Channel Bargaining with Retailer Asymmetry

Transcription

1 Channel Baganng wh Reale Asymmey Anhony ukes Eshe Gal-O annan Snvasan 3 Shool of Eonoms & Managemen, Unvesy of Aahus, Åhus enmak, adukes@eon.au.dk Glenn Snson Cha n Comeveness and Pofesso of Busness Admnsaon and of Eonoms, az Gaduae Shool of Busness, Unvesy of Psbugh, Psbugh PA 560, Phone , eshe@kaz..edu 3 H.J. Henz II Pofesso of Managemen, Makeng and Infomaon Sysems, Gaduae Shool of Indusal Admnsaon, Canege Mellon Unvesy, Psbugh PA 53, Phone , kannans@andew.mu.edu

2 Channel Baganng wh Reale Asymmey ABSTRACT Manufaues of onsume odus ofen omlan of lowe ofs n lgh of gowng hannel domnane of owe eales. Ths omlan mgh no be vald. An analyal model of omeng manufaues and mul-odu eales, mgh see manufaues ofs nease when a eale gans a os advanage ove s val. Effenes ae geneaed when he lowe-os eale does a lage shae of a manufaue s sales. If manufaues sell he odus a a lowe e o a low-os eale han o he hghos eale, hey ansfe make shae o he moe effen eale, hus neasng hannel ofs. In a baganng elaonsh beween manufaue and eale, some of hese enhaned effenes ae ansfeed o he manufaues. e examne he effe of bee odu nfomaon on he dsbuon of hannel ofs and show ha, by nfomng onsumes abou odu abues, manufaues move he baganng oson vs-à-vs eales.

3 Inoduon al-ma s emakable oeaonal effenes gve an advanage ove omeng hans suh as ma and Tage. Ths advanage enables al-ma o offe famously lowe eal es and geneae hghe sales volumes of many odus. In fa, al-ma s he nle buye fo many manufaues nludng, fo examle, sney, Poo & Gamble, and Revlon. 4 h suh hgh volumes, al-ma s able o ommand onessons fom s sules hough edued es o quany dsouns. Ths ovokes some sules o omlan ha al-ma s usng s buyng advanage o ea a hghe shae of hannel ofs a he exense. 5 Bu have manufaues neessaly suffeed n ems of ofs as a esul of al-ma s gowng hannel owe? e llusae ha hs omlan mgh be unsuoed. Sefally, we ague ha sules an be, ndeed, moe ofable when an advanaged eale gans buyng advanage elave o s eal omeos. Fo a fxed amoun of odus sold, hee ae addonal effenes geneaed when he lowe os eale does a lage shae of he sale. If manufaues sell he odus a a lowe e o a low-os eale han o he hgh os eale, hey ansfe make shae o he moe effen eale, hus neasng hannel ofs. In a baganng elaonsh beween a manufaue and eale, some of hese enhaned effenes ae ansfeed o he manufaues. Some manufaues, suh as Newell Rubbemad, have eognzed ha oblgng a domnan eale mgh be moe ofable han fghng fo hannel owe. Rubbemad, among ohes, has devoed a lage oon of s makeng esoues o seve al-ma. Fo examle, Rubbemad onsuls wh al-ma fo all new odu desgns fo whh al-ma ges he bes wholesale e, suggesng ha ohe eales don. Lowe wholesale es mgh mean lowe magns fo Rubbemad, bu, ombned wh al-ma s low ealng oss, hs means a shf n he dsbuon of Rubbemad s odus fom adonal eal hannels o moe effen ones, whh 4 See Foune, Mah 3, See, fo examle, Mexo s a of he Megasoe, Busness eek, Seembe 6, 00. 3

4 makes ohe hannels beome elavely less moan. Newell Rubbemad an, n nle, heefoe, negoae fo bee ems wh ohe eales. The evous examle llusaes he nuon of ou fs of wo man esuls, whh s llusaed n a model wh wo eales who sell one o wo dffeenaed odus sold by omeng sules e.g. manufaues. e model he ansaon beween a eale and a manufaue as a blaeal elaonsh, whh akes lae hough baganng. Ths baganng elaonsh s ual fo ou esul beause endogenously aues he make owe whn he hannel as daed by he omeve seng a eah veal level e.g. eal omeon and odu omeon. Moeove, ou negoaons-based famewok aues baganng owe asymmees beween eales vs-à-vs a gven manufaue, unde ealng os asymmees. e fuhe use ou model o sugges a saeg esonse fo manufaues, whh an l he baganng owe n he favo. Fo a gven odu lass, mos eales yally ay bands fom seveal dffeen manufaues. Suh mul-odu eales ofen ely on onsumes who vs he soe knowng wha geneal odu hey wsh o buy bu no he aula model o band. Fo examle, onsde a onsume who wshes o buy a small household alane bu needs o vs he soe and nse he feaues of he models aed by hs eale befoe makng a deson. Gven suffenly hgh seah oss, hs onsume mgh buy one of hese models ahe han vs anohe eale n hoes of leanng abou a moe suable model. The eale n hs ase has aued nfomaonal ens assoaed wh he onsume s nomlee nfomaon. If, on he ohe hand, he onsume s nfomed a o abou odu abues, she wll vs he eale who aes he mos desed model. In negoaons beween a eale and a manufaue, he manufaue s n a bee baganng oson when onsumes ae nfomed elave o beng unnfomed. In he even ha negoaons beak down, hs eale wll no ay hs odu and an nfomed onsume who efes hs odu wll fs vs anohe eale nsead, o buy he manufaue s odu. Ths movemen n baganng oson gves an nenve o he manufaue o endow he onsume wh odu nfomaon, by usng advesng fo examle, befoe 4

5 she makes he eale hoe. Ths nuon, whh s based on ou seond man esul, ndaes ha manufaues have makeng saeges a he dsosal, whh an omba he onenaon of make owe owad a domnan eale. Connung wh he evous examle, Rubbemad s een makeng saegy llusaes hs dea. Even hough al-ma lays a sgnfan ole n develong Rubbemad s new odus, Rubbemad lams sole esonsbly fo advesng hem. hen onsumes ae nfomed of Rubbemad s new odus, al-ma has a bgge nenve o ay hem. Ohewse, neesed onsumes wll seek omeng eales, whh mles ha al-ma msses ou on he sale of ohe odus. Hene, by advesng, Rubbemad elams some leveage n s hannel elaonsh wh al- Ma. 6 Summazng, he emegene of domnan eales wh sgnfan os advanages, lke hose allegedly ossessed by he owe eales, mgh no neessaly leave manufaues wose off, dese he fa ha hese eales weld neased hannel owe. Moeove, manufaues of ean odus an elam some of he hannel owe by ommunang dely wh usomes. The effes ha may move manufaue s ofs, ealng advanages and usome ommunaon, ae boh augmened by an addonal seond ode benef. Sefally, saeg omlemenay n eal es, whh s esen fo omeng eales offeng smla odus, gves eales an oouny fo e oodnaon a olluson. In he esene of ealng os advanages, manufaues ea hghe wholesale es wh he weake eale. Ths ndues he weak eale o ase s eal e, whh n un, allows he advanaged eale o kee s e a b hghe han would have had s val no ased e. Smlaly, when a manufaue moves s baganng oson vs-à-vs eales, va nfomed onsumes, boh eales fae hghe wholesale es, whh oesondngly gves eales an nenve o ase eal es. Bu an nenve of one eale o ase es gves s val an addonal nenve of 6 To senghen hs effe, Rubbemad has even ed loal eales o some of s advesng messages. See Adeek, Januay 8, 999. Geylan e al 003 exloes hs ssue n moe deal. 5

