中级微观济学课件尼科尔森ch15

柯孔林浙江工商大学金融学院1Chapter15GAMETHEORYMODELSOFPRICING柯孔林浙江工商大学金融学院2GameTheoryGametheoryinvolvesthestudyofstrategicsituationsGametheorymodelsattempttoportraycomplexstrategicsituationsinahighlysimplifiedandstylizedsettingabstractfrompersonalandinstitutionaldetailsinordertoarriveatarepresentationofthesituationthatismathematicallytractable柯孔林浙江工商大学金融学院3GameTheoryAllgameshavethreeelementsplayersstrategiespayoffsGamesmaybecooperativeornoncooperative柯孔林浙江工商大学金融学院4PlayersEachdecision-makerinagameiscalledaplayercanbeanindividual,afirm,anentirenationEachplayerhastheabilitytochooseamongasetofpossibleactionsThespecificidentityoftheplayersisirrelevantno“goodguys”or“badguys”柯孔林浙江工商大学金融学院5StrategiesEachcourseofactionopentoaplayeriscalledastrategyStrategiescanbeverysimpleorverycomplexeachisassumedtobewell-definedInnoncooperativegames,playersareuncertainaboutthestrategiesusedbyotherplayers柯孔林浙江工商大学金融学院6PayoffsThefinalreturnstotheplayersattheendofthegamearecalledpayoffsPayoffsareusuallymeasuredintermsofutilitymonetarypayoffsarealsousedItisassumedthatplayerscanrankthepayoffsassociatedwithagame柯孔林浙江工商大学金融学院7NotationWewilldenoteagameGbetweentwoplayers(AandB)byG[SA,SB,UA(a,b),UB(a,b)]whereSA=strategiesavailableforplayerA(a

SA)SB=strategiesavailableforplayerB(b

SB)UA=utilityobtainedbyplayerAwhenparticularstrategiesarechosenUB=utilityobtainedbyplayerBwhenparticularstrategiesarechosen柯孔林浙江工商大学金融学院8NashEquilibriuminGamesAtmarketequilibrium,noparticipanthasanincentivetochangehisbehaviorIngames,apairofstrategies(a*,b*)isdefinedtobeaNashequilibriumifa*isplayerA’sbeststrategywhenplayerBplaysb*,andb*isplayerB’sbeststrategywhenplayerAplaysa*柯孔林浙江工商大学金融学院9NashEquilibriuminGamesApairofstrategies(a*,b*)isdefinedtobeaNashequilibriumifUA(a*,b*)

UA(a’,b*)foralla’

SAUB(a*,b*)

Ub(a*,b’)forallb’

