 8 Product dfferentaton s prevalence n procurement makes nvestgatng ts effect on behavor worthwhle. A second reason we consder product dfferentaton s that pror research fnds that some aucton formats gve the buyer more surplus than do multlateral negotatons, whch leaves open the queston of why multlateral negotatons are so commonly used. One reason may be that 5 See Thomas and Wlson [2002, 2005], along wth related work n Cason, et al [2003]. 6 For example, see Mlgrom and Weber [1982], McAfee and McMllan [1987], Wolfram [1998], Waehrer and Perry [2003], and Thomas and Wlson [2002, 2005]. 7 Arbus and Boeng Duke t Out to Wn Lucratve Ibera Deal, Wall Street Journal, March 10, See the followng artcles n Purchasng, or at purchasng.com: HP s Purchasng Organzaton Looks Beyond Prce, September 11, 2008; It s Not Just About Cost, March 15, 2007; Procurement Brngs Green Intatves to Lfe at Kaser Permanente, December 13, 2007; Nssan Pushes Supplers on Qualty, October 5, 2006; Pfzer s Procurement Provdes 12 Tps for Reverse Aucton Success, December 11, 2008; Sun s e-aucton Evoluton, September 13,

4 real strategc envronments dffer n mportant dmensons from the settngs that so far have been examned. Dfferentaton may be one such dmenson, and when t s present we hypothesze that the dynamc nature of multlateral negotatons allows the buyer to proftably explot ts prvately known preferences n a way that one-shot auctons do not. If so, then n ths settng the buyer may receve relatvely more surplus by usng negotatons than by usng auctons. We ntroduce horzontal product dfferentaton by usng a lnear random utlty model that we modfy so each seller s producton cost s ts prvate nformaton. 9 Prvate nformaton about the buyer s values and the sellers costs contrbutes to the man dfference between the auctons and the negotatons, namely that the communcaton allowed by the negotatons provdes opportuntes for each party to sgnal or msrepresent ts prvate nformaton n an attempt to secure more of the gans from trade. 10 We use experments to evaluate the effect of product dfferentaton on auctons and multlateral negotatons because theoretcal characterzaton of equlbrum behavor n the settng we consder remans an open problem. Our approach accords wth the theoretcal perspectve of Muthoo [1999, p.342] that a prmary role of barganng experments should be to make new dscoveres about barganng for example, to dentfy new forces that may have a sgnfcant mpact on the barganng outcome. In that way barganng experments can help n the further development of the theory of barganng. Muthoo s nsghts complement the expermental perspectve artculated by Smth [1982]. He advocates heurstc nvestgatons of new envronments and nsttutons, especally when strategc complexty leads to analytc ntractablty, because t s through exploratory probes of new phenomena that attenton may be redrected, old belef systems may be reexamned, and new scentfc questons may be asked 9 See Anderson, de Palma, and Thsse [1992] for a comprehensve treatment of dscrete choce models. 10 Smlar ncentves exst n blateral barganng wth prvate nformaton. See Fudenberg and Trole [1983] for an early treatment. 3

5 (p. 942). In ths ven, economc experments have recently played a major role n test-beddng spectrum auctons, wholesale markets for electrc power, and NOx allowance auctons. 11 Introducng product dfferentaton yelds several questons of nterest. Frst, how do the outcomes of auctons and multlateral negotatons compare when there s product dfferentaton? We fnd that both nsttutons yeld the buyer the same expected surplus, whch helps explan the prevalence of multlateral negotatons despte earler results suggestng that buyers mght prefer auctons. Wth homogeneous products Thomas and Wlson [2002] fnd that auctons yeld hgher surplus than do multlateral negotatons wth two sellers, but yeld the same surplus wth four sellers. The present fndngs suggest that havng prvately known preferences over the sellers products allows the buyer to extract relatvely more surplus from the sellers when negotatng than when usng an aucton, at least when there are few sellers. Second, can we determne how these changes n the nsttutons relatve performance occur? That s, from the buyer s perspectve, does ntroducng product dfferentaton mprove the negotatons performance, degrade the auctons performance, or lead to some other change? To address ths ssue we measure the ntensty of competton among the sellers, and we fnd a surprsng result. Wth two sellers followng the ntroducton of product dfferentaton, prce competton n both nsttutons ntensfes to dfferent extents. Ths fndng suggests that the buyer benefts from havng prvately known preferences, and ths beneft s greater n the negotatons. Wth four sellers there s no dscernble change n the ntensty of prce competton n ether nsttuton. Whle the latter fndng s dfference from the former smply may reflect that the settngs wth four sellers are ntensely compettve regardless of product 11 See Banks, et al [2003], Rassent, Smth, and Wlson [2002], and Porter, et al [2009]. 4