6 seond ode o ase eal e, whh leads o hghe magns. Manufaues lam a oon of hs added sulus n negoaons. 7 The esen ae addesses hee seams of eseah whn he makeng leaue on hannel managemen. The fs seam egads sudes ha denfy he laman of hannel owe. Fo examle, Cho 99 and Lee & Saeln 997 use heoeal models o llusae ha he mng of ng desons and he omeve suue a manufaue and eal levels an dasally ale he dsbuon of ofs whn a hannel. Asymmey n oss beween wo omeng mul-odu eales, whh s ual fo ou esul, has no been addessed n he exsng heoeal leaue. Though Cho 99 does onsde a mul-odu eale, does no addess omeon beween wo suh eales. And omeng mul-odu eales n Lee & Saeln 997 ae symme and, hus, he ae s unable o denfy how asymmey among eales affes manufaue ofs. 8 Lal & Naasmhan 996 examne he mlaon of advesng on he dsbuon of hannel ofs wh a sngle, mul-odu eale ayng a banded good and an unbanded good. The ae llusaes ha he manufaue of he banded good an move s shae of he hannel sulus by neasng demand hough advesng. Smlaly n ou ae, odu nfomaon, n he fom of advesng fo examle, an move he manufaue s of. Howeve, beause we onsde omeng eales, we ae able o addonally aue he effe ha manufaue advesng has on a onsume s hoe of eales, as well as, hoe of odus. Also een sudes suh as dyal e al 000 and Sudh 00 use suual models o esmae he dsbuon of hannel owe fo seveal onsume odus. Agan, he fous of hese woks s on suaons wh a sngle mul-odu eale, ahe han omeng ones. The seond seam of eseah egads he mlaon of baganng on he dsbuon and level of hannel ofs. Lke hs ae, Indes & ey 00, Iye & Vllas-Boas 003, Shaffe 00, onsde baganng onas ahe han ake-o- 7 Ths saeg effe, whh ases n omeng hannels wh nemedaes, has been well-esablshed n he makeng leaue MGue & Saeln, 983, Coughln, 985, Moohy, Tyag 00 has evously oned ou he nenve of sules o e dffeenly o sules deendng on he sze. 6

7 leave e offes, whh s done n evous models of hannel neaon. The fous of Shaffe 00 s o assess he ably of a hannel o maxmze ofs when mulodu eales bagan blaeally wh manufaues. Smlaly, Iye & Vllas-Boas 003 ae also neesed n measung how he baganng elaonsh affes hannel oodnaon usng a model of a sngle manufaue and sngle eale. Fnally, Indes & ey 00 examne how gowng baganng owe of a eale o downseam buye affes he nenves of a manufaue useam sule o saegally engage n oduon o os movemens. Gven he fous of hese hee aes, hey do no exlly onsde how he saeg effes fom omeon beween eales affe he dsbuon of suluses whn eah hannel, as s done n hs ae. The hd seam of eseah ou ae addesses s he effe of nfomaon on he dsbuon of hannel ofs. Chu & Messnge 997 on ou ha, n he esene of asymme nfomaon, he shae of hannel ofs moves fo he nfomed hannel membe. See also Messnge & Naasmhan, 995. Naa & Naasmhan 00 examne nfomaon shang saeges and he onsequenes on sulus dsbuon wh nomlee and mefe nfomaon. In boh of hese sudes, he soue of uneany s wh ese o demand, whle n he uen ae, uneany s wh ese o onsumes odu nfomaon. On he ohe hand, Shaffe & Zeelmeye 00 examne he effe of onsume nfomaon on he dvson of hannel ofs. In he ae, as well as hee, ean foms of hd ay onsume nfomaon an move hannel ofs. Howeve, n he model of Shaffe & Zeelmeye 00, hee s one eale who as as ommon agen who an oodnae omeng eal es. Ou esul s aheved n a dffeen manne, namely wh omeng eales, and eles ually on onsumes desons egadng whh eale o vs. In he nex seon, we desbe he bas model and esablsh ha, n equlbum, eales oban dffeen wholesale es as a esul of eale os asymmees efeed o as eale advanages. In seon 3, we llusae how ealng advanages shf he dsbuon of suluses houghou he hannel. A modfed veson of he model s esened n seon 4, whh llusaes he shf n hannel owe as a esul of onsume 7

8 nfomaon. e offe manageal mlaons and onludng ommens n seon 5. The Aendx onans all ehnal deals omed fom he man ex. Model Ou model s desbed as a sequenal game layed by wo manufaues, 9 denoed M and M, eah of whom offe a odu o wo omeng eales, denoed and. Reales sell one o boh of he odus o a se of onsumes wh dffeenaed ases aoss odus and aoss eales. e assume ha onsumes efeenes aoss odus ae dsbued ndeendenly fom he efeenes aoss eales. In he fs sage eah manufaue and eah eale negoae ove a wholesale e. All negoaons ae blaeal and smulaneous. Fgue llusaes all fou negoaons akng lae n sage. [INSERT FIGURE ] A he end of sage, eales ay he odus of he manufaues wh whom hey have eahed ageemen n negoaons. e assume ha eales know he ouome of he own negoaons bu no hose of he omeo. Then n sage, eales se eal es fo he odus hey ay. Afe sage, onsumes dede whh soe o vs and fnally, wha odu o buy. e sa he analyss wh onsumes and wok bakwad o deve he equlbum ng desons of eales n sage gven he ouomes of he negoaons n sage. A onsume s efeene ove eales s fomally eesened by a loaon x on he neval [0,]. Assume ha onsumes ae unfomly dsbued on hs neval and eales ae loaed a oose endons. Ths saal dsbuon of onsumes eesens heeogeneous efeenes aoss eales and may eesen any fao n whh onsumes vew eales dffeenly loaon, seve, aeaane, e. A onsume s efeene ove odus s smlaly eesened on anohe neval [0,] by a loaon y, whh s ndeenden of x. Podus ae loaed a oose endons. Fgue lafes hs dsbuon of efeenes. 9 The em manufaue s used n ode o fx he onex. These agens an be onsdeed wholesales, dsbuos, o any sule dely useam fom eales. 8