SB柯孔林浙江工商大学金融学院10NashEquilibriuminGamesIfoneoftheplayersrevealstheequilibriumstrategyhewilluse,theotherplayercannotbenefitthisisnotthecasewithnonequilibriumstrategiesNoteverygamehasaNashequilibriumpairofstrategiesSomegamesmayhavemultipleequilibria柯孔林浙江工商大学金融学院11ADormitoryGameSupposethattherearetwostudentswhomustdecidehowloudlytoplaytheirstereosinadormeachmaychoosetoplayitloudly(L)orsoftly(S)柯孔林浙江工商大学金融学院12ADormitoryGameALSAchoosesloud(L)orsoft(S)BBLSLSBmakesasimilarchoice7,55,46,46,3PayoffsareintermsofA’sutilitylevelandB’sutilitylevelNeitherplayerknowstheother’sstrategy柯孔林浙江工商大学金融学院13ADormitoryGameSometimesitismoreconvenienttodescribegamesintabular(“normal”)form柯孔林浙江工商大学金融学院14ADormitoryGameAloud-playstrategyisadominantstrategyforplayerBtheLstrategyprovidesgreaterutilitytoBthandoestheSstrategynomatterwhatstrategyAchoosesPlayerAwillrecognizethatBhassuchadominantstrategyAwillchoosethestrategythatdoesthebestagainstB’schoiceofL柯孔林浙江工商大学金融学院15ADormitoryGameThismeansthatAwillalsochoosetoplaymusicloudlyTheA:L,B:LstrategychoiceobeysthecriterionforaNashequilibriumbecauseLisadominantstrategyforB,itisthebestchoicenomatterwhatAdoesifAknowsthatBwillfollowhisbeststrategy,thenListhebestchoiceforA柯孔林浙江工商大学金融学院16ExistenceofNashEquilibriaANashequilibriumisnotalwayspresentintwo-persongamesThismeansthatonemustexplorethedetailsofeachgamesituationtodeterminewhethersuchanequilibrium(ormultipleequilibria)exists柯孔林浙江工商大学金融学院17NoNashEquilibriaAnystrategyisunstablebecauseitofferstheotherplayersanincentivetoadoptanotherstrategy柯孔林浙江工商大学金融学院18TwoNashEquilibriaBothofthejointvacationsrepresentNashequilibria柯孔林浙江工商大学金融学院19ExistenceofNashEquilibriaTherearecertaintypesoftwo-persongamesinwhichaNashequilibriummustexistgamesinwhichtheparticipantshavealargenumberofstrategiesgamesinwhichthestrategieschosenbyAandBarealternatelevelsofasinglecontinuousvariablegameswhereplayersusemixedstrategies柯孔林浙江工商大学金融学院20ExistenceofNashEquilibriaInagamewhereplayersarepermittedtousemixedstrategies,eachplayermayplaythepurestrategieswithcertain,pre-selectedprobabilitiesplayerAmayflipacointodeterminewhethertoplaymusicloudlyorsoftlythepossibilityofplayingthepurestrategieswithanyprobabilitiesaplayermaychoose,convertsthegameintoonewithaninfinitenumberofmixedstrategies柯孔林浙江工商大学金融学院21ThePrisoners’DilemmaThemostfamoustwo-persongamewithanundesirableNashequilibriume柯孔林浙江工商大学金融学院22ThePrisoners’DilemmaAnironcladagreementbybothprisonersnottoconfesswillgivethemthelowestamountofjointjailtimethissolutionisnotstableThe“confess”strategydominatesforbothAandBthesestrategiesconstituteaNashequilibrium柯孔林浙江工商大学金融学院23TheTragedyoftheCommonThisexampleisusedtosignifytheenvironmentalproblemsofoverusethatoccurwhenscarceresourcesaretreatedas“commonproperty”Assumethattwoherdersaredecidinghowmanyoftheiryakstheyshouldletgrazeonthevillagecommonproblem:thecommonissmallandcanrapidlyeovergrazed柯孔林浙江工商大学金融学院24TheTragedyoftheCommonSupposethattheperyakvalueofgrazingonthecommonisV(YA,YB)=200–(YA+YB)2whereYAandYB=numberofyaksofeachherderNotethatbothVi<0andVii<0anextrayakreducesVandthismarginaleffectincreaseswithadditionalgrazing柯孔林浙江工商大学金融学院25TheTragedyoftheCommonSolvingherderA’svaluemaximizationproblem:MaxYAV=Max[200YA–YA(YA+YB)2]Thefirst-orderconditionis200–2YA2–2YAYB–YA2–2YAYB–YB2=200–3YA2–4YAYB–YB2=0Similarly,forBtheoptimalstrategyis200–3YB2–4YBYA–YA2=0柯孔林浙江工商大学金融学院26TheTragedyoftheCommonForaNashequilibrium,thevaluesforYAandYBmustsolvebothoftheseconditionsUsingthesymmetryconditionYA=YB200=8YA2=8YB2YA=YB=5Eachherderwillobtain500[=5·(200-102)]inreturnGiventhischoice,neitherherderhasanincentivetochangehisbehavior柯孔林浙江工商大学金融学院27TheTragedyoftheCommonTheNashequilibriumisnotthebestuseofthecommonYA=YB=4providesgreaterreturntoeachherder[4·(200–82)=544]ButYA=YB=4isnotastableequilibriumifAannouncesthatYA=4,BwillhaveanincentivetoincreaseYBthereisanincentivetocheat柯孔林浙江工商大学金融学院28CooperationandRepetitionCooperationamongplayerscanresultinesthatarepreferredtotheNashebybothplayersthecooperativeeisunstablebecauseitisnotaNashequilibriumRepeatedplaymayfostercooperation柯孔林浙江工商大学金融学院29ATwo-PeriodDormitoryGameLet’sassumethatAchooseshisdecibellevelfirstandthenBmakeshischoiceIneffect,thatmeansthatthegamehaseatwo-periodgameB’sstrategicchoicesmusttakeintoaccounttheinformationavailableatthestartofperiodtwo柯孔林浙江工商大学金融学院30ATwo-PeriodDormitoryGameALSAchoosesloud(L)orsoft(S)BBLSLSBmakesasimilarchoiceknowingA’schoice7,55,46,46,3Thus,weshouldputB’sstrategiesinaformthattakestheinformationonA’schoiceintoaccount柯孔林浙江工商大学金融学院31ATwo-PeriodDormitoryGameB’sStrategiesL,LL,SS,LS,SA’sStrategiesL7,57,55,45,4S6,46,36,46,3EachstrategyisstatedasapairofactionsshowingwhatBwilldodependingonA’sactions柯孔林浙江工商大学金融学院32ATwo-PeriodDormitoryGameB’sStrategiesL,LL,SS,LS,SA’sStrategiesL7,57,55,45,4S6,46,36,46,3Thereare3NashequilibriainthisgameA:L,B:(L,L)A:L,B:(L,S)A:S,B:(S,L)柯孔林浙江工商大学金融学院33ATwo-PeriodDormitoryGameB’sStrategiesL,LL,SS,LS,SA’sStrategiesL7,57,55,45,4S6,46,36,46,3A:L,B:(L,S)andA:S,B:(S,L)areimplausibleeachincorporatesanoncrediblethreatonthepartofB柯孔林浙江工商大学金融学院34ATwo-PeriodDormitoryGameThus,thegameisreducedtotheoriginalpayoffmatrixwhere(L,L)isadominantstrategyforBAwillrecognizethisandwillalwayschooseLThisisasubgameperfectequilibriumaNashequilibriuminwhichthestrategychoicesofeachplayerdonotinvolvenoncrediblethreats柯孔林浙江工商大学金融学院35SubgamePerfectEquilibriumA“subgame”istheportionofalargergamethatbeginsatonedecisionnodeandincludesallfutureactionsstemmingfromthatnodeToqualifytobeasubgameperfectequilibrium,astrategymustbeaNashequilibriumineachsubgameofalargergame柯孔林浙江工商大学金融学院36RepeatedGamesManyeconomicsituationscanbemodeledasgamesthatareplayedrepeatedlyconsumers’regularpurchasesfromaparticularretailerfirms’day-to-daycompetitionforcustomersworkers’attemptstooutwittheirsupervisors柯孔林浙江工商大学金融学院37RepeatedGamesAnimportantaspectofarepeatedgameistheexpandedstrategysetsthateavailabletotheplayersopensthewayforcrediblethreatsandsubgameperfection柯孔林浙江工商大学金融学院38RepeatedGamesThenumberofrepetitionsisalsoimportantingameswithafixed,finitenumberofrepetitions,thereislittleroomforthedevelopmentofinnovativestrategiesgamesthatareplayedaninfinitenumberoftimesofferamuchwiderarrayofoptions柯孔林浙江工商大学金融学院39Prisoners’DilemmaFiniteGameB’sStrategiesLRA’sStrategiesU1,13,0D0,32,2Ifthegamewasplayedonlyonce,theNashequilibriumA:U,B:Lwouldbetheexpectede柯孔林浙江工商大学金融学院40Prisoners’DilemmaFiniteGameB’sStrategiesLRA’sStrategiesU1,13,0D0,32,2ThiseisinferiortoA:D,B:Rforeachplayer柯孔林浙江工商大学金融学院41Prisoners’DilemmaFiniteGameSupposethisgameistoberepeatedlyplayedforafinitenumberofperiods(T)AnyexpandedstrategyinwhichApromisestoplayDinthefinalperiodisnotcrediblewhenTarrives,AwillchoosestrategyUThesamelogicappliestoplayerB柯孔林浙江工商大学金融学院42Prisoners’DilemmaFiniteGameAnysubgameperfectequilibriumforthisgamecanonlyconsistoftheNashequilibriumstrategiesinthefinalroundA:U,B:LThelogicthatappliestoperiodTalsoappliestoperiodT-1TheonlysubgameperfectequilibriuminthisfinitegameistorequiretheNashequilibriumineveryround柯孔林浙江工商大学金融学院43GamewithInfiniteRepetitionsInthiscase,eachplayercanannouncea“triggerstrategy”promisetoplaythecooperativestrategyaslongastheotherplayerdoeswhenoneplayerdeviatesfromthepattern,thegamerevertstotherepeatingsingle-periodNashequilibrium柯孔林浙江工商大学金融学院44GamewithInfiniteRepetitionsWhetherthetwintriggerstrategyrepresentsasubgameperfectequilibriumdependsonwhetherthepromisetoplaycooperativelyiscredibleSupposethatAannouncesthathewillcontinuetoplaythetriggerstrategybyplayingcooperativelyinperiodK柯孔林浙江工商大学金融学院45GamewithInfiniteRepetitionsIfBdecidestoplaycooperatively,payoffsof2canbeexpectedtocontinueindefinitelyIfBdecidestocheat,thepayoffinperiodKwillbe3,butwillfallto1inallfutureperiodstheNashequilibriumwillreassertitself柯孔林浙江工商大学金融学院46GamewithInfiniteRepetitionsIf