6 characterstcs, both fndngs contrast wth the conventonal wsdom that product dfferentaton softens competton among sellers. 12 The rest of the paper s organzed as follows. Secton 2 descrbes the theoretcal framework underlyng our strategc settng, whle Secton 3 descrbes related research. Sectons 4 and 5 present our expermental desgn and fndngs, whle Secton 6 brefly concludes. 2. Modelng Framework In ths secton we present a model of the strategc envronment n whch auctons and multlateral negotatons are used. It s dentcal to the model n Thomas and Wlson [2002, 2005], but for the addton of the buyer s prvately known preferences for the sellers products. The model llustrates detals underlyng our expermental desgn and provdes gudance for future theoretcal analyses. We conclude by descrbng our conjectures about the effects of ntroducng product dfferentaton n multlateral negotatons and auctons. Buldng upon the modelng framework used n earler analyses allows us to compare our new results wth pror observatons. Ths comparson lets us clearly see the effect of ntroducng prvately known preferences for the buyer, usng as a startng pont an establshed set of results nvolvng homogeneous products. 13 Consder a settng n whch T rsk-neutral sellers producng horzontally dfferentated products compete to fulfll one ndvsble contract for a rsk-neutral buyer. Seller s cost c of fulfllng the contract s a prvately known ndependent draw from the commonly known contnuous dstrbuton functon G, wth densty g that s strctly postve on the nteror of the 12 For example, see Trole [1988, Ch. 7]. 13 Another lne of frutful research would be to evaluate exstng models of product dfferentaton, but that s beyond the scope of our paper. Moreover, n Secton 3 we descrbe how no exstng models have all of the features that are relevant to the strategc scenaros we consder. 5

7 support [c,c]. The buyer places a prvately known value V on havng the contract fulflled by seller, where each V s an ndependent draw from the commonly known contnuous dstrbuton functon H, wth densty h that s strctly postve on the nteror of the support [ v, v]. 14 The players learn ther prvate nformaton before ntatng the exchange process. Exchange s conducted va frst-prce auctons or nonverfable multlateral negotatons. In both mechansms, for a gven contract the wnnng seller s payoff s p c w, where p s the prce pad to the wnnng seller and c w s the wnnng seller s cost of fulfllng the contract. All other sellers payoffs are 0. The buyer s payoff s V w p, where V w s the buyer s value from havng the wnnng seller fulfll the contract. Effcency s (V w c w )/Max [V - c ] f Max [V - c ] > 0, and otherwse s undefned. In a frst-prce aucton the sellers smultaneously and secretly submt prce offers. The seller offerng the buyer the largest payoff wns the contract and s pad the prce that t offered, condtonal on that payoff beng postve. That s, seller wns and s pad prce p f V p > Max j [0, V j p j ]. In the case of tes, the wnner s selected at random from the set of sellers whose offers yeld the buyer ts greatest postve payoff. In a nonverfable multlateral negotaton the sellers smultaneously and secretly submt ntal prce offers. The buyer can accept one ntal offer or reject them all. If the buyer rejects all ntal offers, then t can ndvdually engage each seller n non-bndng dscussons concernng further concessons. A seller has no nformaton about other sellers offers, so t cannot verfy any clams the buyer makes about the attractveness of those offers. 15 At any tme each seller can make a new offer by reducng ts prce from ts current offer. Importantly, each 14 The homogeneous product settng consdered by Thomas and Wlson [2002, 2005] corresponds to the dstrbuton H beng degenerate at a specfc value. 15 Ths contrasts wth the verfable multlateral negotatons consdered n Thomas and Wlson [2005]. 6

8 seller s best offer remans vald, so the buyer can hold a seller s offer whle t searches for a better one. Negotatons contnue untl agreement s reached or the partes abandon the process. Wth homogeneous products Thomas and Wlson [2002] conjectured that the outcomes of nonverfable multlateral negotatons and frst-prce auctons would look smlar. Ths conjecture was guded by the followng theoretcal arguments nvolvng a varant of the button aucton descrbed by Mlgrom and Weber [1982]. Suppose that a prce clock declnes from a suffcently hgh level that all sellers would be wllng to fulfll the contract at the startng prce. Each seller sgnals ts wllngness to supply at the current prce by depressng a button, and sgnals ts lowest offer by releasng ts button at that prce. A seller cannot re-enter the bddng, and t cannot see when ts rvals release ther buttons. The aucton concludes when the last seller releases ts button, and that seller s awarded the contract at the prce showng on the clock when t released ts button. Ths aucton s smlar conceptually to nonverfable multlateral negotatons, because n ether nsttuton a seller must be concerned that t s makng unnecessary prce concessons when t already s wnnng the competton. Moreover, the button aucton s strategcally equvalent to a frst-prce aucton. In both auctons, strateges consst of mappngs from costs nto prces, and seller s choosng ts prce to maxmze the objectve functon p c Pr p wns. The evdence wth homogeneous products showed the conjectured relatonshp held only partly. Negotatons and auctons yelded the buyer statstcally ndstngushable amounts of surplus wth four sellers, but negotatons yelded statstcally less surplus than dd auctons wth two sellers. The dfference n duopoly occurred when a seller wth especally low costs faced a rval wth especally hgh costs. Even though the sellers costs were prvate nformaton, when there was a large gap between ther costs the buyer for some reason was unable to extract 7

