Joint Venture for Product Innovation and Cartel Stability under Vertical Differentiation

Lambertini, Luca; Iori, Cristina Working Paper Joint Venture for Product Innovation and Cartel Stability under Vertical Differentiation Quaderni - Working Paper DSE, No. 385 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Lambertini, Luca; Iori, Cristina (2000) : Joint Venture for Product Innovation and Cartel Stability under Vertical Differentiation, Quaderni - Working Paper DSE, No. 385, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4924 This Version is available at: https://hdl.handle.net/10419/159226 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ JointVentureforProductInnovation and CartelStabilityunderVertical Di¤erentiation CristinaIori#-LucaLambertinix DepartmentofEconomics,UniversityofBologna StradaMaggiore45,40125 Bologna,Italy fax +39-051-2092664 #e-mail: [email protected] § e-mail: [email protected] July 18,2000 Abstract Wedescribeaverticallydi¤erentiatedmarketwhere…rmschoose betweenactivatingeitherindependentventuresleadingtodistinct productqualities,orajointventureforasinglequality.Then,…rms either repeat theone-shotNashequilibriumforever,orbehave collusively,accordingtodiscountfactors.Weprovethat there existsa parameter regionwherethejointventuremakesitmoredi¢cultfor …rmstosustaincollusivebehaviour,ascomparedtoindependentventures.Therefore,publicpoliciestowardsR&Dbehaviourshould be designedso asnot tobecomeinconsistentwiththepro-competitive attitude characterisingthe currentlegislationonmarketingpractices. J.E.L.classi…cation:C72,D43,L13 Keywords:productquality,R&Dinvestment, implicitcollusion, jointventure, independentventures 1 1Introduction Oligopolytheoryhasproducedarelevantliteratureonrepeatedmarketinteraction.Therelative e¢ciencyofBertrand and Cournotcompetitioninstabilizingcartelscomposedby…rmswhoseproductsareimperfectsubstituteshas beenanalysed byDeneckere(1983),Rothschild(1992)and Albækand Lambertini(1998),showingthatwhensubstitutabilitybetween productsishigh, collusionisbettersupportedin price-setting gamesthaninquantity-setting games,whilethereverseistrueincaseoflowsubstitutability.1Majerus (1988)hasprovedthat thisresultisnotcon…rmedasthenumberof…rms increases.These contributionscompareCournotand Bertrand supergames toconcludethataquantity-settingcartelshouldalmostalwaysbepreferred to a price-settingcartelonstabilitygrounds.2Finally,thein‡uence ofendogenousproductdi¤erentiationonthestabilityofcollusionin priceshas beeninvestigated byChang(1991,1992),Ross (1992)and Häckner(1994, 1995,1996).Themain …ndingreached bythese contributionsisthat,under verticaldi¤erentiation,collusionismore easilysustained,themoresimilar theproductsare,whiletheoppositeappliesunderhorizontaldi¤erentiation. The consequencesofcollusiononthe extentofoptimaldi¤erentiationin thehorizontaldi¤erentiationmodelhavealsoreceivedattention.Friedman and Thisse(1993)have consideredarepeated price gameinthehorizontal frameworkand found out thatminimumdi¤erentiationobtainsif…rmscolludeinthemarketstage.Inmostofthesemodels,although di¤erentiation can be endogenouslydetermined by…rmsthroughstrategicinteraction,the issueofcartelstabilityis studied bymakingthedegree ofdi¤erentiation varysymmetricallyaround theidealmidpointoftheintervaloftechnologicallyfeasibleorsociallypreferredvarieties, leadingtothe conclusionthat producersmayprefertochoosethe characteristicsoftheir respectivegoods di¤erentlyfromwhatpro…tmaximizationwouldsuggest, ifthishelpsthem minimize theincentivetodeviatefromtheimplicitcartelagreement. 