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首页 演化博弈论-瑞典乔根·W·威布尔.pdf

演化博弈论-瑞典乔根·W·威布尔.pdf

演化博弈论-瑞典乔根·W·威布尔.pdf

上传者: 铁臂阿拉丁 2011-06-05 评分 0 0 0 0 0 0 暂无简介 简介 举报

简介:本文档为《演化博弈论-瑞典乔根·W·威布尔pdf》,可适用于经济金融领域,主题内容包含EvolutionaryGameTheoryJörgenWWeibullTheMITPressCambridge,MassachusettsLond符等。

EvolutionaryGameTheoryJörgenWWeibullTheMITPressCambridge,MassachusettsLondon,EnglandSecondprinting,MassachusettsInstituteofTechnologyAllrightsreservedNopartofthispublicationmaybereproducedinanyformbyanyelectronicormechanicalmeans(includingphotocopying,recording,orinformationstorageandretrieval)withoutpermissioninwritingfromthepublisherThisbookwassetinTimesRomanbyWindfallSoftwareusingZzTEXandwasprintedandboundintheUnitedStatesofAmericaLibraryofCongressCataloginginPublicationDataWeibull,JörgenW,EvolutionarygametheoryJörgenWWeibullpcmIncludesbibliographicalreferencesandindexISBN(alkpaper)GametheoryEvolutionMathematicalmodelsITitleQAWdcCIPContentsForewordbyKenBinmoreIntroductionAcknowledgmentsMathematicalNotationElementsofNoncooperativeGameTheoryStrategiesandPayoffFunctionsDominanceRelationsandBestRepliesNashEquilibriumRefinementsofNashEquilibriumSymmetricTwoPlayerGamesEvolutionaryStabilityCriteriaEvolutionarilyStableStrategiesCharacterizationsofESSWeakerEvolutionaryStabilityCriteriaSetwiseEvolutionaryStabilityCriteriaSocialEfficiencyinDoublySymmetricGamesPreplayCommunicationRoleConditionedBehaviorsTheReplicatorDynamicsPreliminariesDominatedStrategiesNashEquilibriumStrategiesPerfectEquilibriumStrategiesEvolutionarilyandNeutrallyStableStrategiesandSetsDoublySymmetricGamesPureStrategySubsetsClosedunderBetterRepliesAppendixOtherSelectionDynamicsDiscreteTimeVersionsoftheReplicatorDynamicsTheReplicatorDynamicsinCheapTalkGamesGeneralSelectionDynamicsReplicationbyImitationMultipopulationModelsEvolutionaryStabilityCriteriaTheStandardandAdjustednPopulationReplicatorDynamicsReplicationbyImitationReplicationbyContaminationClassesofSelectionDynamicsImplicationsofEvolutionaryDynamicsforNoncooperativeSolutionConceptsRobustCriteriaforEvolutionaryDynamicStabilityAppendixElementsoftheTheoryofOrdinaryDifferentialEquationsDifferentialEquationsandVectorFieldsTheInducedSolutionMappingInvarianceandStationarityStabilityConceptsLyapunov'sDirectMethodLiouville'sFormulaBibliographyIndexForewordKenBinmoreWhenvonNeumannandMorgenstern'sTheoryofGamesandEconomicBehaviorappearedin,itwasgreetedwithgreatenthusiasmItwasthoughtthatacompletetheoryofstrategicbehaviorhadsprungintoexistencefromnowhere,asAthenaburstfullyarmedfromtheforeheadofZeusHowever,itsoonbecameapparentthatvonNeumannandMorgensternhadprovidedonlythebeginningsofatheory,andthoseseekingquickapplicationsbecamedisillusionedGametheorythenspentalongperiodinthedoldrumsThemathematicsofthetheoryoftwoperson,zerosumgamescontinuedtobestudiedMucheffortwasalsodevotedtodevelopingcooperativegametheoryButtheproblemsofnoncooperativegametheoryingeneralwereleftlargelyuntouchedVonNeumannandMorgensternbeingnomore,theNobelPrizeforEconomicswasrecentlyawardedtothreegametheorists,JohnNash,JohnHarsanyi,andReinhardSeltenNash'sworkwaspublishedintheearlys,butitwasnotuntiltheearlysthatitwasfullyrealizedwhatapowerfultoolNashhadprovidedinformulatingtheequilibriumconceptthatbearshisnameGametheorythenenjoyedarenaissanceaseconomistsappliedtheideatoawiderangeofproblemsHowever,aflyintheointmentwasawaitingdiscoveryGamestypicallyhavemanyNashequilibriaIntwoperson,zerosumgames,thiscreatesnoproblembecauseallequilibriaaretheninterchangeableandpayoffequivalentButtheequilibriumselectionproblemformoregeneralgameshasnosucheasysolutionAtfirstitwasthoughtthattheproblemcouldbetackledbyrefiningtheNashequilibriumconceptDespiteNash'sremarksinhisthesisaboutapossibleevolutionaryinterpretationoftheideaofaNashequilibrium,attentionatthattimewasfocusedalmostentirelyonitsinterpretationastheonlyviableoutcomeofcarefulreasoningbyideallyrationalplayersVariousbellsandwhistleswerethereforeappendedtothedefinitionofrationalityTheseallowedsomeNashequilibriatobediscardedasinadequatelyrationalaccordingtowhatevernewdefinitionofrationalitywasbeingproposedHowever,differentgametheoristsproposedsomanydifferentrationalitydefinitionsthattheavailablesetofrefinementsofNashequilibriumbecameembarrassinglylargeEventually,almostanyNashequilibriumcouldbejustifiedintermsofsomeoneorother'srefinementAsaconsequenceanewperiodofdisillusionmentwithgametheoryseemedinevitablebythelatesFortunatelythessawanewdevelopmentMaynardSmith'sbookEvolutionandtheTheoryofGamesdirectedgametheorists'attentionawayfromtheirincreasinglyelaboratedefinitionsofrationalityAfterall,insectscanhardlybesaidtothinkatall,andsorationalitycannotbesocrucialifgametheorysomehowmanagestopredicttheirbehaviorunderappropriateconditionsSimultaneouslytheadventofexperimentaleconomicsbroughthomethefactthathumansubjectsarenogreatshakesatthinkingeitherWhentheyfindtheirwaytoanequilibriumofagame,theytypicallydosousingtrialanderrormethodsAstheappearanceofthisbookindicates,theshavethereforeseenaturningawayfromattemptstomodelpeopleashyperrationalplayersThenewapproachtotheequilibriumselectionproblememphasizesthealmosttautologicalassertionthattheequilibriumselectedwillbeafunctionoftheequilibriatingprocessbymeansofwhichitisachievedTheprocessmaybeslow,asinbiologicalevolutionItmaybefast,asinsocialevolution,whenthemechanismforthetransmissionofsuperiorstrategiesfromoneheadtoanotherisimitationItmaybealmostinstantaneous,aswhenthepriceadjuststoequatesupplyanddemandintheChicagowheatmarketHowever,wehavelearnedthatallthesedifferentprocesseshavefeaturesincommonthatmakeitworthwhileconsideringevolutionaryprocessesintheabstractSuchstudiesteachussomepainfullessonsWelearnthatthereisnearlyalwaysevolutionarypressureagainstthevarioustypesofbehaviorlabeledas"irrational"intherefinements'literature,butthesepressurescanvaryenormouslyintheirrelativestrengthsIfthepressureagainstonetypeofirrationalityisweak,thepressuresagainstothertypesofirrationalitymayrushthesystemtoanequilibriumbeforethepressureagainstthefirsttypeofirrationalityhasachancetohavemucheffectForexample,weaklydominatedstrategiesneednotbeeliminatedEvenstronglydominatedstrategiescansurviveincertainspecialcasesWealsolearnthathistoricalandinstitutionalfactorscannotbeignoredThisisnotahardlessonforbiologists,forwhomtherealitiesofgeneticinheritanceandtheaccidentsofgeographyarebrutefactsthatcannotbeoverlookedButeconomistsremainresistanttotheideathatthesamegamemightreceiveadifferentanalysisiftheplayershaveadifferenthistoryofexperience,orliveindifferentsocieties,oroperateindifferentindustriesOnesometimesevenreadsthattheoriesthatignoresuchconsiderationsare"superior"tothosethatdobecausetheyareabletogeneratepredictionswithlessdata!However,ifthereisonefactthatworkonevolutionarygameshasestablishedbeyonddoubt,itisthatsomedetailsoftheequilibriatingprocesscanhaveamajorimpactontheequilibriumselectedOneofthemajortasksawaitingusistoidentifysuchsignificantdetailssothatappliedworkersknowwhattolookforintheenvironmentswithinWhichthegamestheycareaboutareplayedHowever,suchaprogramisforthefutureJörgenWeibull'sbookisacompendiumofprogresssofarintheareainwhichbiologyandeconomicsoverlapMuchofthematerialishisownworkandthatofhiscollaboratorsItisdistinguishedbytheclarityoftheexpositionandtheeleganceofthemathematicsHedoesnotpretendtocoverthewholefieldOnemustlookelsewhereforthenittygrittyofpopulationgeneticsorthepropertiesofevolutionaryprocesseswithastrongstochasticcomponentButwithinhischosenarea,hiscoverageissatisfyinglycomprehensiveEvolutionarygametheoryisheretostay,andIsuspectthisbookwillbeastapleofitsliteratureformanyyearstocomeItsauthoristobecongratulatedonhavingdonesuchafinejobIntroductionThestandardinterpretationofnoncooperativegametheoryisthattheanalyzedgameisplayedexactlyoncebyfullyrationalplayerswhoknowallthedetailsofthegame,includingeachother'spreferencesoveroutcomesEvolutionarygametheory,instead,imaginesthatthegameisplayedoverandoveragainbybiologicallyorsociallyconditionedplayerswhoarerandomlydrawnfromlargepopulationsMorespecifically,eachplayeris"preprogrammed"tosomebehaviorformallyastrategyinthegameandoneassumesthatsomeevolutionaryselectionprocessoperatesovertimeonthepopulationdistributionofbehaviorsWhat,ifany,aretheconnectionsbetweenthelongrunaggregatebehaviorinsuchanevolutionaryprocessandsolutionconceptsinnoncooperativegametheoryMorespecifically:AredominatedstrategieswipedoutinthelongrunWillaggregatebehaviortendtowardaHashequilibriumofthegameAresomeHashequilibriamorelikelytoemergeinthisfashionthanothersWhatisthenatureoflongrunaggregatebehaviorifitdoesnotsettledownonsomeequilibriumThesearethekindsofquestionsaddressedinthisbookSimilarquestionshave,ofcourse,beenraisedinthedomainsofeconomicsandbiologyMarketcompetitionisusuallythoughttoweedoutfirmsthatarenotprofitmaximizersandtobringabouttheequilibriumoutcomespredictedbyeconomictheoryThisisthebasisforthesocalled"asif"defenseofeconomictheory,whichclaimsthatitisnotimportantthatmanagersthinkthewaymicroeconomictheorysaystheydowhatcountsiswhethertheybehaveasiftheydid(Friedman)LikewisenaturalselectionisusuallythoughttoresultinanimalbehaviorthatiswelladaptedtotheenvironmentInthesimplestcasesthisenvironmentisexogenouslyfixed,whileinothercasestheenvironmentofanindividualisitselfcomposedofotherindividualswhoaresubjecttothesameforcesofnaturalselection(thisisalsotrueformarketselection)WhatisoptimalforanindividualorfirminsuchaninteractivesettingisendogenousinthesenseofdependingonthedistributionofbehaviorsinthepopulationwithwhichtheindividualorfirminteractsEvolutionarygametheoryisdesignedtoenableanalysisofevolutionaryselectioninpreciselysuchinteractiveenvironmentsInhisunpublishedPhDdissertation(Nasha)JohnNashsuggestsapopulationstatisticalinterpretationofhisequilibriumconceptinwhichheimaginesthatplayersarerandomlydrawnfromlargepopulations,oneforeachplayerpositioninthegameTheseplayerswerenotassumedto"havefullknowledgeofthetotalstructureofthegame,ortheabilityandinclinationtogothroughanycomplexreasoningprocess"(opcit,p)seeLeonard(),Weibull(),andBjörnerstedttandWeibull().PlanoftheBookEvolutionarygametheoryprovidesatoolkitofwideapplicabilityItspotentialdomainrangesfromevolutionarybiologytothesocialsciencesingeneralandeconomicsinparticularThisbookdoesnottrytocoverallthedevelopmentsinthefield,notevenallthemostimportantones:Instead,itstrivestogiveaserfcontainedtreatmentofaselectedsetofcoreelements,focusedonconceptualandtechnicalconnectionsbetweenevolutionaryandnoncooperativegametheoryChaptergivesaconciseintroductiontononcooperativegametheoryNotation,definitions,andresultsofrelevancetothesubsequentdiscussionareintroduced,alongwithanumberofexamplesthatareusedthroughoutthebookChaptersthroughdealwithsinglepopulationevolutionarymodelsofpairwiseinteractionsrepresentedasasymmetrictwoplayergameChapterconsidersafewstaticmodels,centeredaroundthekeyconceptofanevolutionarilystablestragegyChapterfocusesonaparticulardynamicmodelofevolutionaryselectionincontinuoustime,thesocalledreplicatordynamicsChapterdevelopsafewvariationsonthethemeinchapter,includingdynamicmodelsofsocialevolutionChapterdevelopsbothstaticanddynamicmodelsofmultipopulationinteractionsrepresentedasannplayergameThedynamicmodelsdevelopedinchaptersthroughusesystemsofordinarydifferentialequationstodescribetheevolutionofaggregatebehaviorovertimeChapterprovidesaconciseintroductiontothetheoryofOrdinarydifferentialequationsAllchapterscontainexamplesthatillustratetheworkingsofthediscussedmethodsThepresentationofthematerialinmanyinstancesproceedsfromthespecialtothegeneralSeveralthemesfirstappearinsimpleexamples,thereafterinspecificbutbroadercontexts,andfinallyinmoregeneralandabstractsettingsItmayannoysomemathematicallywellversedreaderstofirstseeaclaimprovedinaspecialcaseandlaterinamoregeneralcaseHowever,itishopedthatthisprocedurewillfacilitateanoperational''handson''andnotonlyabstract,understandingofthemethodsusedThereaderisassumedtohavesomefamiliaritywithstandardnotionsinmathematics(basicsettheory,topology,andcalculus)ataboutthelevelachievedafterthefirstyearofgraduatestudiesineconomicsAlthoughchapterprovidesthetoolsneededfromnoncooperativegametheory,thistreatmentwillmostlikelyappearterseforareaderwhoisnotacquaintedwiththebasicideasinnoncooperativegametheoryAlsoherethereaderispresumedtohaveaknowledgeataboutthelevelachievedafterfirstyeargraduatestudiesineconomicsHowtoreadthebook,andhowtouseitinclassOneobviouswayistoreadchapter,selectedpartsofchapter,makeashortexcursionintoselectedpartsofchapter,andfinallyreadselectedpartsofchaptersthroughAshortercoursecouldfocusonpartsofchapters,,,and(eg,sections,,,,,and)Toenableaselfcontainedandyetconcisetreatment,onlydeterministicmodelsofgamesinnormalformarediscussedinthisbook,despitethefactthattherenowareafewpromisingevolutionarystochasticmodelsandevolutionarymodelsofextensiveformgamesEachofthesetwoextensionsofthescopewouldrequireadditionaltechnicalmachineryThereaderwhoisinterestedintheseandotherdevelopmentsinevolutionarygametheorynotcoveredheremayconsultthebibliographyattheendofthebookForexample,stochasticmodelsarediscussedinFosterandYoung(),Kandori,Mailath,andRob(),andYoung()ModelsofgamesinextensiveformmaybefoundinSelten(),vanDamme(),andNöldekeandSamuelson()AnumberofotherimportantcontributionscanbefoundinrecentissuesofeconomicsandbiologyjournalsAcknowledgmentsDuringthewritingofthisbookIbenefitedgreatlyfromconversationswithcolleaguesandstudentsIamparticularlygratefulforcommentsonvariousdraftsofthemanuscriptfromJonasBjörnerstedt,AnetteBjørsted,ImmanuelBomze,RossCressman,EricvanDamme,MartinDufwenberg,JosefHofbauer,OliverKirchkamp,JohanLindén,OlegMalafeyev,PerMolander,PeterNorman,JörgOesschler,KlausRitzberger,LarrySamuelson,KarlSchlag,BjörnSegendorff,KarlSigmund,BirgitteSloth,TonyESmith,JoakimSonnegård,JohanStennek,DavidStrömberg,andKarlWärnerydIwouldalsoliketothankAssarLindbeck,JanosKornai,andLarsEOSvenssonfortheirmoralandintellectualsupportduringmytransitionfromappliedmathematicstoeconomics,andforgenerouslysharingtheirprofoundinsightsEspeciallystimulatingforthepresentprojectwasacourseItookmanyyearsbackindynamicmodelingofecologicalsystems,taughtbyIngemarNåsell,aswellasconversationsIhadwithJanosKornai,alsoalongtimeago,abouttheevolutionoffirmbehaviorinmarketswithvaryingdegreesofstateinterventionTerryVaughnofTheMITPresswasagreatsupportduringthepreparationofthemanuscriptSpecialthanksgotoDanaAndrusofTheMITPressforherfineediting,andinStockholm,Sweden,toJonasBjörnerstedtforallcomputerillustrationsinthebook,toMollyÅkerlundforherexcellenthelpwithpageproofs,andtoKarlWärnerydforhiscontributiontothecoverillustrationIamgratefultotheIndustrialInstituteforEconomicandSocialResearch(IUI),Stockholm,foritssponsoringofpartoftheresearchbehindthistextMathematicalNotationLowercaselettersaremostlyusedforrealnumbers,vectorsofrealnumbers,andforfunctions,whilecapitallettersusuallysignifymatricesandsetsEuclideanspacesaretypicallydenotedRn,wherenisapositiveintegerthedimensionofthespaceThesubsetofvectorsxinRnthathaveallcoordinatesxinonnegativeisdenoted,andthesubsetofvectorsthathaveallcoordinatespositiveiswrittenTheinner(orscalar)productoftwovectorsxandyinRnisarealnumber(scalar)writtenTheeuclideannorm(orlength)ofavectorisdenoted,andthedistancebetweentwopoints(vectors)xandyinRniswrittend(x,y)=||xy||ThetransposeofannnmatrixAisdenotedATInthisbookdenotesweaksetinclusionHencesignifiesthatallelementsofXarealsoelementsofYThecomplementofasetiswritten~XByaneighborhoodofapoint(vector)xinRnismeantanopensetcontainingxTheinteriorofasetiswrittenint(X)thisisthesubsetofpointsxinXsuchthatXalsocontainssomeneighborhoodofxTheboundaryofasetiswrittenbd(X)thisisthesetofpointssuchthateveryneighborhoodofycontainssomepointfromXandsomepointfrom~XTheclosureofasetisdenotedthisistheunionofXanditsboundaryAfunctionffromasetXtoasetYisviewedasarulethattoeachelementxofXassignspreciselyoneelement,f(x),ofYLikewiseacorrespondenceϕfromasetXtoasetYisarulethattoeachelementxofXassignspreciselyonenonemptysubset,ϕ(x),ofYElementsofNoncooperativeGameTheoryThischapterprovidesanintroductiontotheconceptsandresultsinnoncooperativegametheorythatwillbeusedinthesubsequentevolutionaryanalysisThematerialinthischapterisorganizedasfollows:InsectionthestructureoffinitenormalformgamesisoutlinedInparticular,thegeometryofstrategyspacesandmultilinearityofpayofffunctionsisemphasizedSectiondiscussesdominanceorderingsofa

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