9 sgnfcant concessons from the low-cost seller once the hgh-cost seller effectvely dropped out of the negotatons. Wth dfferentated products we conjecture that multlateral negotatons wll perform relatvely better for the buyer than wll frst-prce auctons, because the aucton outcomes are lkely to be neffcent. 16 Ineffcency corresponds to lost gans from trade, and we thnk the communcaton avalable wth multlateral negotatons wll allow the buyer to obtan some of the surplus that would be lost n the auctons. 3. Related Research Although to date no theoretcal analyses of multlateral negotatons nclude all of what we consder to be essental elements of the strategc envronment, there s related theoretcal and expermental research. Recognzng how that research dffers from the settng we consder s mportant n formulatng subsequent analyses. For addtonal references, please consult Thomas and Wlson [2002, 2005]. The frst set of relevant papers nvolves the trade of homogeneous products through exchange methods featurng aspects of barganng. Shaked and Sutton [1984] model an alternatng offer settng n whch the buyer can swtch to a dfferent seller after some commonly known length of tme. Both sellers have the same commonly known producton cost, the buyer can bargan wth only one seller at a tme, and swtchng to another seller vods any exstng offer. The authors fnd that the buyer obtans greater surplus than f swtchng were mpossble. 16 Frst-prce auctons are predcted to be 100% effcent wth homogeneous products n our settng. To see from a theoretcal perspectve why frst-prce auctons mght be neffcent wth dfferentated products, suppose that sellers set ther prces accordng to a functon that s strctly ncreasng n ther prvately known producton costs. The wnnng seller wll not necessarly be the one wth the largest dfference between the buyer s value and the seller s cost, because equlbrum prce-settng functons lkely ncrease less than one for one wth the seller s cost. 8

10 McAfee and Vncent [1997] model an aucton wth a publc reserve prce, n whch the auctoneer cannot commt not to solct future offers f t rejects all current offers. They show that as the tme between offers goes to zero, expected revenues converge to those from a statc aucton wth no reserve prce. The nablty to forego seekng future offers gves ths aucton a feel smlar to multlateral negotatons, and results such as thers support conjectures about the smlarty of the nsttutons outcomes. Wang [2000] models a procurement settng n whch the buyer has the same prvately known value for each seller s product, and the sellers have prvately known costs. After the sellers make smultaneous prce offers, the buyer can reject all offers, accept the lowest offer and pay t, or negotate wth the seller makng the lowest offer. The negotated outcome conssts of the equlbrum payoffs from an alternatng offers barganng model wth one-sded ncomplete nformaton, because the author assumes that the seller s cost becomes common knowledge once negotatons commence. Cason, Fredman, and Mlam [2003] expermentally evaluate a tradng envronment n whch several sellers and buyers engage n blateral negotatons that start from the seller s lst prce. A buyer can abandon negotatons wth one seller by ncurrng a cost to ntate negotatons wth another seller. The authors fnd that effcency s lower and prces are hgher n ths settng than n a posted offer envronment. The next set of relevant papers consders the trade of dfferentated products through varous aucton formats. Che [1993] models scorng auctons n whch sellers make prcequalty offers to a buyer who evaluates the offers accordng to a scorng rule. The man dfference between our approach and the lterature on scorng auctons s that we assume that 9

11 sellers do not talor ther product to a partcular buyer. Whether product dfferentaton s endogenous or exogenous s an emprcal matter specfc to the market n queston. Engelbrecht-Wggans, Haruvy, and Katok [2007] theoretcally and expermentally analyze a procurement settng n whch the buyer s value for seller s product s known by the buyer and by seller, and the sellers have prvately known costs. The authors study a prcebased mechansm n whch the seller offerng the lowest prce wns the contract at the prce that t offered, and a buyer-determned mechansm n whch the seller offerng the hghest payoff to the buyer wns the contract at the prce that t offered. The latter mechansm s equvalent to the frst-prce aucton n the present paper, but ther assumpton that a seller knows the buyer s value for ts product makes that mechansm somorphc to a standard aucton wth homogeneous products. 17 The aucton n our settng s not solvable through smlar means. Rezende [2009] models a duopoly procurement settng n whch the buyer can credbly reveal ts preferences for the sellers products. The sellers partcpate n a dynamc aucton n whch they observe all exstng prce offers, and n alternate perods they choose whether or not to cut ther exstng prce offer by a specfed amount. The aucton concludes f the sellers refran from cuttng prce n consecutve perods, after whch the buyer can negotate wth one of the sellers. The author fnds that the buyer should fully reveal ts preferences, but that t may prefer not to learn ts actual values for the sellers products. 4. Expermental Desgn and Procedures Usng Secton 2 s framework as a gude, for the experment we par two treatments, one wth 16 frst-prce auctons and one wth 16 nonverfable multlateral negotatons. We vary 17 Two other dfferences are that they assume proftable trades always exst, and that the buyer mght not select the wnner that maxmzes ts payoff. 10