1ThesamequestionisaddressedinLambertini(1996),wherethe evaluationofcartel stabilityunderBertrand and Cournotbehaviouriscarriedoutintermsofthe concavity/convexityofthemarketdemand function. 2Thisapproachcannotgraspanystrategicinteraction behind the choice ofthemarket variable.Usingthesamedemand structureasinDeneckere(1983)and analysingasymmetric cartelswhereone…rmisaBertrand agentwhiletheotherisaCournotone,Lambertini (1997)provesthat the choice ofthemarketvariableinordertostabilize implicitcollusion producesaPrisoner’sDilemma. 2 To ourknowledge, littleattention hasbeen paidsofartotheinterplay between …rms’technologicaldecisionsand theirabilitytobuildupand maintaincollusiveagreementsovertime.Thisisarelevantissue, inthatpublic authoritiesprosecute collusivemarketbehaviour,whiletheyseldomdiscourage cooperationinR&Dactivities.Indeed,there existmanyexamplesof policymeasuresdesignedso astostimulatetheformationofresearchjoint ventures.3However,encouragingcooperativeR&Dand discouragingmarket collusioncan bemutuallyinconsistentmoves, ifR&D cooperationtendsto facilitate collusionintheproductmarket. Inthisrespect,Martin(1995)analysesthestrategic e¤ectsofaresearch jointventure(JVhenceforth)designedto achieveaprocess innovationfor anexistingproduct.Then,theproductismarketed by…rmsengagingin repeatedCournotbehaviouroveranin…nitetimehorizon.Martinshows thatcooperationin process innovationenhancesimplicitcollusion,whichcan jeopardisethewelfareadvantageofeliminatinge¤ortduplicationthroughthe JV.Thisresulthaspotential implicationsforthe caseofproductinnovation aswell.4 Wereassess Martin’sframework,byconsidering a verticallydi¤erentiated marketwhere…rmsaregiventhepossibilityofchoosingbetweenactivating eitherindependentventuresleadingtodistinctproductqualities,orajoint ventureforasinglequality,aimedatreducingtheinitialR&D expenditure visàvisindependentventures.Then,…rmsmarket theproduct(s)overanin- …nitehorizon.In doingso,theyeither repeat theone-shotNashequilibrium forever,orbehave collusively,accordingtotheirintertemporaldiscounting. Insuchasetting,weprovethat there existsaparameter regionwhereMartin’sconclusionisreversed, i.e., theJVmakesitmoredi¢cultfor…rmsto sustaincollusivebehaviourinthemarketsupergame,ascomparedtoindependentventures.Thisholdsindependentlyofwhether…rms setpricesor quantitiesduringthesupergame. Our resultentailsthatpublicpoliciestowardstheR&Dbehaviourof…rms should betailoredcasebycase,so asnot tobecomeinconsistentwiththepro-competitiveattitude characterisingthe 3See theNationalCooperativeResearchActintheUS;EC Commission(1990);and, forJapan,Goto and Wakasugi(1988). 