The Coase Theorem amp;Game Theory - The Progress amp;Freedom 科斯定理amp；博弈过程amp；自由

TheCoaseTheorem&

GameTheoryPresentedbyDr.ElizabethHoffmanProfessorofEconomicsandCUPresidentEmeritaIRLEMay22,2006

CoaseExperimentCoaseExperimentsPayoffSheet

NumberA’sPayoffB’sPayoff1$0.00$12.0024.0010.0037.504.0047.504.0059.002.50610.501.00712.000.00CoaseTheoremRonaldCoaseBritishEconomistBornDecember29,1910WonNobelMemorialPrizeinEconomicsin1991TheProblemofSocialCost,1960CoaseTheoremOwnerofpropertyrightwillmanageproductionornegotiateapricesuchthatthosenotowningpropertyrightwillpayAssignpropertyrights:TopolluteTobreathcleanairToafisheryToanoilpoolCoaseTheoremCoasearguedoutcomewouldbeefficient,onlythedistributionofresourceswouldbeaffected.Examples:FarmerandrancherdecidehowmuchlandtofenceforfarmingandhowmuchtoallowasopenrangeforcattleRailroadandfarmerwilldecidehowclosetothetrackstoallowcropstogrowandhowmuchburningfromsparkstoallowCoaseTheoremExperimentalTestsoftheCoaseTheoremPropertyrightsbytheflipofacoinLargebargaininggroupsPropertyrightsbyearnedentitlementandmoralauthorityCoaseTheorem

ExperimentalResults

ExperimentNumberofDecisions(N)NumberofJointMaxima(N1)EqualSplit(N2)A.Coinflip:1.Nomoralauthority2220102.Moralauthority20199B.Gametrigger:1.Nomoralauthority221892.Moralauthority22214Total867832CoaseTheoremProblemswiththeCoaseTheoremAssignmentofpropertyrightscanbedisputedinthelegalsystem(tortlaw)TransactioncostsmayleadtodifferentoutcomesdependingonwhichsidehaspropertyrightImperfectorasymmetricinformationaboutvaluationsFreeriderproblemcomesintoeffectwhenmorethanonepersonsharespropertyrightPoolingcanresultinlastownerholdingouttogetalltheprofitsOthers,notincludedinbargaining,maybeaffectedbyoutcomeNashEquilibriumJohnNashAmericanMathematicianBornJune13,1928WonNobelMemorialPrizeinEconomicsin1994forGameTheoryCournot-NashEquilibrium Cournot–19thcenturyeconomistwhofirstcameupwithanideatoformalizeAdamSmith’stheoryofperfectcompetitionGamesandEconomicBehaviorbyvonNeumannandMorgenstern(1944),firstrealbookingametheoryNashdevelopedasimplewaytoillustratepointsmadebybothCournotandvonNeumannandMorgensternCournot-NashEquilibriumDefinition:Assumingplayersaremaximizingintheirowninterest,eachplayerplaysastrategywhichoptimizesforthatplayer,givenwhatstrategiestheotherplayersareplaying.ANashequilibriumisasetofstrategies,suchthatwheneveryoneismaximizing,givenallotherplayers’strategies,noplayerhasanincentivetochangehisorherstrategy.SimplestExample:

AMonopolistwithzeromarginalcostandmanycustomersP6030=PmMR90=QmQ180SimplestExample:

AMonopolistwithzeromarginalcostandmanycustomers Thedemandcurveintersectsthequantityaxisat180units.Therefore,themarginalrevenuecurveintersectsthequantityaxisat½of180,or90.Themonopolistmaximizesprofitsbyequatingamarginalcostof0andamarginalrevenueof0,producing90unitsandchargingapricethatsells90units.Sincetherearemanyconsumers,nooneconsumercanaffectthemarketbyunilaterallychanginghisorherbehavior.Thus,themonopolist’sdecisionisaNashequilibrium.Enteranotherseller.

Wecallthisaduopoly.P6030=PmMR90=QmQ180Theduopolist(entrant)observesthatthereare90unitsgoingunsoldinthismarket.Whatishisorherbeststrategyforenteringthismarket?DuopolyP60304590Q180Residualmarginalrevenue15Theentrantobservesthatthereisnowresidualdemandalongthelowerhalfofthedemandcurve.Tomaximizeagainstthemonopolist’sdecision,theentrantwouldproduce45unitsatapriceof15,effectivelygivingthemonopolist½ofthemarketandtheentrant¼ofthemarket.IsthisaNashEquilibrium?