12 these two treatments by changng the number of sellers from two per buyer to four per buyer, whch yelds four treatments n total. For each of the four treatments we have four groups of subjects, whch we also refer to as sessons. Each subject s assgned a specfc role n a specfc group for the duraton of the experment. A seller s characterstcs consst of 16 prvately known random cost draws from the Unform dstrbuton on the support [0, 600] (n cents), one for each tme perod. Of the eght groups wth four sellers, seller ( = 1, 2, 3, 4) has the same cost draws across groups. Of the eght groups wth two sellers, seller ( = 1, 2) has the same cost draws across groups. Moreover, the costs of sellers 1 and 2 n the two-seller treatment are the same as the costs of sellers 1 and 2 n the four-seller treatment. These desgn features reduce the varaton across subjects, and consequently tghten the standard errors of our estmates. The buyer s characterstcs consst of 16 sets of prvately known random preference draws from the Unform dstrbuton on the support [300, 900]. Each set conssts of ether two or four draws for each tme perod, dependng on the number of sellers. Analogously to the sellers costs, the buyers n all 16 groups have the same preference draws for seller ( = 1, 2, 3, 4). The presence of product dfferentaton s the dfference between the envronment n ths experment and the one reported n Thomas and Wlson [2002]. In that experment the buyer s value for each seller s product was commonly known to be 600, whle here the unbased expectaton of the buyer s value s 600. Consequently, a transacton between the buyer and a randomly chosen seller has the same expected total surplus n both envronments, but ntroducng product dfferentaton ncreases expected total surplus from the surplus-maxmzng transacton. The frst-prce aucton proceeds wth each seller smultaneously submttng a prce offer, at whch pont the wnner s determned as descrbed n Secton 2. The nonverfable multlateral 11

13 negotaton proceeds wth each seller smultaneously submttng an ntal prce offer. If the buyer rejects all ntal offers, the negotatons are mplemented by the buyer engagng n nonbndng text messagng wth each seller over the computer network. The buyer cannot credbly reveal to a seller ts preferences or the other sellers offers. Sellers can respond to these communcatons by makng lower prce offers, the buyer can accept or reject these new offers, and so on. Each seller s best offer remans vald whle the negotatons are conducted, so seekng better offers does not vod exstng ones. Partcpants, undergraduate students recruted from the general student populaton of a large state unversty, receved $5 for showng up on tme, plus ther salent earnngs. In the four-seller sessons the buyers exchange rate was US$1 for 7 expermental dollars, and the sellers exchange rate was US$1.50 for 1 expermental dollar. In the two-seller sessons the respectve exchange rates were 4 and 2 expermental dollars for each US$1. In addton to the $5 show-up payment, the average subject earned $ The average sesson lasted 90 mnutes. 5. Expermental Results For each perod we observe the transacton prce, the buyer s value for each seller s product, each seller s cost, each seller s offer n the auctons, and each seller s ntal and subsequent offers n the multlateral negotatons. We analyze the data usng a lnear mxedeffects model for repeated measures, 18 and we pool the data from the present experment wth the data from Thomas and Wlson [2002] that consders homogeneous products. 19 Combnng the 18 See Longford [1993] for a descrpton of ths technque commonly employed n expermental scences. 19 In partcular, we use the data from the frst twelve perods of the experment descrbed n Thomas and Wlson [2002]. That experment used a crossover desgn, and so the outcomes followng a change from one nsttuton to another are not drectly comparable to the outcomes n the present experment. 12

14 data permts parsmonous comparsons across nsttutons wthn a dfferentaton regme, and wthn nsttutons across dfferentaton regmes Dfferentaton s Effect on Surplus Comparsons Across Insttutons We focus our attenton on the buyer s surplus rather than on the transacton prce, because prces do not provde a meanngful way to compare settngs wth and wthout product dfferentaton, from the perspectve of the partcpants payoffs. 20 Moreover, even acrossnsttuton comparsons usng prces may be msleadng n settngs wth product dfferentaton. For example, auctons may lead to hgher transacton prces but hgher buyer s surplus, f n the auctons the buyer more frequently purchases from the seller whose product has the hghest ntrnsc value. In that case the buyer would prefer the exchange mechansm wth hgher prces. Table 1 reports the model s regresson results, wth the buyer s surplus as the dependent varable. The treatment effects (Two vs. Four Sellers, Nonverfable Multlateral Negotaton vs. Frst-Prce Aucton, and Dfferentaton (D) vs. Homogeneous Products) and the two- and threeterm nteracton effects from a 2 3 desgn are modeled as (zero-one) fxed effects. The 32 ndependent sessons are modeled as random effects, e. Followng Thomas and Wlson [2002], we control for across-perod surplus varaton by ncludng perod-specfc devatons of the hghest and second-hghest surpluses from ther theoretcal expected values. We denote those devatons by s 1 and s Ths formulaton captures each treatment s expected buyer s surplus n the treatment coeffcent, because on average s 1 = s 2 = 0. Specfcally, we estmate the model 20 The results n Thomas and Wlson [2002] regardng transacton prces wth homogeneous products can be easly translated nto surplus terms, because the buyer s value for all sellers products s a known constant. 21 Wth homogeneous products and two sellers, the expected values of the hghest and second-hghest surpluses are 400 and 200. Wth four sellers the expected values are 480 and 360. Wth horzontally dfferentated products and two sellers, the expected values are 440 and 160. Wth four sellers the expected values are and