9 [INSERT FIGURE ] Consumes fs dede whh of he eales o vs. Afe avng a one of he eales, a onsume buys one odu. Inally, a onsume s awae of he loaon x, wha odus ae aed by eah eale and he oesondng eal es,,,. The onsume s unawae, howeve, of he loaon y. Afe vsng a eale, she examnes he avalable odus and nfoms heself of he loaon y., One neeaon of hs se-u s ha boh eales send ou flyes ha nfom onsumes of he avalable odus and es. To dsove he loaon y, a onsume mus vs a eale n ode o hysally examne he avalable odus. An mlaon of hs se-u s ha he model s mos aoae fo duable and sem-duable goods, suh as small alanes, fo whh onsumes yally nse hysally befoe buyng. To analyze he uhase deson, suose a onsume vss eale and leans ha he loaon s y. Gven es,,, a onsume eeves uly v y fom band and v y fom band, whee v denoes he uly of onsumon of a odu whh s an exa mah of he efeenes and denoes he degee of dffeenaon beween he wo odus. If eale aes boh bands, hen he onsume buys he band gvng he hghe uly. e assume ha v s suffenly lage ha any onsume who vss a eale who aes only one band, buys a odu. hen dedng whh eale o vs, a onsume mus anae he benef fom uhasng a odu a ehe soe gven ha he loaon y s unknown a ha me. The anaed benef fom vsng eale, f ayng boh bands, s he exeed uly of uhase ove all ossble values of y gven known es E v y dy v y dy, whee 0 y y y. and : 9

10 The value y denoes he loaon of a onsume who s ndffeen beween he wo bands a eale. The fs and seond negal n exess he even ha he onsume loaed a y buys band.e. y < y esevely. and buys band.e. y > y, If eale aes only one odu, hen all onsumes exe o nu he aveage ansoaon oss n odu sae, o /. Hene, he exeed benef of vsng eale, when ayng only band s E ~ v /. In ode o aue dffeenaon among eales, we assume ha onsumes avel o a eale and nu a oss of e un aveled. Theefoe, a onsume loaed a x eeves ulye x when vsng and E x when vsng. enoe he demand fo band a eale by. Lemma sefes he odu demand faed by eah eale, when boh eales ay wo odus o when exaly one eale aes boh bands. As we show lae, boh eales ay boh bands n equlbum and no unlaeal devaon fom he equlbum an esul n any ohe ouome han he ases esened n he lemma. Lemma If eales and ay boh bands and hage es hen eales odu demands ae: I [ ] δ,,, ;, whee I [ ] s an ndao funon akng he value f and 0 ohewse, and δ

11 If eale aes only band m and hages e ~, and eale l aes boh bands and hages,,, hen demands ae: l l l l l ~ ~ ~ m, 0, m, 4 l l l ~ m and l l ~ l ~ m ~. Lemma exesses eale s demand fo band as exeed soe aff mes he ondonal demand fo band. The exesson δ s he dffeene beween a onsumes exeed benef E and E, when boh eales ae ayng boh bands. Ths dffeene, δ, s a funon of he mean and vaane of odu es fo eah eale. Ths efles ha he onsume evaluaes he sk assoaed wh he uneany of he loaon n odu sae when makng he soe hoe. Ths uneany mles ha, wh osve obably, some onsumes wll, ex os, buy he odu hey efe leas. Fo examle, f eale aes only band m, some onsumes would have been bee off vsng eale m. l and buyng odu Eah eale faes a onsan magnal os of ealng, whh may nlude nvenoy, dsbuon, o handlng oss. enoe eale s magnal ealng os by. e assume ha he ealng advanage omes n he fom of lowe magnal eal oss fo eale. enoe he os advanage by 0. Manufaues fae symme and onsan magnal oss of oduon, whh ae nomalzed o 0. Befoe eal es ae sefed, a gven manufaue negoaes wh eah eale a un wholesale e fo he manufaue s odu. e desgnae by he un e negoaed beween manufaue and eale. Aodngly, f negoaons beween manufaue and eale esul n ageemen, eale ays o manufaue. If negoaons esul n dsageemen, he eale ays nohng o he manufaue and does no ay he band.

12 To model he negoaons beween a gven manufaue-eale a we ulze he Nash baganng soluon. Ths ooeave soluon one mles ha he aes o he negoaon agee o sl evenly he sulus geneaed n he ade beween hem. If V and Π desgnae he ayoffs ha aue o manufaue and eale, esevely, n ase hey an eah an ageemen and V and Π desgnae he eseve ayoffs when hey ae unable o eah an ageemen he ousde oons, hen he gan fom ade s equal o V Π V Π. The dsbuon of hese gans beween manufaue and eale, as defned by he Nash baganng soluon, s deemned by he wholesale e ha yelds V V Π Π. In se of beng a ooeave soluon one, he Nash baganng soluon does no even us fom aung he omeve essues ha exs among he aes n he wholesale and eal makes. Sne he ousde oons V and Π deend uon he naue of omeon among manufaues and eales, hs omeon s efleed n he ouome of he negoaons. 0 Anohe modelng ssue, whh ases as a esul of he mul-ay baganng aangemen, s he fa ha eah agen n ou model an negoae wh mulle aes, hus yeldng omlex nedeendenes aoss negoaon ouomes. Any equlbum baganng ouome n suh a seng should have he oey ha no manufaueeale a would wan o enegoae afe leanng he negoaed ouome beween any ohe negoang a. Usng he exessons fo make shaes deved n Lemma, we an sae he ageemen ayoffs elevan o he negoaons beween manufaue and eale as follows: V,, fo, 3 Π, fo,., 0 I s ossble o onsde ohe soluons o ou mul-ay baganng oblem. Fo examle, a ooeave soluon usng Shaley values ould be used n he onex of oalonal baganng. Howeve, n ou nsuonal seng, an-us law may onsan baganng o be blaeal, beween one manufaue and one eale. Fo oalons lmed o sze wo, he Shaley value s equvalen o he Nash soluon used hee.

13 The ayoff o manufaue s he oal sales fom boh eales a wholesale es and. The ayoff o eale s he oal sales o onsumes less magnal eal oss and wholesale oss. Unde hs senao, eah eale, hooses es,, n ode o maxmze Π as exessed by 3, whh mles he followng fs ode ondon: Π l 4 l l 0,,; l ;,. Symmey aoss manufaues mles ha, n any equlbum, eah eale, ses and ha. Aly symmey o 4 n ode o yeld he eales omal seond sage ng ules when all sage negoaons esul n ageemen: l l 5,, l, ; l. 3 3 Noe fom 5 ha fo any fxed wholesale es, eale obans hghe of magns > dese lowe es <. I s hs advanage ha makes a oenally moe ofable hannel fo manufaues han. In ode o ensue ha boh eales ae eanng osve magns, we nvoke he followng assumon: A: 3 >. Assumon A, guaanees ha he saal ase of eale omeon s suffenly lowe han he os dffeene. If he os dffeene wee lage han 3, hen he weake eale s unable o aheve any make shae a osve magns. Now suose one of he negoaons esul n dsageemen. Sefally, suose ha f manufaue and eale anno eah an ageemen, eale aes only band m and manufaue sells only o eale l. The dsageemen ayoffs n hs ase ae: 6 7 V ~ ~ l l, fo l, Π m m m, fo ~ m. 3