4Lambertini, Poddarand Sasaki(1998)adopt thesameviewasinMartin(1995),althoughtheyconsidertherelationship betweenstandardizationand thestabilityofimplicit cartelagreeements.See alsoLambertini, Poddarand Sasaki(2000).Cabral(1996), ina somewhatdissimilarvein,provesthepossibilitythatcompetitivepricingisneededto sustainmore e¢cientR&Dagreements. 3 currentlegislationonmarketingpractices. Theremainderofthepaperis structuredasfollows.Thebasicmodel ofverticaldi¤erentiationisdescribedinsection2.Section3describesthe caseofcollusionalongthefrontierofmonopolypro…ts.Section4dealswith partialcollusionundereitherCournotorBertrandbehaviour.Finally,section 6providesconcludingremarks. 2Theverticaldi¤erentiationmodel Weadoptawell knownmodelofduopolyunderverticaldi¤erentiation(see Gabszewicz and Thisse,1979,1980;Motta,1993;Aokiand Prusa,1997; Lehmann-Grube,1997;Lambertini, 1999,interalia).5Twosingle-product …rms, labelledasHand L,produce goodsof(di¤erent) qualitiesqHand qL2[0;1),withqH¸qL;throughthesametechnology,C(qi)=cq2 i;with c > 0:Thiscan beinterpretedas…xedcostduetotheR&D e¤ortneededto produce acertainquality,whilevariableproductioncostsareassumedaway. Productsareo¤eredonamarketwhere consumershaveunitdemands,and buyifand onlyifthenetsurplusfromconsumptionvµ(qi;pi)=µqi¡pi¸0; wherepiistheunitprice ofthegoodofqualityqi,purchased bya generic consumerwhosemarginalwillingness topayisµ2[0;µ]:Weassumethatµ isuniformlydistributedwith densityoneoversuchinterval, sothat thetotal mass ofconsumerisµ. Firmsinteractovert2[0;1);asfollows: ²Att=0;theyconductR&Dtowardsthedevelopmentofproduct quality,througheitherajointventure(JVhenceforth)orindependent ventures(IVhenceforth).If…rmsundertakeajointventure,then qi=qj=qand each …rmbearshalfthedevelopmentcost,cq2=2. Otherwise,…rmsmarketdi¤erentiated products,eachofthembearing thefull developmentcostoftheir respectivevarieties,cq2 i.6 ²Overt2[1;1);…rmsmarket theproduct(s)resultedfromprevious R&Dactivity,eitheràlaCournotoràlaBertrand. 5Adi¤erentmodel isusedin Shakedand Sutton(1982,1983),where…xedcostsare exogenous. 6TheR&De¤ortsof…rmsoperatinginverticallydi¤erentitedmarketsareinvestigated inBeathetal. (1987),Motta(1992),Duttaetal. (1995),Rosenkranz(1995,1997),van Dijk(1996).In particular,Motta(1992)and Rosenkranz(1997)describetheincentives towardscooperativeR&D. 4 ²Inthein…nitelylongmarketingphase,…rmsmaycolludeiftheir respectivetimediscountingallowsthemtodoso. Otherwise,theyalwaysplay àlaNash.De…neas±ithediscountfactorof…rmi;and ±I i(K)the criticalthresholdforthestabilityofcollusion,withsuperscriptI=B;C standingforBertrand and Cournot,and K=IV;JV;indicatingthe organizationaldesignchosenfortheR&Dphase. Asa…rststep,observethat thelocationsofindi¤erentconsumersalong [0;µ]are: µH=pH¡pL qH¡qL;µL=pL qL(1) whereµHisthemarginalwillingness topayoftheconsumerwhoisindi¤erent betweenqHand qL;and µListhemarginalwillingness topayofthe consumer whoisindi¤erentbetweenqLand notbuying atall. Then,marketdemands arexH=µ¡µH;xL=µH¡µL:(2) Notice that (2)can beinvertedtoyieldtherelevantdemand functionsfor theCournotcase: pH=qH³µ¡xH´¡qLxL;pL=qL³µ¡xH¡xL´:(3) Atanyt¸1;…rmiobtainsrevenuesRI i=pixi;I=B;C:Thediscounted ‡owofpro…tsoverthewholegameisthen: ¼I i= 8 > > > < > > > : ±i 1¡±i¢RI i(qi;qj)¡cq2 iunderIV ±i 1¡±i¢RI i(q)¡cq2 2underJV(4) Tomodelcollusioninmarketing,weadopt thePerfectFolkTheorem(PFT henceforth;see Friedman,1971),wherethein…nitereversiontotheone-shot Nashequilibriumisusedasapunishmentfollowing anydeviationfromthe prescribedcollusivepath.7The collusivepathcaninstruct…rmstocollude eitherfully(i.e., at theParetofrontierofmonopolypro…ts)orpartially,at 7There existother(less grim)penalcodes(see Abreu,1986;1988;Abreu,Pearce and Stacchetti, 1986;Fudenberg and Maskin,1986),usingsymmetricoptimalpunishments. However,theasymmetryofourmodelpreventsusfromadopting optimalpunishments. Fortheapplicationofoptimalpunishmentsinasymmetricduopolymodelwith product di¤erentiation,see Lambertiniand Sasaki(1999,2000). 5 anypairofpricesorquantities suchthatper-periodindividualrevenuesare atleastaslargeastheNashequilibriumrevenues. De…ne: [1]Theinstantaneousbestreplyof…rmias®¤ i: [2]Thecollusiveactionas®coll 2³minn®N;®Mo;maxn®N;®Moi;®=p;x: [3]The collusiverevenuesto…rmiasRIcoll i(¢);(¢)=f(q);(qi;qj)g: [4]Theone-shotNashrevenuesto…rmiasRIN i(¢): [5]Theone-shotdeviationrevenuesto…rmiasRID i(¢): TherulesofthePFTestablishwhatfollows: ²Att=0;…rmsplay®coll: ²Att¸1;…rmsplay®coll i¤®i=®coll att¡1forall i; …rmsplay®¤ iotherwise. De…nitions[3-5]and therulesofPFTyieldsthatimplicitcollusionat ®coll is sustainablei¤ ±i¸±I i(K)=RID i(¢)¡RIcoll i(¢) RID i(¢)¡RIN i(¢)forall i:(5) Inthenextsection,wequicklydealwiththe caseof full collusion,where ®coll =®M: 3Full collusion First,notice thatwhen …rmsoperatealongthefrontierofmonopolypro…ts, theyareindi¤erentbetweensetttingpricesoroutputlevels.Therefore,we con…neourattentiontotheBertrand case. Suppose…rmschooseindependentventuresatt=0:Then,overt2 [1;1),theyshouldmarketdi¤erentproducts.Wearegoingtoshowthat thiscannotbeanequilibrium.Atanyt2[1;1),the cartelaimsat max pH;pLRM=RB H(qH;qL)+RB L(qL;qH):(6) 6 Monopolypricesare: pM H=µqH 2;pM L=µqL 2;(7) atwhichxM H=µ 2,whilexM L=0:Therefore, ¼B H=±H 1¡±H¢µ2qH 4¡cq2 H;¼B L=¡cq2 L:(8) Onthebasisoftheaboveresult, independentventuresimplythat,forall qL2(0;qH);thelow-quality…rmwouldexit,gettingthuszeropro…ts. Alternatively,…rmLmayproduce qL=qH:Thisimmediatelyentailsthat ±B i=1=2forall i;as…rmso¤erhomogeneousgoods. Itneedsnoprooftoshowthat thesameholdsinthe caseofajoint venture,asthiswouldyield producthomogeneityasaresultoftechnological decisionstakenatt=0:Wehavethusprovedthefollowing: Lemma1Underfull collusion,thelow-qualityproductenjoys zero demand. Asaconsequence,…rmswill onlysupplyhomogeneousgoods,withJVÂIV duetothe cost-saving e¤ect. Corollary1Underfull collusioninprices,±B i=1=2forall i;independently of…rms’venturedecisions. AstotheCournotcase,notice that,aslong as…rmsprovidedi¤erent qualities,wehave xM H=µ 2;xM L=0(9) whichagainentailsthat thelow-quality…rmsurvivesonlyifqL=qH;eitherbecause…rmsactivateaJV,orbecause…rmsdevelopthesamequality independentlyofeachother.Asaresult,we canstatethefollowing: Lemma2Underfull collusioninquantities,±C i=9=17 forall i;independentlyof…rms’venturedecisions. Insummary, independentlyofthemarketvariable chosenforthesupergameovert2[1;1),the…rms’venturedecisionsatt=0haveno bearingsonthestabilityofcollusion,as settingeithermonopolypricesor quantitiesinduces…rmstoplayasupergamewith homogeneousgoods. 