演化博弈论(清华大学)

1EvolutionaryGames13Chapter13Slide2EvolutionaryGamesWehavesofarstudiedgameswithmanydifferentfeatures:„Simultaneousandsequentialmoves„Zero-sumandnon-zero-sumpayoffs„Strategicmovestomanipulaterulesofgamestocome„One-shotandrepeatedplay„Gamesofcollectiveactioninwhichalargenumberofpeopleplaysimultaneously2Slide3EvolutionaryGames……Alltheplayersinallthesegamesarerational:eachplayer……„……hasaninternallyconsistentvaluesystem„……cancalculatetheconsequencesofherstrategicchoices„……makeschoicethatbestfavorsherinterestsSlide4EvolutionaryGames……Onepossiblealternativetorationalitycanbefoundinthebiologicaltheoryofevolutionandevolutionarydynamics,where……„……goodstrategieswillberewardedwithhigherpayoffs„……playerscanobserveorimitatesuccessandexperimentwithnewstrategies„……goodstrategieswillbeusedmoreoftenandbadstrategieslessoften,asplayersgainexperienceplayingthegame.3Slide5Outline*Theframework**Prisoners’dilemmaChickenTheassurancegame*InteractionsacrossspeciesThehawk-dovegame*ThreePhenotypesinthePopulationSomeGeneralTheoryPlayingthefieldSlide6TheFrameworkTheprocessofevolutioninbiologyoffersaparalleltothetheoryofgamesusedbysocialscientists.Thistheoryrestsonthreefundamentals:„Heterogeneity„Fitness„Selection4Slide7TheFrameworkAsignificantpartofanimalbehaviorisgenericallydetermined;acomplexofoneormoregenes(genotype)governsaparticularpatternofbehavior,calledabehaviorphenotype.Examples„Aerodynamiccharacteristicsofabird’swings„Aggressiveorcooperativebehavior„LocationsofnestingsitesSlide8TheFrameworkNaturaldiversityofthegenepoolensuresaheterogeneityofphenotypesinthepopulation.Somebehaviorsarebettersuitedthanotherstotheprevailingconditions,andthesuccessofaphenotypeisgivenaquantitativemeasurecalleditsfitness.5Slide9TheFrameworkThefitterphenotypesthenbecomerelativelymorenumerousinthenextgenerationthanthelessfitphenotypes.Thisprocessofselectionisthedynamicthatchangesthemixofgenotypesandphenotypesandperhapsleadseventuallytoastablestate.Slide10TheFrameworkFromtimetotime,chanceproducesnewgeneticmutations.Manyofthesemutationsproducebehavior(thatis,phenotypes)thatareillsuitedtotheenvironment,andtheydieout.Butoccasionallyamutationleadstoanewphenotypethatisfitter.Thensuchamutantgenecansuccessfullyinvadeapopulation–thatis,spreadtobecomeasignificantproportionofthepopulation.6Slide11TheFrameworkBiologistscallaconfigurationofapopulationanditscurrentphenotypesevolutionarystableifthepopulationcannotbeinvadedsuccessfullybyanymutant.Thisisastatictest;butoftenamoredynamiccriterionisapplied:aconfigurationisevolutionarystableifitisthelimitingoutcomeofthedynamicofselection,startingfromanyarbitrarymixtureofphenotypesinthepopulation.Slide12TheFrameworkThefitnessofaphenotypedependsontherelationshipoftheindividualorganismtoitsenvironment.Italsodependsonthewholecomplexoftheproportionsofdifferentphenotypesthatexistintheenvironment.Forourpurpose,thisinteractionbetweenphenotypeswithinaspeciesisthemostinterestingpartofthestory.7Slide13TheFrameworkThebiologicalprocessofevolutionfindsareadyparallelingametheory.„Phenotypevs.Strategy„Fitnessvs.PayoffsSlide14TheFrameworkBecausethepopulationisamixofphenotypes,differentpairsselectedfromitwillbringtotheirinteractionsdifferentcombinationsofstrategies.Theactualquantitativemeasureofthefitnessofaphenotypeistheaveragepayoffthatitgetsinallitsinteractionswithothersinthepopulation.8Slide15TheFrameworkThetheoryofevolutionarygamesseemsaready-madeframeworkforanewapproachtogametheory,relaxingtheassumptionofrationalbehavior.Theideaofinheritanceofstrategiescanbeinterpretedmorebroadlyinapplicationsofthetheoryotherthanbiology.Slide16TheFramework“”Thereasonsthatthefitterstrategiesproliferateandthelessfitonesdieoutinsocioeconomicgamesdiffersfromthestrictgeneticmechanismofbiology:„ObservationsandImitations„Purposivethinkingandrevisionofpreviousrulesofthumb„Consciousexperimentation9Slide17TheFrameworkWhyaplayerplayssuchastrategy?„Rationalchoices„Genetics„Socialization,culturalbackground,educations„AruleofthumbbasedonpastexperienceWillsocietyendupwithasituationinwhichallpoliticiansareconcernedwithreelection,andallfirmswithprofit?Slide18TheFrameworkEvolutionarystableconfigurationsofbiologicalgamescanbeoftwokinds.Monomorphism:Asinglephenotypeprovesfitterthananyothersandthepopulationcomestoconsistofitalone.Inthiscase,theuniqueprevailingstrategyiscalledanevolutionarystablestrategy(ESS).Polymorphism:Twoormorephenotypesareequallyfit(andfitterthansomeothersnotplayed);sotheymaybeabletocoexistincertainproportions.10Slide19TheFrameworkThewholeset-upwhichconstitutesanevolutionarygameis:„ThePopulation„Itsconceivablecollectionofphenotypes„Thepayoffsmatrixintheinteractionsofthephenotypes„TherulefortheevolutionofpopulationproportionsofthephenotypesinrelationtotheirfitnessAnevolutionarystableconfigurationofthepopulationcanbecalledanequilibriumoftheevolutionarygame.Slide20Prisoners’DilemmaSupposeapopulationismadeupoftwophenotypes:cooperators,defectors.Eachindividual(eitheracooperatororadefectors)inthepopulationischosenatrandomtocompeteagainstanotherrandomrival.11S