14 Reall ha eale l anno obseve ha negoaons beween and esuled n dsageemen and heefoe does no modfy s omal sage ng ule gven n 5. Reale, howeve, evses s ng ule fom 5 n aodane o he maxmzaon of Π wh ese o ~ m. In aula, beause onsumes efe vaey, when eale aes only one odu, onsumes bae he sk ha he loaon y s fa fom odu l and mus be omensaed by a lowe eal e n ode o vs he eale. Reale s omal sage ng ule unde dsageemen wh manufaue efles hs omensaon: ~ 8. 8 Consumes nomlee nfomaon and heeogeneous efeenes ove odus mly ha eales ae able o aa onsumes by offeng a vaey. Bu when eale s ayng only one odu, mus omensae onsumes fo s omeve dsadvanage by edung s e. The esul says, n fa, ha he geae he dffeenaon beween odus he geae hs omensaon sne hs neases he os of onsumes whose loaon y s fa fom band l. e make he followng addonal assumon o guaanee ha, uon dsageemen, he weak eale manans a osve make shae: A: / >/ 8. Assumon A says ha onsume loyaly o eales s suffenly hgh so ha odu demand ~ fo he eale ayng only one band s osve. If A fals o hold, mgh be ossble ha a eale n dsageemen wh a manufaue s unable o aa any onsumes a all osve e magns. Gven eales omal ng ules as funons of ossble sage ouomes, we exess he ageemen and dsageemen ayoffs usng equaons, 3 and 5-8 along wh symmey aoss manufaues: 9 Π l 3 l, 4

15 5 0, Π l l l l, 6 6 V l l l V 6 6, whee, ;, ; l. Equlbum wholesale es ae deemned by nvokng he followng ondon, 3 V V Π Π fo,, whh s mled by he Nash baganng soluon, usng 9-, and assumes a slng ule of equal shaes. The ondon n 3 says ha he equlbum wholesale e, denoed, s ha e whh ensues ha eah ay eeves half of he ne sulus deved fom he blaeal ageemen: V V Π Π. Noe ha he exessons 9- deend on os dffeene bu no on absolue oss,. Hene, an be useful o examne he dsbuon of baganng owe aoss eales vs-à-vs manufaue when hee exss a eale advanage of he fom 0 >. Reale s ageemen ayoff, exessed by 9, s neasng n fo and deeasng fo. Beause of s os advanage, eale onbues moe o he hannel elaonsh wh manufaue han does. Theefoe, an nease n also benefs manufaue uon ageemen wh beause he Nash baganng soluon mles ha all blaeal suluses ae sl beween he wo aes. See Aendx fo devaon of he sef equlbum wholesale e ondons. The assumon of equal shaes s made fo onvenene and he man esuls hold fo abay slng ules.

16 Fuhemoe, an neasng os advanage moves eale s dsageemen ayoff whle deeasng s. See 0. Uon dsageemen wh, eale enoys bgge magns han would and, heefoe, does no suffe as muh n he absene of odu vaey. Fom a manufaue s eseve, he ealng advanage hus s baganng oson vs-à-vs eale, bu enhanes elave o. Noe fom he dsageemen ayoff of manufaue, as exessed n, ha V s neasng n, fo any fxed a of es and V. As s deeasng and neases, beomes a elavely moe effen ealng hannel and an sell moe of manufaue s odu han. Ths says ha manufaue s oson uon dsageemen wh delnes wh he ealng advanage and suggess ha he baganng oson of manufaue vs-à-vs eale wosens wh hghe. Noe, howeve, ha he manufaue ofs ae no neessaly hamed as a esul, as s shown n he nex seon, beause hey lam a oon of he hannel ofs enhaned hough effeny gans, whh s efleed n he sum Π V. The above nuon, whh saes ha eale s n a bee negoang oson han eale, suggess ha he ouome of he negoaons, as defned by 3, yelds a lowe un wholesale e fo eale han fo eale. The followng ooson onfms he nuon. 3 Pooson Unde assumon A, f > 0 hen <. Ths ooson saes ha when ealng os advanages exs, he advanaged eale, n hs ase, obans an addonal advanage hough s baganng elaonsh wh manufaues. I s nsuve o noe he ole manufaue omeon lays n hs esul. I an be shown, fo nsane, ha he equlbum wholesale e odeng s oose.e. 3 e ae unable o oban exl exessons fo and fom he ondons n 3. Neveheless, we ae able o oban an ode elaon aoss he negoaed wholesale es, as desbed n Pooson. 6

17 > when hee s one, ahe han wo, manufaues. In hs ase, eales have no ousde oon uon dsageemen wh he manufaue, whh lams half of eah hannel s ofs hough negoaons. And sne hannel ofs ae hghe wh he low os eale, >. Howeve, wh omeng manufaues, a eale moves s baganng oson vs-à-vs manufaues sne, uon dsageemen wh a manufaue, s sll able o sell he omeng band. Moeove, hs movemen s geae fo he low os eale sne s moe ofable when sellng only one band. Noe n addon ha hs ouome esembles an ouome n whh a manufaue, wh some degee of make owe, engages n hd degee e dsmnaon by sellng s odu a dffeen es. Howeve, he baganng se u n ou model endogenzes he dsbuon of make owe whn he hannel n aodane wh he elave baganng osons of he eale and manufaue. Hene he e dsmnaon n hs ase s a esul of he shf n make owe of he buye, eale, ahe han fom saeg ng on he a of he selle. 3 sbuon of Sulus In hs seon we use he model desbed n seon o haaeze he dsbuon of suluses aoss manufaues, he wo eales, and onsumes. Fs we llusae how he ealng advanage, n ems of, and make suue aamees,, affe he dsbuon of ofs aoss fms. Nex, we onsde he effe of eale advanages on onsume sulus. and The ondon sefed by 3, whh defnes he equlbum wholesale es does no em an exl soluon. As suh, he esuls of hs seon ae based on numeal smulaons n whh we solve 3 fo a ange of aamees 0,, and ha sasfy assumons A, A, and he equlbum wholesale e ondon sefed n he Aendx. e gahally esen he numeal esuls fo eesenave ons n he aamee sae. Fuhemoe, all quanes ae omued usng he os dffeene wh > 0 onsan fo all 0 n ode o aue he effe of s asymme movemens n ealng oss. 7