7 4Partialcollusion Here,weinvestigatethebearingsoftechnologicalchoicesoncartelstability, undertheassumptionthat…rmsmayactivatepartialcollusion, i.e., theymay colludeatany®coll 2³minn®N;®Mo;maxn®N;®Moi;®=p;x: 4.1Cournotbehaviour Considerpartialcollusionatxcoll 2³xM;xN´,fora genericqualitypair fqH;qLg:Inthelimit,asqL!qH;weobtainthedescriptionoftheJVcase. Wede…nethepartiallycollusiveoutputof…rmias: xcoll i=axN i+(1¡a)xM i;a2(0;1);(10) wherexM i=xM=2=µ=4and8 xCN H=µ(2qH¡qL) 4qH¡qL;xCN L=µqH 4qH¡qL:(11) TheassociatedNashequilibriumrevenuesare: RCN H=µ2qH(2qH¡qL)2 (4qH¡qL)2;RCN L=µ2q2 HqL (4qH¡qL)2:(12) Substituting(11)into(10)and rearranging,wehave: xcoll H=µ[4qH(1+a)¡qL(1+3a)] 4(4qH¡qL);xcoll L=µ[4qH¡qL(1¡a)] 4(4qH¡qL)(13) whichallowtocalculateRCcoll i: RCcoll H=µ2[4q2 H(3¡a)¡qHqL(7¡3a)+q2 L(1¡a)][4qH(1¡a)¡qL(1+3a)] 16(4qH¡qL)2 RCcoll L=µ2qL[2qH(2¡a)¡qL(1+a)][4qH¡qL(1¡a)] 8(4qH¡qL)2 (14) 8Weomit the explicitderivationoftheNashequilibriumquantities,asitiswell known frompreviousliterature(see Motta,1993). 8 0 0.2 0.4 0.6 0.8 1 a 0 0.2 0.4 0.6 0.8 1 ql 0 0.1 0.2 0.3 0.4 0.5 deltaL 0 0.2 0.4 0.6 0.8 1 a Figure4.Plotof±B Loverfa;qLg,witha2[0;1]and qL2[0;1]. Consider…rst±B L(…gure4).Wehave: ±B L=1 2(34) ifqL qH=4h5¡2a§3p2a2¡1i 17+7a:(35) Theabovesolutionscoincideata=1=p2'0:707;whereqL'0:653: Then,observethebehaviourof±B H(…gure3).Theborderalongwhich ±B H=1=2iseverywheretothenorth-westoftheborder(35). Moreover,the curvexBD H=µisalsotothenorth-westoftheborder (35).14 14Indeed,the equation 4£5¡2a+3p2a2¡1¤ 17+7a=7¡a¡pa2¡22a+25 3+a hasnorealrootfora2[0;1];withther.h.s.being alwayslargerthanthel.h.s.overthe unitinterval. 15 The caseswheredeviationgivesrisetoamonopolyremaintobeinvestigated.Thiswouldentail recalculating±B ianew,takinginto account the additional informationconveyed bythe complementsto(28)and (29).Yet, totheaimsofthepresentpaper,thefollowing argumentwill su¢ce. First,observethat, ingeneral: @±I i @RID i=RIcoll i¡RIN i (RID i¡RIN i)2>0:(36) At theboundarywherexBD H=µ;criticaldiscountfactorsaregiven by(32) and (33).When qL qH2Ã7¡a¡pa2¡22a+25 3+a;19¡3a¡p9a2¡114a+169 8 !;(37) the criticaldiscountfactorfor…rmLis still given by(33),whilethatassociatedto…rmHis: b ±B H=RM¡RBcoll H RM¡RBN H>±B H=RBD H¡RBcoll H RBD H¡RBN H>1 2:(38) Finally,whenqL qH>19 ¡3a¡p9a2¡114a+169 8;(39) wehaveb ±B L=RM¡RBcoll L RM¡RBN L>±B L=RBD L¡RBcoll L RBD L¡RBN L>1 2;(40) alongwith(38). Theabovediscussionsu¢cestoestablishthefollowingresult: Proposition2Implicitcollusioninpricesismore easilysustainedunder independentventuresthanunderajointventure, forall qL qH2 0 @4h5¡2a¡3p2a2¡1i 17+7a;4h5¡2a+3p2a2¡1i 17+7a 1 A Outsidetheabove range,theoppositeholds. Astheintensityofcollusion decreasestowardstheBertrand-Nashequilibriumpro…ts, i.e., asagrowslarger,therangeofproductdi¤erentiation whereincollusioniseasierunderIVthan underJVincreases.Theintuitive explanation behind thisconclusionisthesameasintheCournotcase. 