[数学]演化博弈理论进化博弈论ppt课件.ppt

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1、EvolutionaryGameTheoryAmitBahlCIS620OutlineEGTversusCGTEvolutionaryStableStrategiesConceptsandExamplesReplicatorDynamicsConceptsandExamplesOverviewof2papersSelectionmethods,finitepopulationsEGTv.ConventionalGameTheoryModelsusedtostudyinteractivedecisionmaking.Equil

2、ibriumisstillatheartofthemodel.Keydifferenceisinthenotionofrationalityofagents.AgentRationalityInGT,oneassumesthatagentsareperfectlyrational.InEGT,trialanderrorprocessgivesstrategiesthatcanbeselectedforbysomeforce(evolution-biological,cultural,etc…).Thislackofratio

3、nalityisthepointofdeparturebetweenEGTandGT.EvolutionWheninbiologicalsense,naturalselectionismodeofevolution.StrategiesthatincreaseDarwinianfitnessarepreferable.Frequencydependentselection.EvolutionaryGameTheory(EGT)HasoriginsinworkofR.A.Fisher[TheGeneticTheoryofNat

4、uralSelection(1930)].Fisherstudiedwhysexratioisapproximatelyequalinmanyspecies.MaynardSmithandPriceintroduceconceptofanESS[TheLogicofAnimalConflict(1973)].Taylor,Zeeman,Jonker(1978-1979)providecontinuousdynamicsforEGT(replicatordynamics).ESSApproachESS=NashEquilibr

5、ium+StabilityConditionNotionofstabilityappliesonlytoisolatedburstsofmutations.SelectionwilltendtoleadtoanESS,onceatanESSselectionkeepsusthere.ESS-DefinitionConsidera2playersymmetricgamewithESSgivenbyIwithpayoffmatrixE.Letpbeasmallpercentageofpopulationplayingmutant

6、strategyJI.FitnessgivenbyW(I)=W0+(1-p)E(I,I)+pE(I,J)W(J)=W0+(1-p)E(J,I)+pE(J,J)RequirethatW(I)>W(J)ESS-DefinitionStandardDefinitionforESS(MaynardSmith).IisanESSifforallJI,E(I,I)E(J,I)andE(I,I)=E(J,I)E(I,J)>E(J,J)whereEisthepayofffunction.ESS-DefinitionAssumptio

7、ns:1)Pairwise,symmetriccontests2)Asexualinheritance3)Infinitepopulation4)CompletemixingESS-ExistenceLetGbeatwo-payersymmetricgamewith2purestrategiessuchthatE(s1,s1)E(s2,s1)ANDE(s1,s2)E(s2,s2)thenGhasanESS.ESSExistenceIfa>c,thens1isESS.Ifd>b,thens2isESS.Otherwise,

8、ESSgivenbyplayings1withprobabilityequalto(b-d)/[(b-d)+(a-c)].ESS-Example1ConsidertheHawk-DovegamewithpayoffmatrixNashequilibriumgivenby(7/12,5/12