18 ese he fa ha eale s n an moved baganng oson vs-à-vs a gven manufaue, we fnd ha manufaue s ofs an nease wh eale advanage. As Fgue 3 suggess, he ofs of manufaues nease n. Thee ae wo soues of hs ofably: effen hannelng and e oodnaon olluson. The fs of hese soues omes fom he fa ha a ealng os advanage ndues a geae oon of eah manufaue s sales o be hanneled hough he moe effen eale. Fo any gven ealng os advanage, > 0, obans lowe wholesale es han eale, as mled by Pooson, whh means ha eale enoys hghe magns han. See equaon 5, and he subsequen dsusson. As a esul, eal hannel s magnally moe ofable.e. hghe magns han. In addon, he os advanages > 0 and > 0 mly ha eal es ae lowe fo han fo see agan equaon 5, whh means ha eah manufaue sells moe of s odu hough eale han hough. [INSERT FIGURE 3] Hene, ealng advanages ndues eah manufaue o hannel s odu hough he moe effen eale, eale n hs ase. The manufaue s enled o a oon of effeny gans, as guaaneed by he Nash baganng soluon. On he ohe hand, noe ha a oon of all effeny losses assoaed wh he eale s also nued by he manufaues. Howeve, n ne, eah manufaue gans fom he ealng advanage beause a geae shae of s odu s sold o. In addon o he ofably soue dsussed above, a saeg effe ndued by he eale advanage esuls n a ollusve ouome wh ese o he ng behavo eales. As he dsadvanaged eale s foed o ase s e, eale has a seond ode, saeg nenve o ase e. See 5. To be sue, s deeasng n, as ndaed n Fgue 5. Howeve, hs deease s smalle han he sum of he deeases n and. On he ohe hand, eale has a saeg nenve o lowe s e n esonse o a lowe e by s val,. Bu sne make shaes ae hghe fo eale, he ne gan n exaed onsume sulus fom he saeg effe 8

19 s osve. Ths fa s llusaed n Fgue 6 by he fa ha ha he ae of nease n onsume sulus wh ese o s less han. 4 And, as n he ase above, a oon of hs addonal sulus s shaed wh manufaues, as guaaneed by he Nash baganng soluon. Ths las on s llusaed n Fgue 4 by he fa ha wholesale es ae hangng a a deeasng ae, wh ese o. [INSERT FIGURE 4] To summaze, manufaues ae moe ofable as a esul of eale advanages beause he moved baganng oson of he advanaged eale seves o shf he dsbuon of odus owad hough he moe ofable hannel; and ne saeg effes of eal es yelds addonal exaed onsume sulus aung, n a, o manufaues. Fnally, we examne he omaave sas wh ese o band and odu dffeenaon and, esevely, n ode o evaluae how he omeve suue a eah veal level affes he dsbuon of ofs whn he hannel. In geneal, moe dffeenaon, ehe a he band o eale level, ases hannel ofs as moe suluses ae exaed hough hghe eal es. In ode o deemne he dsbuon of hese addonal suluses whn he hannel, one mus examne how he eseve baganng oson esond o hanges n dffeenaon aamees and. [INSERT FIGURE 5] Fs, onsde hanges n band dffeenaon. The numeal esuls, as esened n Fgue 6, sugges ha moe band dffeenaon shfs suluses dely fom onsumes o manufaues, byassng eales. Reall ha when eale does no eah an ageemen wh manufaue, mus omensae onsumes fo no ayng a vaey and hs omensaon s neasng n sne onsumes bea a hghe 4 Toal ex ane onsume sulus s exessed CS v [ / ]/ 4, whee s a make shae weghed aveage e ndex. 9

20 os when avng a he eale o lean ha she does no ay he efeed band. Hene, moe band dffeenaon makes eales less ofable uon dsageemen and weakens s baganng oson vs-à-vs he manufaue. Tha s, s dsageemen ayoff Π s lowe fo hghe levels of, whh esuls n hghe wholesale es allowng he manufaue o aue mos of he addonal suluses geneaed by an nease n band dffeenaon. As llusaed n Fgue 6, he effes of hghe wholesale es n hs ase ae no bone by eales, bu by onsumes. Sne neases n ase wholesale es aoxmaely symmeally, s ossble fo eales o ass hs addonal os enely on o onsumes. 5 Hene, he effes of eale advanages ae elavely nvaan o he degee of band dffeenaon. On he ohe hand, hghe degees of dffeenaon beween eales, as measued by, bngs addonal ofs o eales a he os of, no only onsumes, bu also of manufaues. See Fgue 3. On he one hand, an nease n ases he exaed sulus dely hough hghe eale es, as efleed n he omal eale ng ules n 5. Ths onbues o hghe hannel ofs, oenally benefng boh manufaue and eale. Howeve, n he baganng elaonsh wh a gven manufaue, eah eale s oson s moved equally uon ageemen and uon dsageemen as a esul of hghe. To see hs, noe ha ~ s nvaan o mles ha any magnal nease n eale dffeenaon s no lamed by he manufaue.. Ths [INSERT FIGURE 6] The man onluson of hs seon s ha a eale os advanage does no neessaly ham manufaues. In fa, a lage os advanage neases hannel ofs n he moe effen eal hannel and benefs hs eale and boh manufaues. 5 Fomally, assumng d / d d / d and dffeenang eale s omal ng ule n 5 wh ese o mly ha d / d d / d. 0

21 4 hen Consumes ae Infomed of Podu Pefeenes The bas model dsussed n he evous seons assumes ha onsumes ae a o unnfomed abou he odu efeenes and mus vs a eale o know he loaon n odu sae. In hs seon we omae ha ase o he ase n whh onsumes know he odu efeenes befoe makng he eale hoe. Ths dsnon has an moan mlaon wh egad o he dsbuon of suluses Reall fom seon, some onsumes buy he band hey efe leas, ex os, ne of e wheneve he eale hey vs aes only one band. Howeve, f nfomed, a onsume would vs he eale who aes he efeed band. Thus, n a seng wh nfomed onsumes, a manufaue who sells o only one eale obans a hghe demand fo s odu han when onsumes ae unnfomed, all else equal. And even hough hs ouome neve ous n equlbum, he ayoffs deemned n hs ouome affe he baganng osons of he negoang aes. In aula, sne onsume nfomaon ases demand fo he manufaue sellng hough only one hannel, he manufaue s baganng oson s moved, elave o he unnfomed ase. Consequenly, a lage shae of he hannel sulus aues o he manufaue. Ths las on llusaes an nenve fo he manufaue o advese dely o onsumes. Fo examle, a manufaue who nfoms onsumes abou odu abues n ode o hel hem lean he efeenes ove odus, an move s negoang oson vs-à-vs eales. e fomalze hs nuon by llusang ha when onsumes ae nfomed of he loaon n odu sae, manufaue ofs nease. 4. Model wh Infomed Consumes Reonsde he game fom seon n whh onsumes know he loaon y befoe makng he eale hoe. The emande of he game s as n he ognal model. Blaeal negoaons beween manufaue and eale ove wholesale e ou n sage. Reales se eal es n sage followed by onsumes eal soe hoes and odu hoes. e manan he assumon fom seon ha all onsumes ae also nfomed abou es and odu avalably a eah eal soe. As a esul, a onsume s soe hoe nvolves no uneany sne she knows wha odu she wll buy befoe vsng