15 B j e Two Negotaton Two Negotaton s 4 1j s 8 2j D s D s s s 1j 2j D s Two s Two s 1j D s 2j Two D s Negotaton s Negotaton s D D Two D Negotaton D Two Negotaton j 9 2j j 10 2j j Two D s j 7 1j j Negotaton D s Two Negotaton Two Negotaton 19 1j Negotaton D s 23 2j Two Negotaton Two Negotaton j where 2 denotes the buyer s surplus n perod j of sesson, wth e ~ N(0, ) and B j 1 2 j ~ N(0, 2, ). 22 We accommodate heteroskedastc errors by sesson when estmatng the model va maxmum lkelhood. Estmates of the treatment effects are easy to compute wth ths specfcaton. The buyer s expected surplus s μ n a four-seller frst-prce aucton wth homogeneous products, μ + β 12 n a four-seller frst-prce aucton wth dfferentated products, μ + β 2 n a four-seller nonverfable multlateral negotaton wth homogeneous products, and so forth. Across-treatment surplus dfferences, and dfferences-n-dfferences, also are easy to compute. For comparson purposes, we begn by restatng a central fndng from Thomas and Wlson [2002] regardng the buyer s surplus wth homogeneous products. Fndng 0: Consder the settng wth homogeneous products. Wth two sellers the buyer s surplus when usng multlateral negotatons s sgnfcantly lower than when usng frst-prce auctons. In contrast, wth four sellers the buyer s surplus s statstcally ndstngushable when usng multlateral negotatons and frst-prce auctons. 22 It s mportant to note that the lnear mxed-effects model for repeated measures treats each sesson as one degree of freedom wth respect to the treatments. 14

16 Evdence: Wth two sellers the sum of the coeffcents on Negotaton and Two Negotaton on the left sde of Table 1 represents the amount by whch the negotaton treatment changes the buyer s surplus relatve to frst-prce auctons. The negotaton treatment sgnfcantly decreases the buyer s surplus by (= ) expermental cents below ts level n frst-prce auctons (p-value = ). Wth four sellers the pont estmate of the negotaton treatment s economcally small (-3.1) and statstcally nsgnfcant (p-value = ). Our explanaton of Fndng 0 comprses part of our explanaton of Fndng 1, so we postpone t brefly. To begn our analyss of product dfferentaton, we evaluate the buyer s surplus across nsttutons. Fndng 1: Consder the settng wth horzontally dfferentated products. Wth a gven number of sellers, the buyer s surplus s statstcally ndstngushable when usng multlateral negotatons and frst-prce auctons. Evdence: The estmates n Table 1 provde the evdence for ths fndng. Wth two sellers the dfference between the buyer s surplus n the negotatons and the auctons s 12.4 (= ) and nsgnfcant (p-value = ), as gven by the sum of the coeffcents on Negotaton, Two Negotaton, Dfferentated Negotaton, and Dfferentated Two Negotaton. Wth four sellers the dfference s 1.6 (= ) and nsgnfcant (p-value = ), as gven by the sum of the coeffcents on Negotaton and Dfferentated Negotaton. 15

17 Unlke wth homogeneous products, a buyer facng two sellers does not receve hgher surplus wth frst-prce auctons than wth multlateral negotatons. Ths relatve mprovement for the buyer n the negotatons performance suggests that the buyer can better explot ts prvately known preferences as a result of the communcatons allowed by the multlateral negotatons. Moreover, ths fndng s consstent wth our hypothess that multlateral negotatons prevalence stems n part from aspects of strategc envronments that are absent from earler analyses. In Secton 2 we conjectured that ntroducng product dfferentaton would yeld a relatve mprovement n the buyer s surplus from negotatons over auctons, because negotatons may capture gans from trade lost by the auctons. To evaluate ths explanaton for Fndng 1, we would lke to estmate product dfferentaton s effect on effcency. However, effcency n each perod s so consstently hgh n all sessons that there s nsuffcent varaton to estmate a lnear mxed-effects model for the rato of realzed total surplus to maxmum avalable surplus. Instead we provde suggestve evdence about effcency by comparng the expected value of the hghest total surplus to the sum of the estmated values of the buyer s surplus and the sellers surplus. Table 2 reports estmates of the wnnng seller s surplus, usng the same lnear mxed-effects approach wth whch we estmated the buyer s surplus n Table 1. These estmates n fact reflect the sum of the sellers surpluses, because losng sellers earn zero. Table 3 reports the sum of the estmated buyer s surplus and wnnng seller s surplus as a fracton of the expected maxmum total surplus. Effcency s hgh n all treatments, and there s no obvous economcally sgnfcant change from ntroducng product dfferentaton. Ths evdence suggests that the negotatons relatve performance mprovement s not drven by neffcency n the frst-prce auctons when there s product dfferentaton. 16