isplayerB’sdiscountrate,thepresentvalueofcontinuedcooperationis2+2+22+…=2/(1-)Thepayofffromcheatingis3+1+21+…=3+1/(1-)Continuedcooperationwillbecredibleif2/(1-)>3+1/(1-)>½柯孔林浙江工商大学金融学院47TheTragedyoftheCommonRevisitedTheovergrazingofyaksonthevillagecommonmaynotpersistinaninfinitelyrepeatedgameAssumethateachherderhasonlytwostrategiesavailablebringing4or5yakstothecommonTheNashequilibrium(A:5,B:5)isinferiortothecooperativee(A:4,B:4)柯孔林浙江工商大学金融学院48TheTragedyoftheCommonRevisitedWithaninfinitenumberofrepetitions,bothplayerswouldfinditattractivetoadoptcooperativetriggerstrategiesif544/(1-)>595+500(1-)>551/595=0.93柯孔林浙江工商大学金融学院49PricinginStaticGamesSupposethereareonlytwofirms(AandB)producingthesamegoodataconstantmarginalcost(c)thestrategiesforeachfirmconsistofchoosingprices(PA

andPB)subjectonlytotheconditionthatthefirm’spricemustexceedcPayoffsinthegamewillbedeterminedbydemandconditions柯孔林浙江工商大学金融学院50PricinginStaticGamesBecauseoutputishomogeneousandmarginalcostsareconstant,thefirmwiththelowerpricewillgaintheentiremarketIfPA=PB,wewillassumethatthefirmswillsharethemarketequally柯孔林浙江工商大学金融学院51PricinginStaticGamesInthismodel,theonlyNashequilibriumisPA=PB=ciffirmAchoosesapricegreaterthanc,theprofit-maximizingresponseforfirmBistochooseapriceslightlylowerthanPAandcornertheentiremarketbutB’sprice(ifitexceedsc)cannotbeaNashequilibriumbecauseitprovidesfirmAwithincentiveforfurtherpricecutting柯孔林浙江工商大学金融学院52PricinginStaticGamesTherefore,onlybychoosingPA=PB=cwillthetwofirmshaveachievedaNashequilibriumweendupwithacompetitivesolutioneventhoughthereareonlytwofirmsThispricingstrategyissometimesreferredtoasaBertrandequilibrium柯孔林浙江工商大学金融学院53PricinginStaticGamesTheBertrandresultdependscruciallyontheassumptionsunderlyingthemodeliffirmsdonothaveequalcostsorifthegoodsproducedbythetwofirmsarenotperfectsubstitutes,thecompetitiveresultnolongerholds柯孔林浙江工商大学金融学院54PricinginStaticGamesOtherduopolymodelsthatdepartfromtheBertrandresulttreatpricecompetitionasonlythefinalstageofatwo-stagegameinwhichthefirststageinvolvesvarioustypesofentryorinvestmentconsiderationsforthefirms柯孔林浙江工商大学金融学院55PricinginStaticGamesConsiderthecaseoftwoownersofnaturalspringswhoaredecidinghowmuchwatertosupplyAssumethateachfirmmustchooseacertaincapacityoutputlevelmarginalcostsareconstantuptothatlevelandinfinitethereafter柯孔林浙江工商大学金融学院56PricinginStaticGamesAtwo-stagegamewherefirmschoosecapacityfirst(andthenprice)isformallyidenticaltotheCournotanalysisthequantitieschosenintheCournotequilibriumrepresentaNashequilibriumeachfirmcorrectlyperceiveswhattheother’soutputwillbeoncethecapacitydecisionsaremade,theonlypricethatcanprevailisthatforwhichquantitydemandedisequaltototalcapacity柯孔林浙江工商大学金融学院57PricinginStaticGamesSupposethatcapacitiesaregivenbyqA’andqB’andthatP’=D