16 5Concludingremarks Wehavereassessedanissuepreviouslyraised byMartin(1995),underanew perspective,where…rms’ initialR&D e¤ortsareaimedatproductrather than process innovation.Wehaveanalysedtherelationship betweenthe organizationaldesignofR&Dforproductinnovationand thestabilityof implicitcollusioneitherinquantitiesorin prices,keepingunalteredtherules governingthemarketsupergame, i.e., usingthePerfectFolkTheorem. Themainconclusionemergingfromthis settingisthataJVmayormay notfacilitate collusioninthemarketsupergame,dependingupon(i) the degree ofdi¤erentiation produced by…rmsactivatingindependentventures; and (ii) theintensityofprice orquantitycollusion. Independentlyofthemarketvariablebeingsetby…rms,wehavefound that,theloweristhelevelofcollusion,theloweristhepro…tabilityofdeviationforanygiven degree ofproductdi¤erentiationresultingfromindependentventures.Thisdrasticallycontributestostabiliseimplicitcollusion, inthatareductionofdeviation pro…tsgoesalongwithareductioninthe criticalthresholdofthediscountfactor. Therefore,publicpoliciestowardsR&Dbehaviourshould bedesignedso asnot tobecomeinconsistentwiththepro-competitiveattitude characterisingthe currentlegislationonmarketingpractices. 17 References [1]Abreu,D.(1986),“ExtremalEquilibria ofOligopolisticSupergames”, JournalofEconomicTheory,39,191-225. [2]Abreu,D.(1988),“OntheTheoryofIn…nitelyRepeatedGameswith Discounting”,Econometrica,56,383-96. [3]Abreu,D.J., D.Pearce and E.Stacchetti(1986),“OptimalCartelEquilibriawithImperfectMonitoring”,JournalofEconomicTheory,39, 251-69. [4]Albæk,S.and L.Lambertini(1998),“CollusioninDi¤erentiated DuopoliesRevisited”,EconomicsLetters,59,305-8. [5]Aoki, R.and T.Prusa(1997),“SequentialversusSimultaneousChoice withEndogenousQuality”,InternationalJournalofIndustrial Organization,15,103-21. [6]Beath,J., Y. Katsoulacosand D.Ulph (1987),“SequentialProduct Innovationand IndustryEvolution”,EconomicJournal,97,32-43. [7]Cabral, L.M.B.(1996),“R&DAlliancesasNon-CooperativeSupergames”,CEPRDiscussionPaperNo.1439. [8]ChangM.(1991),“TheE¤ectsofProductDi¤erentiationonCollusive Pricing”,InternationalJournalofIndustrial Organization,9,453-69. [9]Chang,M.H.(1992),“IntertemporalProductChoice and ItsE¤ectson CollusiveFirmBehavior”,InternationalEconomicReview,33,773-93. [10]Choi, C.J.and H.S.Shin(1992),“ACommentonaModelofVertical ProductDi¤erentiation”,JournalofIndustrialEconomics,40,229-31. [11]Deneckere,R.(1983),“DuopolySupergameswithProductDi¤erentiation”,EconomicsLetters,11,37-42. [12]Dutta,P.K., S.Lachand A.Rustichini(1995),“BetterLatethanEarly: VerticalDi¤erentiationintheAdoptionofaNew Technology”,Journal ofEconomicsand ManagementStrategy,4,563-89. 18 [13]EC Commission(1990),CompetitionLawintheEuropeanCommunities,VolumeI,RulesApplicabletoUndertakings,Brussels-Luxembourg, EC Commission. [14]Friedman,J.W.(1971),“A NoncooperativeEquilibriumforSupergames”,ReviewofEconomicStudies,38,1-12. [15]Friedman,J.W.and J.-F.Thisse(1993),“PartialCollusionFostersMinimumProductDi¤erentiation”,RANDJournalofEconomics,24,63145. [16]Fudenberg,D.and E.Maskin(1986),“TheFolkTheoreminRepeated GameswithDiscounting orwithIncompleteInformation”,Econometrica,54,533-54. [17]Gabszewicz,J.J.and J.