22 he eale. Fomally, he onsume loaed a x, y fang eal es,, and,, hooses a eale and odu o maxmze uly: v v U, v v x y x y x y x y,,,,. Noe ha f sage negoaons beween eale and manufaue end n dsageemen, hen se. The man analyal dsnon beween he nfomed ase and he unnfomed ase of seon s n deemnng make shaes o eah eale and manufaue. Moeove, s he dffeene n make shae beween he wo ases ha s enal o he man esul. e fous, heefoe, on he make shae analyss and elegae o he Aendx he emanng deals, whh follow he same analyal log as he unfomed ase of seon. Make shaes o eah eale and manufaue ae defned by aeas n a aon of he un ube, [ 0,], sefed by a sysem of nequales fomed fom he onsume s maxmzaon oblem. Of he many ossble aons allowable by he looses esons on he aamee sae, we fous only on a seal lass of aons n whh manufaues ean hghe ofs n hs modfed game. In aula, we onsde ouomes ha have osve make shaes fo boh eales and boh odus when all negoaons esul n ageemen. See Fgue 7. e also es aenon o he ase when eales ae suffenly dffeenaed elave o odus. Sefally, we elae assumon A wh a songe assumon: A' / > 7 / 8. Ths assumon s suffen o guaanee ha all onsumes loaed a he eales loaon wll sho a ha eale even when aes only one odu. 6 To llusae he dsbuon of make shaes when boh eales ay boh odus, suose ha and le * x denoe he loaon of a onsume ndffeen beween buyng odu fom eales and. Unde hs ondon, 6 I s no lamed ha hs assumon s neessay fo ou esul.

23 eale s moe aave o onsumes who efe odu and eale o hose who efe odu. Beause onsumes know he loaon y befoe vsng he eale, hey vs he soe ha offes a bee value fo he efeed band. Fgue 7 llusaes hs by he fa ha x > * * x. Ths effe s no esen n he unnfomed ase n whh a onsume s soe deson s based only on exeed uly of odu onsumon ove all ossble values of y. In he onex of Fgue 7, wh unnfomed onsumes yelds x. * * x [INSERT FIGURE 7] [INSERT FIGURE 8] ese hs dsnon n make shaes, he magnal hanges n make shae wh ese o eal e eman unhanged wh nfomed onsumes. As s shown n he aendx, gven wholesale es,, and,, he omal eal ng ules s gven by 5. Consequenly, he ageemen ayoffs n he nfomed ase, denoed Πˆ and Vˆ, eman exessed by equaons 9 and. As a esul, f odu nfomaon auses any dffeene n negoaed wholesale es, hen mus be efleed n he dsageemen ayoffs. Now onsde he make shaes when a eale, say, and a manufaue, say, fal o eah an ageemen n sage negoaons. In he unnfomed ase, hee s a se of onsumes who vs eale bu would have been bee off, ex os, shong a eale. h odu nfomaon, howeve, hese onsumes always make he bes deson ex os. Ths se of onsumes s eesened n Fgue 8 by he angula egon defned by ons ABC. Comaed o he unnfomed ase, manufaue s dsageemen oson s moved sne odu nfomaon has aused hs se of onsumes o swh soes n ode o oban s odu. As a esul, s negoang oson vs-à-vs eale s moved, leadng o a shae of he hannel sulus n he fom of hghe negoaed wholesale e. 3

24 Fuhemoe, as n he bas model, hee exss a seond ode saeg effe ha woks o fuhe nease wholesale es beyond he fs ode effe of he moved baganng oson. In aula, eah eale faes hghe wholesale es, whh ndues o ase s e. Consequenly, eah eale saegally eas o s val s e nease by asng s e fuhe. Reall he dsusson n seon 3. As a esul, hee s addonal exaon of onsume sulus o whh he manufaues eeve a oon hough he negoaons. These wo effes ae ombned and genealzed n he followng ooson, whee equlbum wh nfomed onsumes. ˆ denoes he equlbum wholesale es n he Pooson Unde Assumon A', ˆ > fo,. The ooson saes when he ao / s suffenly lage, he manufaue obans a lage wholesale e as a esul of nfomed onsumes. And, as we llusae numeally n he nex seon, hs an move manufaues ofs. Sne ou nen s o llusae how onsume nfomaon mgh ossbly move he baganng oson of he manufaue, we have no fully haaezed he wholesale ng ouome unde ohe ondons. In aula, he queson of whehe onsumes odu nfomaon an edue wholesale es when A' does no hold emans unansweed. 4. sbuon of Sulus wh Infomed Consumes In hs seon, we esablsh ha nfomng onsumes an move manufaue ofs. In aula, we llusae ases whee V ˆ > V. Table esens a samle of suh esuls fom numeal smulaons. Noe ha manufaue ofs nease n he esene nfomaon. [INSERT TABLE ] 4

25 The evous seon llusaed ha onsume nfomaon abou odus an ase he magnal os of eales by ˆ. I s no neessaly he ase, howeve, ha eales suffe a loss n ofs. In fa, beause eales ean a oon of he addonal magnal exaed sulus geneaed fom he oodnaed nease n eal e, he advanaged eale wll benef fo all 0. 7 ha s aulaly noewohy abou hs las esul s ha even hough onsumes beome bee nfomed, hey an be wose off. Ths oune-nuve esul sems fom he ollusve effe dsussed above. Consequenly, nfomaon does no neessaly always lead o moe omeve ouomes. 5. Manageal Imlaons & Conlusons The esuls fom he dsussons n seons -4 have seveal mlaons ha should be of nees o manufaues when hnkng abou he elaonsh wh eales. Fs, he man esul of seon saes ha equlbum wholesale es, as daed n he baganng elaonsh beween manufaue and eale, ae no equal. Sefally, he low-os eale s n a bee baganng oson vs-à-vs he manufaue and s hus able o ge a bee e han he weak eale. Ths suggess ha a manufaue, when faed wh a songly osoned eale, eevaluae s baganng oson wh s ohe, weake eales, and exe o eeve hghe wholesale es. 8 Seond, he esuls of seon 3 mly ha manufaues ofs mgh aually be moved as a esul of moved hannel oson of a eale, when hs movemen s a esul of effeny gans. As suh, manufaues need no always fea he eale wh he elavely song hannel esene. Rahe, he effeny gans of he domnan eale and he oesondng hannel owe gans an seve o ad make foes owad shfng he dsbuon of a manufaue s goods owad moe effen oules. 7 Cabal and Vllas-Boas 00 efe o he ouome as a Beand Suea. They llusae ha n mulodu Beand omeon, when he saeg effe of a symme nease n magnal oss exeeds he de effe, omeos an be bee off. e have llusaed hs same dea n an asymme seng. 8 Thee ae delae ssues onenng he legaly of hs ae, as daed by he Robnson-Paman A of 934. Manages should be awae of hese ssues and of how o se wholesale es n aodane wh he law. 5