-1(qA’+qB’)whereD-1istheinversedemandfunctionAsituationinwhichPA=PB<P’isnotaNashequilibriumtotalquantitydemanded>totalcapacitysoonefirmcouldincreaseitsprofitsbyraisingitspriceandstillsellitscapacity柯孔林浙江工商大学金融学院58PricinginStaticGamesLikewise,asituationinwhichPA=PB>P’isnotaNashequilibriumtotalquantitydemanded<totalcapacitysoatleastonefirmissellinglessthanitscapacitybycuttingprice,thisfirmcouldincreaseitsprofitsbytakingallpossiblesalesuptoitscapacitytheotherfirmwouldenduploweringitspriceaswell柯孔林浙江工商大学金融学院59PricinginStaticGamesTheonlyNashequilibriumthatwillprevailisPA=PB=P’thispricewillfallshortofthemonopolypricebutwillexceedmarginalcostTheresultsofthistwo-stagegameareindistinguishablefromtheCournotmodel柯孔林浙江工商大学金融学院60PricinginStaticGamesTheBertrandmodelpredictscompetitiveesinaduopolysituationTheCournotmodelpredictsmonopoly-likeinefficienciesThissuggeststhatactualbehaviorinduopolymarketsmayexhibitawidevarietyofesdependingonthewayinwhichcompetitionoccurs柯孔林浙江工商大学金融学院61RepeatedGamesandTacitCollusionPlayersininfinitelyrepeatedgamesmaybeabletoadoptsubgame-perfectNashequilibriumstrategiesthatyieldbetteresthansimplyrepeatingalessfavorableNashequilibriumindefinitelydothefirmsinaduopolyhavetoenduretheBertrandequilibriumforever?cantheyachievemoreprofitableesthroughtacitcollusion?柯孔林浙江工商大学金融学院62RepeatedGamesandTacitCollusionWithanyfinitenumberofreplications,theBertrandresultwillremainunchangedanystrategyinwhichfirmAchoosesPA>cinperiodT(thefinalperiod)offersBtheoptionofchoosingPA>PB>cA’sthreattochargePA

inperiodTisnoncredibleasimilarargumentappliestoanyperiodpriortoT柯孔林浙江工商大学金融学院63RepeatedGamesandTacitCollusionIfthepricinggameisrepeatedoverinfinitelymanyperiods,twin“trigger”strategiesefeasibleeachfirmsetsitspriceequaltothemonopolyprice(PM)providingtheotherfirmdidthesameinthepriorperiodiftheotherfirm“cheated”inthepriorperiod,thefirmwilloptforcompetitivepricinginallfutureperiods柯孔林浙江工商大学金融学院64RepeatedGamesandTacitCollusionSupposethat,afterthepricinggamehasbeenproceedingforseveralperiods,firmBisconsideringcheatingbychoosingPB<PA

=PMitcanobtainalmostallofthesingleperiodmonopolyprofits(

M)柯孔林浙江工商大学金融学院65RepeatedGamesandTacitCollusionIffirmBcontinuestocolludetacitlywithA,itwillearnitsshareoftheprofitstream(M+M+2

M+…+n

M+…)/2=(M/2)[1/(1-)]

whereisthediscountfactorappliedtofutureprofits柯孔林浙江工商大学金融学院66RepeatedGamesandTacitCollusionCheatingwillbeunprofitableif

M<(M/2)[1/(1-)]