18 Another possble explanaton for Fndng 1 begns by notng that product dfferentaton does not obvously affect the orgnal ntuton for the conjectured relatonshp between frstprce auctons and nonverfable multlateral negotatons. As we descrbed n Secton 2, Thomas and Wlson [2002] argued that a seller n nonverfable multlateral negotatons wth homogeneous products must be concerned that the buyer s lyng about the seller s current standng n the competton. Ths concern translates nto decsons about what prcng concessons to make, and those relate to prcng ncentves n aucton formats that are strategcally equvalent to frst-prce auctons. Specfcally, seller n the negotatons essentally s choosng a stoppng prce p to maxmze c Pr p wns, p whch has the same form as the seller s objectve functon n a frst-prce aucton. A seller s objectve functon has the same form wth dfferentated products, although the probablty of wnnng depends on prces and the buyer s values for the sellers products. Ths perspectve suggests the same lnk between auctons and negotatons, whether products are homogeneous or dfferentated. 23 As descrbed n Fndng 0, the observed behavor wth homogeneous products partly supported the conjectured relatonshp. Thomas and Wlson [2002] show that the departure occurred n duopoly when one seller had partcularly low costs and the other seller had hgh costs. In such cases t appears that the buyer was unable to obtan sgnfcant concessons from the low-cost seller n the negotatons. Wth four sellers the buyer s ablty presumably s less relevant, because the dfference between the lowest and second-lowest costs on average s smaller than when there are only two sellers. Fndng 1 shows that the across-nsttuton dfference dsappears wth dfferentaton. Gven that the dfference wth homogeneous products appeared for partcular realzatons of the 23 Note that we are not suggestng, for example, that the Bayesan Nash equlbrum n a frst-prce aucton s the same wth homogeneous and dfferentated products. By consderng the prcng behavor of a seller wth the hghest possble cost draw, one can easly show that the equlbra must dffer. 17

19 sellers costs, the dfference wth dfferentated products may dsappear n the same nstances. Fgure 1 supports ths explanaton by plottng transacton prces aganst each perod s lowest realzed cost. The top two panels show average transacton prces n each perod for each nsttuton, wth homogeneous products. The left panel represents the settng wth two sellers, and the rght the settng wth four sellers. Wth two sellers the dfference n outcomes between the auctons and the negotatons s evdent by the gap n the lnear trend lnes when the lowest realzed cost s less than 225. Wth four sellers the smlarty n outcomes across nsttutons s equally apparent for all lowest realzed costs. The bottom two panels nclude the trend lnes from the top two panels, overlad by the data and lnear trend lnes for each nsttuton wth dfferentated products. As s evdent, ntroducng product dfferentaton lowers transacton prces n the two-seller nonverfable multlateral negotatons precsely when the lowest realzed cost s qute low. The change n the sellers prcng behavor may stem from a low-cost seller s reduced lkelhood of beng the buyer s surplus-maxmzng tradng partner. That s, low costs are less of a guarantee that the seller s gong to make a sale wth dfferentated products, because the buyer may have a low ntrnsc value for that seller s product and a hgh ntrnsc value for the other seller s product. Therefore, a low-cost seller may be more easly persuaded to offer prce concessons when there s dfferentaton. If so, ths may serve to mtgate the buyer s unexpected barganng handcap that was observed wth homogeneous products Dfferentaton s Effect on Sellers Prcng Behavor Whle Fndngs 0 and 1 llustrate the change n the relatve performance of auctons and negotatons, consderng how that change comes about may deepen our understandng of how 18

20 product dfferentaton changes behavor n the two nsttutons. That s, whle we know that ntroducng product dfferentaton wth two sellers causes the negotatons to become relatvely more compettve than the auctons, s ths due to more ntense competton n the negotatons, less ntense competton n the auctons, or some other change? In the next fndng we address ths ssue by measurng the ntensty of competton n each treatment. Whle there are many ways one mght attempt to measure competton, care must be taken to account for changes that arse smply because expected surplus s greater n the settngs wth product dfferentaton, or from other effects of changng the strategc envronment. Our measure of the ntensty of competton ncludes the buyer s realzed surplus n a perod, B, as a fracton of the maxmum total surplus possble that perod, S 1. Identfyng what fracton of the avalable surplus the buyer receves, rather than just the amount of surplus receved, accounts for ncreases n the buyer s surplus that may occur solely because greater total surplus s avalable wth product dfferentaton. That s, the buyer s surplus may ncrease even f the sellers become less compettve, wth the end result that the buyer receves relatvely less of the avalable surplus. We use the maxmum possble surplus rather than actual realzed surplus (the sum of the buyer s and sellers surplus) to account for effcency losses that may occur. Wth ths approach, two transactons wth the same buyer s and sellers surplus wll have dfferent measures of competton f one transacton s more effcent than the other. That s, we characterze an effcency loss as a symptom of decreased competton among the sellers. We then subtract from B S 1 the predcted buyer s surplus n a perod as a fracton of maxmum total surplus possble that perod, when usng an effcent exchange mechansm for whch competton among the sellers does not change across treatments. Specfcally, we use the buyer s surplus that would emerge n a second-surplus aucton n whch the sellers have a 19

21 domnant strategy of settng ther prce equal to ther cost n both the homogeneous product and dfferentated product settngs. The buyer s surplus n ths aucton s the second-hghest level of surplus possble, whch we denote by S 2. Consequently, our measure of the ntensty of competton for a specfc perod s values and costs s B S S 1 2. We use the precedng approach to account for changes n the buyer s surplus that emerge smply through changes n the strategc envronment that do not lead to changes n the sellers behavor. To llustrate the ssue, consder a duopoly procurement settng wth homogeneous products n whch the sellers costs are unformly dstrbuted from 0 to 600, the buyer s value for the sellers product s 1000, and frst-prce aucton rules are used. In equlbrum, the expected prce equals the expected value of the second-lowest cost, 400. The average buyer s surplus s 75 percent of the average avalable total surplus. If we modfy the settng by shftng the costs up by 300, then the sellers equlbrum prce offers shft up by 150 and the expected prce s 700. Whle there arguably s no change n the ntensty of competton between the sellers, the average buyer s surplus s only 60 percent of the average avalable total surplus. By subtractng the buyer s surplus n a second-prce aucton (a specfc verson of a second-surplus aucton when products are homogeneous), n both settngs the measure of competton s 0. Fndng 2: Consder movng from homogeneous products to horzontally dfferentated products, holdng fxed the number of sellers and the nsttuton. Wth two sellers the ntensty of competton ncreases when usng multlateral negotatons, and to a lesser extent when usng frst-prce auctons. Wth four sellers there s no change n the ntensty of competton when usng multlateral negotatons or frst-prce auctons. 20