P60

112.5

45 67.5 180 Q

Firm2 Firm1 ¼ 3/8-No,giventhedefinitionofaNashequilibrium,themonopolist’sstrategyisnolongeroptimalbecausethemonopolistnowmaximizesagainstthe45asagivenbytheentrant.However,theentrantwillthenchangehisorherstrategyinresponsetothechangeinstrategybytheoriginalfirm.OnecouldimagineeachfirmchangingitsstrategyinresponsetothechangeinstrategybytheotherfirmuntilaNashequilibriumisreached.¼ofmarketisnotoptimalagainst3/8th,forexample.WhatistheNashEquilibrium?P602012060Q180Firm1Firm2Ifeachfirmproduces1/3andtheyshare2/3ofthemarket,neitherfirmhasanincentivetochangeitsoutputwhenmaximizingagainsttheotherfirm’sbehavior. 60So----

whathappenswhenmorefirmsenter?PFirm1Firm2Firm3?180QThereisstillaresidualdemandof60units.Thenextfirmcouldmaximizeontheresidual60units,producing30units. IsthisNashequilibrium?NashEquilibrium PreviousslideNOTNashEquilibriumbecauseotherfirmswouldonceagainrespond. WhatwouldbeNashequilibrium?Dividein¼’ths?NashEquilibriumSupposeathousandfirmsenter?Supposethereareaninfinitenumberoffirms? Quantityproducedgoesto180,pricegoestozero. Obviously,ifthereisapositivemarginalcost,quantitywillbedriventothequantitythatequatesmarginalcostandmarginalrevenue.Therefore,thesimplestNashequilibriumwithmanyfirmsandmanyconsumersisacompetitiveequilibrium!So,whatisagameineconomics?Asetofplayers(firms,consumers,governments),asetofalternativestrategiesavailabletoeachplayer,andasetofpayoffsobtainableasafunctionofthestrategiessimultaneouslyplayedbyalltheplayers.Cooperativeandnon-cooperativegames: Anon-zerosumgameisagameinwhichthereexistsajoint-profitmaximumiftheplayerscanagreetoplaythegameasacooperativegame.Thus,themonopolygamedescribedabovecouldbeplayedasacooperativegameiftheplayerscouldagreetosplitthemonopolyprofitsandrestrictoutputtothemonopolyoutput.Cooperativeandnon-cooperativegames:

Whenagroupoffirmssucceedsincolludingwecallitacartel.OPECissuchacartel.CartelswererenderedillegalintheU.S.in1890undertheShermanAnti-trustActaftertherailroadconsolidationsandJohnD.Rockefeller’sStandardOilTrust.Cooperativeandnon-cooperativegames: Azero-sumgameisagameinwhichoneplayer’sgainisalwaysanotherplayer’sloss.Zero-sumgamescanonlybeplayedasnon-cooperativegames,sincethereexistsnojointmaximizingsolution.Core: Thecoreofacooperativegameisasolutionthatmaximizesthejointprofitsandguaranteeseachplayeratleastasmuchasheorshecouldearnaloneorbycooperatingwithanysmallergroupamongtheotherfirms.Wecallanysmallergroupacoalition.BacktotheCoaseTheoremExperimentsCoaseExperimentsPayoffSheet

NumberA’sPayoffB’sPayoff1$0.00$12.0024.0010.0037.504.0047.504.0059.002.50610.501.00712.000.00WhatistheCoreandwhy?Number2maximizesthejointprofitsbutthecontrollerhastoearnatleast$12tobeaswelloffasifheorsheplayedthegameasanon-cooperativegame.Iftheplayersweretodividethe$2ofsurplus,equally,wewouldcallitaNashbargainingsolution. Thus,theNashequilibriumoftheCoasegameistotakethe$12andrun,thecoreistoagreetooutcome2,andgivethecontrolleratleast$12,andtheNashbargainingsolutionistoagreetooutcome2andsplitthe$2.ThePrisoner’sDilemma:

Anotherexampleofanon-zerosumgamethatcanbeplayedcooperativelyornon-cooperatively

Intheprisoner’sdilemma,therearetwosuspectsaccusedofacrime.Theyareseparatedintworoomsandgrilled.Iftheysticktogetheranddon’tconfess,eachmightgetofforgetofflightly.Eachisofferedachancetoratontheotherinreturnfornoconvictionandabigconvictionfortheotherperson.Ifbothrat,theybothgetsentences,perhapsnotquiteasbadasifonlyonerats.Prisoner’sDilemmaAServes1yearBServes1yearAServes15yearsBGetsoff(0years)AGetsoff(0years)BServes15yearsAServes10yearsBServes10yearsDon’tconfessConfessDon’tconfessConfessB’sStrategyA’sStrategyPrisoner’sDilemma WhatistheNashequilibriumstrategy?ForprisonerA,ifBdoesn’tconfess,heshouldconfess,becausehegetsoff.Similarly,forprisonerB,ifAdoesn’tconfess,heshouldconfess,becausehegetsoff.Thus,bothconfessandget10years.WecallthisadominantstrategyNashequilibriumorastrongNashequilibriumbecausenootherstrategydominatesunlesstheysucceedinstickingtogetherandactivelycolluding.Wemodelcartelsas:

Prisoner’sDilemmaAgets$50Bgets$50Agets$45Bgets$54Agets$54Bgets$45Agets$48Bgets$48Don’tcheatCheatDon’tCheatCheatFirmB’sStrategiesFirmA’sStrategiesWemodelcartelsas:

Prisoner’sDilemma Thejointprofitmaximumisnottocheatandsplit$100.Buteachhasadominantstrategytocheatfortheextra$4.Theendresultisthattheysplit$96,leaving$4onthetable.RobertAxelrodRobertAxelrodMathandPoliticalScienceMacArthurFellowshipTheEvolutionofCooperation,1984RobertAxelrod

RobertAxelrod,TheEvolutionofCooperation,(1984)studiedthePrisoner’sDilemmawhenplayedbythesametwoplayersrepeatedlyformanyperiods.HeformalizedthetypeofstrategicinteractionthatwouldoccurwhenthePrisoner’sDilemmaisplayedrepeatedly.Intit-for-tat,player1startsbycooperatingandtheneachplayersimplyrepeatswhattheotherplayerdoes.RobertAxelrod

Axelrodcameupwiththisideaafterrunninganiteratedprisoner’sgamecontest,inwhichgametheoristswereinvitedtosubmitcomputerprogramsforhowtoplayaniteratedprisoner’sdilemmagameagainstallotherstrategies.AnatolRapaportsubmittedthewinningstrategy,afour-lineprogram,whichbecameknownastit-for-tat.Sometimesitisplayedwith“forgiveness〞.RobertAxelrodLater,ateamfromSouthamptonUniversity(NicholasJennings,RejdeepDash,SarvapaliRachurn,AlexRogers,andPerukrishnenVytelingum)introducedamorecomplicated,moreforgivingtit-for-tatstrategythatbeatRapaport’s.But,ifitencountersaconstantdefector,italwaysdefects.Whatthisleadstoisanunderstandingthatsocialnormsofbehaviorhavepowerfuleffectonhowpeopleactuallyplayeconomicgamesintherealworld.RobertAxelrodSocialnormsfavoringcooperationhavepowerfulevolutionarybasesbecauseourspecieswouldnothavesurvivedthetrialsoflivingintheAfricangrasslandsifwehadnotlearnedtocooperateeffectivelyandtopunishcheatersswiftlyandeffectively.ThisbringsustoworkbyHoffman,McCabe,andSmithontheultimatumgame.UltimatumGameExperimentUltimatumGameExperimentIntheultimatumgame,therearetwoplayerswhomustsplitasumofmoney.Onemakesaproposal.Theothermustagreeordisagree.Ifthesecondagrees,thedivisiontakesplace.Iftheseconddisagrees,theygetnothing.Thesmallestofferis$1.WhatistheNashequilibriumandwhy?Inthedictatorgame,thefirstmoverproposesadivision.Thesecondmoverhasnorecourse.WhatistheNashequilibriumandwhy?FHSSResults

Figure1Ultimatum;FHSSResults,Divide$10,N=24Dictator;FHSSResults,Divide$10,N=24%Frequency%FrequencyOffer$Offer