orif>1/2Providingthatfirmsarenottooimpatient,thetriggerstrategiesrepresentasubgameperfectNashequilibriumoftacitcollusion柯孔林浙江工商大学金融学院67TacitCollusionSupposeonlytwofirmsproducesteelbarsforjailhousewindowsBarsareproducedataconstantACandMCof$10andthedemandforbarsisQ=5,000-100PUnderBertrandcompetition,eachfirmwillchargeapriceof$10andatotalof4,000barswillbesold柯孔林浙江工商大学金融学院68TacitCollusionThemonopolypriceinthismarketis$30eachfirmhasanincentivetocolludetotalmonopolyprofitswillbe$40,000eachperiod(eachfirmwillreceive$20,000)anyonefirmwillconsideranext-periodpricecutonlyif$40,000>$20,000(1/1-)willhavetobefairlyhighforthistooccur柯孔林浙江工商大学金融学院69TacitCollusionTheviabilityofatriggerpricestrategymaydependonthenumberoffirmssupposethereare8producerstotalmonopolyprofitswillbe$40,000eachperiod(eachfirmwillreceive$5,000)anyonefirmwillconsideranext-periodpricecutif$40,000>$5,000(1/1-)thisislikelyatreasonablelevelsof柯孔林浙江工商大学金融学院70GeneralizationsandLimitationsTheviabilityoftacitcollusioningametheorymodelsisverysensitivetotheassumptionsmadeWeassumedthat:firmBcaneasilydetectthatfirmAhascheatedfirmBrespondstocheatingbyadoptingaharshresponsethatnotonlypunishesA,butalsocondemnsBtozeroprofitsforever柯孔林浙江工商大学金融学院71GeneralizationsandLimitationsInmoregeneralmodelsoftacitcollusion,theseassumptionscanberelaxeddifficultyinmonitoringotherfirm’sbehaviorotherformsofpunishmentdifferentiatedproducts柯孔林浙江工商大学金融学院72Entry,Exit,andStrategyInpreviousmodels,wehaveassumedthatentryandexitaredrivenbytherelationshipbetweentheprevailingmarketpriceandafirm’saveragecostTheentryandexitissuecaneconsiderablymorecomplex柯孔林浙江工商大学金融学院73Entry,Exit,andStrategyAfirmwishingtoenterorexitamarketmustmakesomeconjectureabouthowitsactionswillaffectthefuturemarketpricethisrequiresthefirmtoconsiderwhatitsrivalswilldothismayinvolveanumberofstrategicploysespeciallywhenafirm’sinformationaboutitsrivalsisimperfect柯孔林浙江工商大学金融学院74SunkCostsandCommitmentManygametheoreticmodelsofentrystresstheimportanceofafirm’scommitmenttoaspecificmarketlargecapitalinvestmentsthatcannotbeshiftedtoanothermarketwillleadtoalargelevelofcommitmentonthepartofthefirm柯孔林浙江工商大学金融学院75SunkCostsandCommitmentSunkcostsareone-timeinvestmentsthatmustbemadetoenteramarkettheseallowthefirmtoproduceinthemarketbuthavenoresidualvalueifthefirmleavesthemarketcouldincludeexpendituresonuniquetypesofequipmentorjob-specifictrainingofworkers柯孔林浙江工商大学金融学院76First-MoverAdvantageinCournot’sNaturalSpringsUndertheStackelbergversionofthismodel,eachfirmhastwopossiblestrategiesbealeader(qi=60)beafollower(qi=30)柯孔林浙江工商大学金融学院77First-MoverAdvantageinCournot’sNaturalSpringsThepayoffsforthesetwostrategiesare:柯孔林浙江工商大学金融学院78First-MoverAdvantageinCournot’sNaturalSpringsTheleader-leaderstrategyforeachfirmprovestobedisastrousitisnotaNashequilibriumiffirmAknowsthatfirmBwilladoptaleaderstrategy,itsbestmoveistobeafollowerAfollower-followerchoiceisprofitableforbothfirmsthischoiceisunstablebecauseitgiveseachfirmanincentivetocheat柯孔林浙江工商大学金融学院79First-MoverAdvantageinCournot’sNaturalSpringsWithsimultaneousmoves,eitheroftheleader-followerpairsrepresentsaNashequilibriumButifonefirmhastheopportunitytomovefirst,itcandictatewhichofthetwoequilibriaischosenthisisthefirst-moveradvantage柯孔林浙江工商大学金融学院80EntryDeterrenceInsomecases,first-moveradvantagesmaybelargeenoughtodeterallentrybyrivalshowever,itmaynotalwaysbeinthefirm’sbestinteresttocreatethatlargeacapacity柯孔林浙江工商大学金融学院81EntryDeterrenceWitheconomiesofscale,thepossibilityforprofitableentrydeterrenceisincreasedifthefirstmovercanadoptalarge-enoughscaleofoperation,itmaybeabletolimitthescaleofapotentialentrantthepotentialentrantwillexperiencesuchhighaveragecoststhattherewouldbenoadvantagetoenteringthemarket柯孔林浙江工商大学金融学院82EntryDeterrenceinCournot’sNaturalSpringAssumethateachspringownermustpayafixedcostofoperations($784)TheNashequilibriumleader-followerstrategiesremainprofitableforbothfirmsiffirmAmovesfirstandadoptstheleader’srole,B’sprofitsarerelativelysmall($116)AcouldpushBoutofthemarketbybeingabitmoreaggressive柯孔林浙江工商大学金融学院83EntryDeterrenceinCournot’sNaturalSpringSinceB’sreactionfunctionisunaffectedbythefixedcosts,firmAknowsthatqB=(120-qA)/2andmarketpriceisgivenbyP=120-qA-qBFirmAknowsthatB’sprofitsare

