A Primer in Game Theory.docx
- 文档编号:25637381
- 上传时间:2023-06-11
- 格式:DOCX
- 页数:42
- 大小:51.69KB
A Primer in Game Theory.docx
《A Primer in Game Theory.docx》由会员分享,可在线阅读,更多相关《A Primer in Game Theory.docx(42页珍藏版)》请在冰豆网上搜索。
APrimerinGameTheory
APrimerinGameTheory
APrimerinGameTheoryRobertGibbons
ContentsPrefacexj1StaticGamesofCompleteInformation11.1BasicTheory:
Normal-FormGamesandNashEquilibrium21.1.ANormal-FormRepresentationofGames....21.1.8><#004699'>BIteratedEliminationofStrictlyDominatedStrategies41.1.CMotivationandDefinitionofNashEquilibrium81.2Applications141.2.ACournotModelofDuopoly141.2.<#004699'>BBertrandModelofDuopoly211.2.CFinal-OfferArbitration221.2.DTheProblemoftheCommons271.3AdvancedTheory:
MixedStrategiesandExistenceofEquilibrium291.3.AMixedStrategies291.3.<#004699'>BExistenceofNashEquilibrium331.4FurtherReading481.5Problems481.6References512DynamicGamesofCompleteInformation552.1DynamicGamesofCompleteandPerfectInformation572.1.ATheory:
BackwardsInduction572.1.<#004699'>BStackelbergModelofDuopoly612.1.CWagesandEmploymentinaUnionizedFirm642.1.DSequentialBargaining682.2Two-StageGamesofCompletebutImperfectInformation^vn
Contentsbe12.A;Theory:
SubgamePerfection714.2.<#004699'>Bjob-MarketSignaling190IB4.2.CCorporateInvestmentandCapitalStructure.205BankRuns73-CTariffsandImperfectInternationa4.2.DMonetaryPolicy208lCompetition754.3OtherApplicationsofPerfectBayesian2.2.DTournaments79Equilibrium.2102.3RepeatedGames824.3.ACheap-TalkGames210;ATheory:
Two-StageRepeatedGames824.3.<#004699'>BSequentialBargainingunderAsymmetric2.3.<#004699'>BTheory:
InfinitelyRepeatedGames88Information218:
.CCollusionbetweenCoumotDuopolists....1024.3.CReputationintheFinitelyRepeated23-DEfficiencyWages107Prisoners’Dilemma224ETime-ConsistentMonetaryPolicy1124.4RefinementsofPerfectBayesianEquilibrium2332.4DynamicGamesofCompletebut4.5FurtherReading244ImperfectInformation1154.6Problems245-;.AExtensive-FormRepresentationofGames..1154.7References2532.4.<#004699'>BSubgame-PerfectNashEquilibrium1222.5FurtherReading129Index7^716Problems13017References138StaticGamesofIncompleteInformation1433.1Theory:
StaticBayesianGamesandBayesianNashEquilibrium1443.1.AAnExample:
CournotCompetitionunderAsymmetricInformation1443.1.<#004699'>BNormal-FormRepresentationofStaticBayesianGames1463.1.CDefinitionofBayesianNashEquilibrium...14931Applications1523.2.AMixedStrategiesRevisited1523.2.<#004699'>BAnAuction1553.2.CADoubleAuction1583.3TheRevelationPrinciple1643.4FurtherReading1683.5Problems1693.6References1721DynamicGamesofIncompleteInformation173IntroductiontoPerfectBayesianEquilibrium175SignalingGames183PerfectBayesianEquilibriuminSignalingGames183
PrefaceGametheoryisthestudyofmultipersondecisionproblems.Suchproblemsarisefrequentlyineconomics.Asiswidelyappreciated,forexample,oligopoliespresentmultipersonproblemseachfirmmustconsiderwhattheotherswilldo.Butmanyotherap?
?
plicationsofgametheoryariseinfieldsofeconomicsotherthanindustrialorganization.Atthemicrolevel,modelsoftradingprocesses(suchasbargainingandauctionmodels)involvegametheory.Atanintermediatelevelofaggregation,laborandfinan?
?
cialeconomicsincludegame-theoreticmodelsofthebehaviorofafirminitsinputmarkets(ratherthanitsoutputmarket,asinanoligopoly).Therealsoaremultipersonproblemswithinafirm:
manyworkersmayvieforonepromotion;severaldivisionsmaycompeteforthecorporation’sinvestmentcapital.Finally,atahighlevelofaggregation,internationaleconomicsincludesmodelsinwhichcountriescompete(orcollude)inchoosingtariffsandothertradepolicies,andmacroeconomicsincludesmodelsinwhichthemonetaryauthorityandwageorpricesettersinteractstrategicallytodeterminetheeffectsofmonetarypolicy.Thisbookisdesignedtointroducegametheorytothosewhowilllaterconstruct(oratleastconsume)game-theoreticmodelsinappliedfieldswithineconomics.Theexpositionemphasizestheeconomicapplicationsofthetheoryatleastasmuchasthepuretheoryitself,forthreereasons.First,theapplicationshelpteachthetheory;formalargumentsaboutabstractgamesalsoap?
?
pearbutplayalesserrole.Second,theapplicationsillustratetheprocessofmodelbuildingtheprocessoftranslatinganinfor?
?
maldescriptionofamultipersondecisionsituationintoaformal,game-theoreticproblemtobeanalyzed.Third,thevarietyofap?
?
plicationsshowsthatsimilarissuesariseindifferentareasofeco?
?
nomics,andthatthesamegame-theoretictoolscanbeappliedinXI
PrefacevixmiIlearnedgametheoryfromDavidKreps,JohnRoberts,andeachsetting.InordertoemphasizethebroadpotentialscopeofBobWilsoningraduateschool,andfromAdamBrandenburger,tiietheory,conventionalapplicationsfromindustrialorganizationDrewFudenberg,andJeanTiroleafterward.Iowethetheoreti?
?
largelyhavebeenreplacedbyapplicationsfromlabor,macro,andotherappliedfieldsineconomics.1calperspectiveinthisbooktothem.ThefocusonapplicationsWandotheraspectsofthepedagogicalstyle,however,arelargelyewilldiscussfourclassesofgames:
staticgamesof5><#880000'>com?
?
pleteinformation,dynamicgamesofcompleteinformationduetothestudentsintheMITEconomicsDepartmentfrom1985,staticgameto1990,whoinspiredandrewardedthecoursesthatledtothissofincompleteinformation,anddynamicgamesofincom?
?
pleteinformation.(Agamehasincompletebook.Iamverygratefulfortheinsightsandencouragementallinformationifoneplayerdoesnotknowanotherplayer’sthesefriendshaveprovided,aswellasforthemanyhelpful<#880000'>com?
?
payoff,suchasinanauc?
?
tionwhenonebidderdoesnotknowmentsonthemanuscriptIreceivedfromJoeFarrell,MiltHarris,howmuchanotherbidderiswillingtopayforthegoodbeingsold.)CorrespondingtotheseGeorgeMailath,MatthewRabin,AndyWeiss,andseveralanony?
?
fourclassesofgameswillbefournotionsofequilibriumingames:
mousreviewers.Finally,IamgladtoacknowledgetheadviceandNashequilibrium,subgame-perfectNashequilibrium,BayesianencouragementofJackRepcheckofPrincetonUniversityPressandNashequilibrium,andperfectBayesianequilibrium.financialsupportfromanOlinFellowshipinEconomicsattheNa?
?
TwotionalBureauofEconomicResearch.(related)waystoorganizeone’sthinkingabouttheseequi?
?
libriumconceptsareasfollows.First,onecouldconstructse?
?
quencesofequilibriumconceptsofincreasingstrength,wherestronger(i.e.,morerestrictive)conceptsareattemptstoeliminateimplausibleequilibriaallowedbyweakernotionsofequilibrium.Wewillsee,forexample,thatsubgame-perfectNashequilibriumisstrongerthanNashequilibriumandthatperfectBayesianequi?
?
libriuminturnisstrongerthansubgame-perfectNashequilib?
?
rium.Second,onecouldsaythattheequilibriumconceptofin?
?
terestisalwaysperfectBayesianequilibrium(orperhapsanevenstrongerequilibriumconcept),butthatitisequivalenttoNashequilibriuminstaticgamesofcompleteinformation,equivalenttosubgame-perfectionindynamicgamesofcomplete(andper?
?
fect)information,andequivalenttoBayesianNashequilibriuminstaticgamesofincompleteinformation.Thebookcanbeusedintwoways.Forfirst-yeargraduatestu?
?
dentsineconomics,manyoftheapplicationswillalreadybefamil?
?
iar,sothegametheorycanbecoveredinahalf-semestercourse,leavingmanyoftheapplicationstobestudiedoutsideofclass.Forundergraduates,afull-semestercoursecanpresentthetheoryabitmoreslowly,aswellascovervirtuallyalltheapplicationsinclass.Themainmathematicalprerequisiteissingle-variablecal?
?
culus;therudimentsofprobabilityandanalysisareintroducedasneeded.’AgoodsourceforapplicationsoigametheoryinindustrialorganizationisMie’sTheTheon/offnctusfrialOrganizaiion(MITPress,1988).
Chapter1StaticGamesofCompleteInformationInthischapterweconsidergamesofthefollowingsimpleform:
firsttheplayerssimultaneouslychooseactions;thentheplayersreceivepayoffsthatdependonthecombinationofactionsjustcho?
?
sen.Withintheclassofsuchstatic(orsimultaneous-move)games,werestrictattentiontogamesofcompleteinformation.Thatis,eachplayer’spayofffunction(thefunctionthatdeterminestheplayer’spayofffromthecombinationofactionschosenbytheplayers)iscommonknowledgeamongalltheplayers.Weconsiderdynamic(orsequential-move)gamesinChapters2and4,andgamesofincompleteinformation(gamesinwhichsomeplayerisuncertainaboutanotherplayer’spayofffunctionasinanauctionwhereeachbidder’swillingnesstopayforthegoodbeingsoldisun?
?
knowntotheotherbidders)inChapters3and4.InSection1.1wetakeafirstpassatthetwobasicissuesingametheory:
howtodescribeagameandhowtosolvethere?
?
sultinggame-theoreticproblem.Wedevelopthetoolswewilluseinanalyzingstaticgamesofcompleteinformation,andalsothefoundationsofthetheorywewillusetoanalyzerichergamesinlaterchapters.Wedefinethenormal-formrepresentationofagameandthenotionofastrictlydominatedstrategy.Weshowthatsomegamescanbesolvedbyapplyingtheideathatrationalplayersdonotplaystrictlydominatedstrategies,butalsothatinothergamesthisapproachproducesaveryimprecisepredictionabouttheplayofthegame(sometimesasimpreciseas;anythingcould1
2STATICGAMESOFCOMPLETEINFORMATIOND/ip?
?
rTlionni3happen;).WethenmotivateanddefineNashequilibriumaso?
?
lutionconceptthatproducesmuchtighterpredictionseparatecellsandexplaintheconsequencesthatwillfollowfromsinaverybroadtheactionstheycouldtake.Ifneit
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- Primer in Game Theory