26 Thd, he esuls of seon 4 sugges ha nfomng onsumes abou odu abues e.g. hough manufaue advesng mgh be a way o shf hannel owe vs-à-vs a eale owad manufaues of ean odus. In aula, ou model s bes sued fo odus e.g. small alanes, sem-duable goods, whee onsumes make he fnal band hoe afe vsng a eale. In he absene of full onsume nfomaon, a eale ofen an onsummae a sale o a onsume who, ex os, would have efeed a omeng band aed only by a omeng eale. By nfomng onsumes, va manufaue advesng fo examle, befoe onsumes make he eale hoe, eales ae moe nlned o eah an ageemen wh he manufaue o ay he odu, hus movng he baganng oson of he manufaue. Ths ae hallenges he noon ha he emegene of domnan owe eales suh al-ma, Home eo, Bes Buy and ohes s neessaly bad fo manufaues. In addon, manufaues of odus fo whh onsumes nfom hemselves uon vsng a eale, an egan hannel owe by ommunang odu nfomaon dely o onsumes. The esuls of hs hghly sylzed model smly seve o offe a new way of hnkng abou hannel elaonshs wh a domnan eale. Obvously, ou analyss leaves ou many ohe ases abou aual hannel elaonshs, whh onen aones. Fo examle, ssues suh a ade omoons, slong fees, o exlusve dealng omlae he hannel elaonsh elave o ou smlfed seng. As suh, ou esuls should be aken n he onex of hghlghng some nenves fo manufaues when fang a domnan hannel membe. 6

27 Table sbuon of Pofs & Sulus ove Podu Infomaon Regmes. 00,. 5,, Π Π CS * * * * * * * * * * * enoes Consume Infomaon Regme V 7

28 Fgue Blaeal Negoaons beween Reales, and Manufaues M, M M M 8

29 Fgue sbuon of Consume Pefeenes fo Reales and Podus x y Reale Reale Podu Podu 9

30 Fgue 3 Manufaues and Reales Pofs wh ese o,, 30

31 Fgue 4 Manufaue holesale Pes wh ese o,, 3

32 Fgue 5 Real Pes wh ese o,, 3

33 Fgue 6 Effes fom Changes n Band ffeenaon,, 33

34 Fgue 7 Make Shaes when Reale * x Soe Podu Soe Podu * x Reale Podu Soe Podu * y * y Soe Podu Podu 34

35 Fgue 8 Make Shaes when Reale Caes only Podu Reale Soe Podu * ~x A Soe Podu B Reale Podu Soe Podu ~ y x * C Podu 35

36 Refeenes Cabal, L. and J.M. Vllas-Boas 00, Beand Sueas, wokng ae, Sen Shool of Busness, New Yok Unvesy. Cho, S. Chan 99, Pe Comeon n a Channel Suue h a Common Reale, Makeng Sene Vol. 04: Chu, un and Paul Messnge 997, Infomaon and Channel Pofs, Jounal of Realng Vol. 734: Coughln, Anne T. 985 Comeon and Cooeaon n Makeng Channel Choe: Theoy and Alaon, Makeng Sene Vol. 4: 0-9. Geylan, Tansev, Anhony ukes and annan Snvasan 003 The Ima of Reales Asymme Powe on Channel Relaons, wokng ae, Canege Mellon Unvesy. Indes, R. and Chsan ey 00, Buye Powe and Sule Inenves, wokng ae, London Shool of Eonoms and ssenshafszenum Beln fü Sozalfoshung ZB. Iye, Ganesh and J. M. Vllas-Boas 003, A Baganng Theoy of sbuon Channels, Jounal of Makeng Reseah Vol. 40: Jeuland, Abel and Seven Shugan 983, Managng Channel Pofs, Managemen Sene Vol. 3: adyal, Vnda, Padee Chaguna, and Naufel Vlassm 000, Manufaue- Reale Channel Ineaons and Imlaons fo Channel Powe: An Emal Invesgaon of Png n a Loal Make, Makeng Sene Vol. 9:

37 Lee, Eunkyu and Rhad Saeln 997, Veal Saeg Ineaon: Imlaons fo Channel Png Saegy, Makeng Sene Vol. 63: Lal, Rav and Chakavah Naasmhan 996, The Invese Relaonsh Beween Manufaue and Reale Magns: A Theoy, Makeng Sene Vol. 5: 3-5. MGue, Tmohy and Rhad Saeln 983, An Indusy Equlbum Analyss of ownseam Veal Inegaon, Makeng Sene Vol. : 6-9. Messnge, Paul and Chakavah Naasmhan 995, Has Powe Shfed n he Goey Channel Makeng Sene Vol. 4: 89-3 Moohy,. Sdha 988, Saeg eenalzaon n Channels, Makeng Sene Vol. 74: Na, Rakesh and Chakavah Naasmhan 00, Veal Infomaon Shang n sbuon Channels, wokng ae, Mashall Shool of Busness, Unvesy of Souhen Calfona. Shaffe, Geg 00, Baganng n sbuon Channels wh Mulodu Reales, wokng ae,.e. Smon Shool of Busness, Unvesy of Rohese. Shaffe, Geg and Floan Zeelmeye 00, hen Good News Abou You Rval s Good fo You: The Effe of Thd-Pay Infomaon on he vson of Channel Pofs, Makeng Sene Vol. 3: Sudh,. 00, Suual Analyss of Manufaue Png n he Pesene of a Saeg Reale, Makeng Sene Vol. 03: Tyag, Raeev 00, "hy do Sules Chage Lage Buyes Lowe Pes?" Jounal of Indusal Eonoms. 37

38 Aendx A Ths aendx onans he oofs of Lemma and Poosons and n addon o he equlbum wholesale e ondons. Poof of Lemma The demand fo odu a eale s he make shae of he eale mes he demand fo band, ondonal on vsng he eale. Condonal on vsng eale, odu demands ae gven by y / fo band and y / fo band, whh s omaly wen as he seond mullave exesson of. To deemne he make shae of eale, onsde a onsume loaed a x, who s ndffeen beween he wo soes. Then E x E x mles E E x. By evaluang he negals n fo,, an be vefed ha E E δ, as exessed n he saemen of he lemma. All onsumes x < x vs eale, mlyng make shae fo of δ / / and fo, δ / /. Suose eale aes only band m and dedes whh eale o vs by solvng ~ max{ E x, E x}. The onsume a x ~ s ndffeen beween eales when k aes boh. The onsume 38

39 39. 4 ~ ~ ~ ~ v v E E x Sne all onsumes who vs buy odu m, exeed demand fo odu m a eale s x m ~ ~. The emanng ~ m onsumes sho a eale. Hene, he ndvdual odu demands a eale ae gven by m ~ ~ and m ~ ~. Smlaly suose ha eale aes only band m and aes boh o he dedue he geneal exesson as gven n he saemen of he lemma. Q.E.. Equlbum Pe Condons A he Nash baganng soluon, ag max V V Π Π,,. Fs ode ondons mly ha 0 Π Π V V, whh gves he ondon n 3 fo 0. Usng hs ondon fo,, equlbum es and mus sasfy A A Fo he oof of Pooson, noe ha hese ondons mly ha A

40 40 A , whh ae obaned fom addng A. and A. and subang A. fom A., esevely. The soluon of A. and A. solves he maxmzaon oblem of he Nash baganng soluon unde he seond ode ondons, A ] [ < l I G, fo, and l, whee V V G Π Π. Befoe ovng Pooson, we fs sae and ove an nemedae esul n he fom of Lemma A. Lemma A Unde assumon A, 0 >. Poof of Lemma A If hen he onluson holds mmedaely. On he ohe hand, onsde he ase when < and suose, by onadon, ha 0. Then A.3 mles 8 6 >. Usng hs fa, an be shown va algeba ha he LHS exesson of A.4 mus be less han , whh s non-osve unde he assumon ha < and assumon A. Theefoe, he LHS exesson of A.4 s negave a onadon n equlbum. Hene he onluson holds.