B=PqB-784柯孔林浙江工商大学金融学院84EntryDeterrenceinCournot’sNaturalSpringWhenBisafollower,itsprofitsdependonlyonqATherefore,FirmAcanensurenonpositiveprofitsforfirmBbychoosingqA

64FirmAwillearnprofitsof$2,800柯孔林浙江工商大学金融学院85LimitPricingAretheresituationswhereamonopolymightpurposelychoosealow(“limit”)pricepolicytodeterentryintoitsmarket?Inmostsimplesituations,thelimitpricingstrategydoesnotyieldmaximumprofitsandisnotsustainableovertimechoosingPL<PMwillonlydeterentryifPLislowerthantheACofanypotentialentrant柯孔林浙江工商大学金融学院86LimitPricingIfthemonopolyandthepotentialentranthavethesamecosts,theonlylimitpricesustainableisPL=ACdefeatsthepurposeofbeingamonopolybecause=0Thus,thebasicmonopolymodelofferslittleroomforentrydeterrencethroughpricingbehavior柯孔林浙江工商大学金融学院87LimitPricingandpleteInformationBelievablemodelsoflimitpricingmustdepartfromtraditionalassumptionsThemostimportantsetofsuchmodelsinvolvespleteinformationifanincumbentmonopolistknowsmoreaboutthemarketsituationthanapotentialentrant,themonopolistmaybeabletodeterentry柯孔林浙江工商大学金融学院88LimitPricingandpleteInformationSupposethatanincumbentmonopolistmayhaveeither“high”or“low”productioncostsasaresultofpastdecisionsTheprofitabilityoffirmB’sentryintothemarketdependsonA’scostsWecanuseatreediagramtoshowB’sdilemma柯孔林浙江工商大学金融学院89LimitPricingandpleteInformation1,34,03,-16,0HighCostLowCostEntryEntryNoEntryNoEntry

ABBTheprofitabilityofentryforFirmBdependsonFirmA’scostswhichareunknowntoB柯孔林浙江工商大学金融学院90LimitPricingandpleteInformationFirmBcouldusewhateverinformationithastodevelopasubjectiveprobabilityofA’scoststructureIfBassumesthatthereisaprobabilityof

thatAhashighcostand(1-

)thatithaslowcost,entrywillyieldpositiveexpectedprofitsifE(B)=(3)+(1-)(-1)>0>¼柯孔林浙江工商大学金融学院91LimitPricingandpleteInformationRegardlessofitstruecosts,firmAisbetteroffifBdoesnotenterOnewaytoensurethisisforAtoconvinceBthat

<¼FirmAmaychoosealow-pricestrategythentosignalfirmBthatitscostsarelowthisprovidesapossiblerationaleforlimitpricing柯孔林浙江工商大学金融学院92PredatoryPricingThestructureofmanymodelsofpredatorybehaviorissimilartothatusedinlimitpricingmodelsstresspleteinformationAfirmwishestoencourageitsrivaltoexitthemarketittakesactionstoaffectitsrival’sviewsofthefutureprofitabilityofremaininginthemarket柯孔林浙江工商大学金融学院93GamesofpleteInformationEachplayerinagamemaybeoneofanumberofpossibletypes(tAandtB)playertypescanvaryalongseveraldimensionsWewillassumethatourplayertypeshavedifferingpotentialpayofffunctionseachplayerknowshisownpayoffbutdoesnotknowhisopponent’spayoffwithcertainty柯孔林浙江工商大学金融学院94GamesofpleteInformationEachplayer’sconjecturesabouttheopponent’splayertypearerepresentedbybelieffunctions[fA(tB)]consistoftheplayer’sprobabilityestimatesofthelikelihoodthathisopponentisofvarioustypesGamesofpleteinformationaresometimesreferredtoasBayesiangames柯孔林浙江