22 Evdence: The estmates n Table 4 provde the evdence for ths fndng. Wth two sellers, ntroducng dfferentaton n multlateral negotatons sgnfcantly ncreases our competton measure by (= ) (p-value < ), whle dong so n frstprce auctons sgnfcantly ncreases t by (= ) (p-value < ). The dfference n the change between the nsttutons s and s sgnfcant (p-value = ). Wth four sellers, ntroducng dfferentaton n multlateral negotatons nsgnfcantly ncreases our competton measure by (= ) (p-value = ), whle dong so n frstprce auctons also nsgnfcantly ncreases t by (p-value = ). The changes wth four sellers n the negotatons and the auctons are statstcally ndstngushable. Fndng 2 shows that ntroducng horzontal product dfferentaton equalzes the buyer s surplus across nsttutons by ncreasng or leavng unchanged the ntensty of competton among the sellers. Ths result merts further scrutny because t contrasts wth the conventonal wsdom that product dfferentaton softens competton. One possblty s that the sellers act collusvely wth homogeneous products, but not wth dfferentated products. Such behavor would be consstent wth the conventonal wsdom n the ndustral organzaton lterature that colluson s more dffcult to sustan when products are dfferentated. However, Table 3 s reported hgh effcency wth homogeneous products does not support ths explanaton. Colluson n procurement by sellers who cannot communcate wth each other nvolves neffcency, because the sellers cannot tell who has the lowest cost. 24 Consequently, there s an effcency loss when the wrong seller s allowed to wn the contract. Another possblty suggested to us s that the sellers actually have become more homogeneous followng the ntroducton of asymmetrc nformaton about the buyer s values, n 24 See McAfee and McMllan [1992]. 21

23 whch case the ncreased ntensty of competton s not so counterntutve. The dea of greater homogenety s based on the fact that a seller wth low costs s less sure t s the buyer s surplusmaxmzng choce, whle a seller wth hgh costs s less sure t s not. That s, for gven cost realzatons the sellers now hold more smlar belefs about the lkelhood of ther beng the buyer s surplus-maxmzng tradng partner. The problem wth ths explanaton s that despte the flattenng out of the belefs, the sellers actually are more dfferentated. For example, footnote 21 reports that ntroducng product dfferentaton ncreases the dfference between the expected hghest and second-hghest levels of surplus, whch s the dfference n expected surplus offered by the best and second-best tradng partners. 25 A thrd explanaton for Fndng 2 s that non-collusve equlbrum behavor n ths settng becomes more compettve after ntroducng product dfferentaton, n contrast to what s typcally seen n other olgopoly models. Although the dervaton of equlbrum solutons for models of auctons and multlateral negotatons n ths settng s an open problem, 26 to assess ths possblty we numercally approxmate the sellers Nash equlbrum prce-settng functon n a frst-prce aucton usng the parameters from the experment: The sellers prvately known costs are unformly dstrbuted from 0 to 600, and the buyer s prvately known values are unformly dstrbuted from 300 to 900. Appendx A descrbes the approxmaton technques. Each panel of Fgure 2 plots wth a smaller dashed lne the equlbrum prce-settng functons for frst-prce auctons, ether the analytcally derved one when products are homogeneous or the numercally derved one when products are dfferentated. As s evdent from comparng the panels horzontally, ntroducng product dfferentaton leads to hgher equlbrum prce offers by sellers, for all cost realzatons. Moreover, calculaton of the 25 A smlar argument can be made regardng the varance of the dfference between two sellers surplus as the buyer s tradng partner. 26 Appendx B responds to varous crtcal comments to ths and other facts. 22

24 competton measure B S S 1 2 shows that competton gets less ntense after ntroducng product dfferentaton, exactly as the conventonal wsdom suggests. In our numercal approxmaton, the measure s wth two sellers, and s wth four sellers. That s, after ntroducng product dfferentaton the buyer gets a smaller share of the avalable surplus, relatve to a benchmark n whch the ntensty of competton s unchanged. To see how subjects behavor relates to theoretcal predctons, the wder dashed and sold lnes n each panel of Fgure 2 replcate the lnear trend lnes from Fgure 1 for the observed transacton prces n the frst-prce auctons n the experment. The trend lnes show that prces are lower than predcted wth homogeneous products, but more mportantly that they do not ncrease wth dfferentated products. As we mentoned n our dscusson of Fgure 1, a possble explanaton for ths behavor s that low-cost sellers are concerned they are not the buyer s surplus-maxmzng tradng partner when products are dfferentated. Comparng the expermental results wth the numercally approxmated equlbrum suggests the sellers overcompensate for ths addtonal uncertanty, n a manner that suggests the buyer receves an nformatonal rent from ts prvately known preferences for the sellers products. In summary, Fndngs 1 and 2 jontly demonstrate that addng uncertanty for the sellers ntensfes competton amongst them n both tradng formats, to the buyer s beneft. Wlson and Zllante [2010] fnd smlar effects from uncertanty n a laboratory experment wth sxteen buyers facng four sellers, each of whom s prvately nformed about the qualty of ts products. If the sellers post flexble, take-t-or-leave-t prces that are publcly observed by all buyers and all sellers, rp-offs preval that are assocated wth the classc lemons story: low-qualty sellers overwhelmngly stock out at prces far greater than the buyer s value for the low-qualty product. If the sellers posted prces nstead are observed only by buyers who sequentally vst the sellers, 23