41 4 Poof of Pooson efne x. Then solvng A. and A. fo and yelds A x x x x A x x x x, whee 64 x x. Usng he above exessons A.6 and A.7, an be shown ha > holds f and only f 0 8 < x x. Ths lae ondon holds sne 0 > x by Lemma A. Q.E.. In ode o ove Pooson, we sae and ove a lemma, whh haaezes he demand of eah odu a eah eale when onsumes ae nfomed of he loaon y n odu sae. Lemma A Assume onsumes ae nfomed of he loaon y. If eales and ay boh bands and. Then odu demands ae gven by 4

42 4. 4 If eales and ay boh bands and <. Then odu demands ae gven by 4. 4 Unde Assumon A', f eale aes only band and hages e ~, and eale aes boh bands and hages and 8 ~ >, hen odu demands a eale ae 4 4 ~ ~ ~ ; 0 ~ ; ~ ~ ; ~ ~ ~. Poof of Lemma A efne * x as he loaon of he a onsume who s ndffeen beween buyng odu fom eale o fom eale. Then x *,,. efne * y by he loaon of a onsume ndffeen beween buyng odu and odu a eale. Then

43 If y,,. * hen odu demands ae x y, x * y *, x * y *, * * x * * y, esevely. Ohewse, > mles x > and * * x y >. A onsume a x, y buys odu a eale f and only f * * y * x > x and * y < y. Theefoe x. A onsume a x, y buys odu a eale * * y f and only f * x < x and * * y >. Theefoe x y. A onsume a x, y n * y * * * * x, x y, y suh ha x s ndffeen beween odu a eale and odu a eale. Theefoe, and x y * * y * * y * * x y * x y y dy * * x y dy, whh yeld he exessons saed n a of he lemma. eved smlaly as n above. efne y * y ~* y as he loaon of a onsume ndffeen beween buyng odu and odu fom eale and buyng odu fom ehe eale. Then and ~ * y * ~x as he loaon of a onsume ndffeen beween ~. x~ * A onsume a ~ *, [0, ] [0, ~ * x y x y ] buys odu fom eale. Theefoe, ~ * x ~ * y ~, whh yelds he exesson saed n he lemma. To deve he demand of eale, who sells only odu, onsde a onsume ~ *, [0, ] [0, ~ * x y x y ], suh ha * x < ~x o ~* y > y, and beak he demand no wo as. Pa one onsss of hose onsumes wh * x < ~x and ~* y < y, whh has a 43

44 measue equal o ~ x ~. Fo hose onsumes ~ *, [0, ] [0, ~ * x y x y ] suh ha * * y ~* y > y, hey wll buy odu fom eale f and only f ~ x y h y. Noe ha unde he assumon A' and ~ >, h 0. The seond a of he 8 eale s demand s he aea unde h y fom ~ * * ~ x ~ y h y dy, ~ * y ~* y o. Thus, oal demand s whh, uon evaluaon, yelds he exesson gven n he saemen of he lemma. Fnally, sne we assume ha all onsumes make a uhase, demand ~ an be deemned by omung he emanng aea lef ove fom he wo demands omued above. Equlbum Pe Condons wh Infomed Consumes In hs seon we deve equlbum ondons fo symme wholesale es ˆ, ˆ Q.E... The devaon hee s aallel o ha of he bas model, whh nvolves, fs, deemnng he omal sage ng behavo of he eales gven wholesale es deemned n sage negoaons. Usng Lemma A, he ayoff o eale when ayng boh odus s ˆ Π,, whee ae exessed n Lemma A. Seng ˆ d Π / 0 and nvokng symmey d aoss odus gves he omal seond sage ng ules when eale :, 3 3 whh s analogous o 5. hen negoaons beween eale and manufaue end n dsageemen, leavng o sell only odu ode o maxmze ˆ ~ Π m. m n sage, ses eal e ~ ~ n 44

45 Seng d Π / d ~ 0 and nvokng symmey,, gves he omal seond sage ng ule when eale sells only odu m: ~. Noe ha eale 8 s omal ng ules wh nfomed onsumes, mms hose of he ognal model. 9 The ayoffs elevan fo sage negoaons, gven omal eale behavo, n sage, ae ageemen ayoffs ˆΠ, Vˆ and dsageemen ayoffs Πˆ, Vˆ, ;, ; l. Fo he model wh nfomed onsumes, he exessons fo he ageemen ayoffs fo boh manufaue and eale eman as n equaons 9 and. The dsageemen ayoff fo eale also emans as befoe n. The moan dsnon beween he wo models ous n he dsageemen ayoff of he manufaue, whh n he ase of nfomed onsumes s l l Vˆ The Nash baganng soluon s used o deemne he ouome of he sage negoaons. Sefally, ˆ ˆ ˆ ag max ˆ ˆ Π Π V V,,. Fs ode ondons fo hs maxmzaon oblem mly ha es ˆ, ˆ n an equlbum wh nfomed onsumes, mus sasfy he followng sysem: ˆ ˆ ˆ ˆ 3 A.8 ˆ ˆ ˆ ˆ ˆ ˆ 3 A.9 ˆ ˆ The seond ode neessay ondon fo hs maxmzaon s denal o ha of he ognal model, whh s gven n A.5. 9 Assumon A' s suffen, bu no neessay, fo hs o be he ase. If Assumon A' s elaxed, s ossble ha hese ng ules hange. In aula, by elaxng A', he odu demands of Lemma A ae no guaaneed o hold, whh ales he eale s fs ode ondon wh ese o ~. 45

46 Poof of Pooson efne he LHS exessons of A.8 and A.9 as funons H and H, whh ae deeasng unde he seond ode ondon fo he maxmzaon defned by he Nash baganng soluon. Subsung he unnfomed equlbum es gves sne H > 0 H 4, solve A. and A. and ˆ H 0 ˆ > H, 4, ˆ, ˆ solve A.8 and A.9. The deeasng oey of H mles he esul. Q.E.. Aendx B Ths aendx ovdes moe dealed esuls fom he numeal alulaons used n Fgues 3-6 n Seon 3. Π V Π CS Table B sbuon of Pofs & Sulus,, 46

47 Π V Π CS Table B Effes fom Changes n Band ffeenaon,, 47