-F.Thisse(1979),“Price Competition, Quality and Income Disparities”,JournalofEconomicTheory,20,340-59. [18]Gabszewicz,J.J.and J.-F.Thisse(1980),“Entry(and Exit) inaDi¤erentiatedIndustry”,JournalofEconomicTheory,22,327-38. [19]Goto,A.and R.Wakasugi(1988),“TechnologyPolicy”, inKomiya,R., M. Okuno and K. Suzumura(eds.),IndustrialPolicyofJapan,New York,AcademicPress. [20]Häckner,J.(1994),“CollusivePricinginMarketsforVerticallyDi¤erentiatedProducts”,InternationalJournalofIndustrial Organization,12, 155-77. [21]Häckner,J.(1995),“EndogenousProductDesigninanIn…nitelyRepeatedGame”,InternationalJournalofIndustrial Organization,13, 277-99. [22]Häckner,J.(1996),“OptimalSymmetricPunishmentsinaBertrand Di¤erentiatedProductsDuopoly”,InternationalJournalofIndustrial Organization,14,611-30. [23]Lambertini, L.(1997),“Prisoners’DilemmainDuopoly(Super)Games”, JournalofEconomicTheory,77,181-91. 19 [24]Lambertini, L.(1999),“EndogenousTimingandtheChoiceofQualityin aVerticallyDi¤erentiatedDuopoly”,ResearchinEconomics(Ricerche Economiche),53,101-09. [25]Lambertini, L., S.Poddarand D.Sasaki(1998),“Standardizationand theStabilityofCollusion”,EconomicsLetters,58,303-10. [26]Lambertini, L., S.Poddarand D.Sasaki(2000),“ResearchJointVentures,ProductDi¤erentiation,and Price Collusion”,InternationalJournalofIndustrial Organization,forthcoming. [27]Lambertini, L.and D.Sasaki(1999),“OptimalPunishmentsinLinearDuopolySupergameswithProductDi¤erentiation”,JournalofEconomics,69,173-88. [28]Lambertini, L.and D.Sasaki(2000),“Non-NegativeQuantityConstraintsand the DurationofPunishment”,JapaneseEconomicReview, forthcoming. [29]Lehmann-Grube,U.(1997),“StrategicChoice ofQualitywhenQualityisCostly:ThePersistence oftheHigh-QualityAdvantage”,RAND JournalofEconomics,28,372-84. [30]Majerus,D.W.(1988),“Price vsQuantityCompetitioninOligopoly Supergames”,EconomicsLetters,27,293-7. [31]Martin,S.(1995),“R&DJointVenturesand TacitProductMarketCollusion”,EuropeanJournalofPoliticalEconomy,11,733-41. [32]Motta,M.(1992),“CooperativeR&Dand VerticalProductDi¤erentiation”,InternationalJournalofIndustrial Organization,10,643-61. [33]Motta,M.(1993),“EndogenousQualityChoice:PricevsQuantityCompetition”,JournalofIndustrialEconomics,41,113-32. [34]Rosenkranz,S.(1995),“Innovationand Cooperation underVertical ProductDi¤erentiation”,InternationalJournalofIndustrial Organization,13,1-22. [35]Rosenkranz,S.(1997),“QualityImprovementsand theIncentiveto Leapfrog”,InternationalJournalofIndustrial Organization,15,243-61. 20 [36]Ross,T.W.(1992),“CartelStabilityand ProductDi¤erentiation”,InternationalJournalofIndustrial Organization,10,1-13. [37]Rothschild,R.(1992),“OntheSustainabilityofCollusioninDi¤erentiatedDuopolies”,EconomicsLetters,40,33-7. [38]Shaked,A.and J.Sutton(1982),“Relaxing Price Competitionthrough ProductDi¤erentiation”,ReviewofEconomicStudies,49,3-13. [39]Shaked,A.and J.Sutton(1983),“Natural Oligopolies”,Econometrica, 51,1469-83. [40]vanDijk,T.(1996),“PatentHeightand CompetitioninProductImprovements”,JournalofIndustrialEconomics,44,151-67. 21