25 separatng outcomes occur: low-qualty products sell at low prces, and hgh-qualty products sell at hgh prces. The authors conclude that the buyers uncertanty as to whether or not a seller s peddlng a lemon s completely and remarkably counterbalanced by a correspondng uncertanty on the other sde of the market as to what are the competng market prces. 6. Concluson In ths paper we fnd that ntroducng product dfferentaton nto a standard procurement settng can affect sellers prcng behavor n a way that changes the relatve performance rankngs of auctons and multlateral negotatons. Wth two sellers the buyer s surplus s equal n the auctons and the negotatons when products are dfferentated, whle surplus n the auctons s hgher than n the negotatons when products are homogeneous. Wth four sellers we fnd that dfferentaton leads to no change n the nsttutons relatve performance rankngs, so that auctons and multlateral negotatons contnue to yeld the buyer equal surplus. The equvalence we fnd after ntroducng dfferentaton helps explan the prevalence of multlateral negotatons despte the earler fndngs wth homogeneous products that suggested buyers would tend to prefer auctons. We also nvestgate how the sellers behavor changes as we ntroduce product dfferentaton, whch provdes nsghts nto how the nsttutons relatve performance rankngs are nfluenced. Wth two sellers we fnd that competton becomes more ntense n both the auctons and the negotatons, whle wth four sellers there s no change n the ntensty of competton. Both fndngs contrast wth the typcal ntuton from standard olgopoly models, and wth the predcton from a numercal approxmaton of equlbrum prcng n a frst-prce aucton wth dfferentated products. Ths unexpected fndng may be due to a low-cost seller s 24

26 wllngness to offer concessons when faced wth uncertanty about whether t s the surplusmaxmzng tradng partner. When the buyer s value s the same for all sellers products, a lowcost seller s more confdent that t wll ultmately make the sale. Appendx A In ths appendx we descrbe the teratve procedure by whch we numercally approxmate the sellers Nash equlbrum prce-settng functons n a frst-prce aucton wth horzontally dfferentated products. We evaluate the same 2-seller and 4-seller settngs as n the experment: the sellers costs are Unformly dstrbuted from 0 to 600, and the buyer s values are Unformly dstrbuted from 300 to 900. We solve for a symmetrc equlbrum from the perspectve of seller 1. Our teratve approach begns by fndng seller 1 s best-response to an ntal prce-settng functon used by seller 1 s rvals. In the next teraton seller 1 s rvals use the best-response functon derved n the pror step, and we fnd seller 1 s best-response to that. The procedure stops when seller 1 s best-response functon s wthn a gven dstance of the rvals prce-settng functon, and seller 1 s fnal best-response functon s our approxmaton of the equlbrum prce-settng functon. Gven how seller 1 s rvals set prces, seller 1 s best-response for each cost c s the prce p that maxmzes (p c)pr(p wns). The probablty functon depends on the rvals prce-settng functon, and that probablty functon s nature creates the dffculty n dervng analytc equlbrum solutons. Roughly speakng, wth homogeneous products the probablty a partcular prce wns s a length, whle wth dfferentated products the probablty s an rregularly shaped volume. 25

27 We approxmate the probablty functon n seller 1 s objectve functon n the followng manner. Gven the rvals prce-settng functon, we take two mllon random draws of values and costs for each rval, and of values for seller 1. We dscretze the prce space, and for each prce p n {0, 1, 2,, 900} the probablty that p wns s the fracton of the two mllon cases n whch wth prce p seller 1 offers the buyer a postve payoff that exceeds the payoff from the rvals. We approxmate seller 1 s best-response to ts rvals prce-settng functon n the followng manner. We dscretze the cost space, and for each cost c n {0, 5, 10,, 600} we fnd the prce n {0, 1, 2,, 900} that gves seller 1 the hghest expected payoff. Havng found seller 1 s best-response at a dscrete set of costs, we ft a cubc to those ponts. The ftted cubc s set as the rvals prce-settng functon, and we repeat the procedure descrbed above. We use the same set of value and cost draws for each teraton. The procedure concludes when the maxmum dfference between the rvals prce-settng functon and seller 1 s best-response s less than 1, evaluated at each cost n {0, 5, 10,, 600}. The procedure converged n fewer than 10 teratons, and wth dfferent ntal prce-settng functons the process converged to approxmately the same prce-settng functon. Wth the approxmated prce-settng functon n hand, we used the same random draws to calculate our measure of the ntensty of competton. 26