基于演化博弈理论的有限理性交通选择行为模型

36820108JOURNALOFBEIJINGUNIVERSITYOFTECHNOLOGYVol．36No．8Aug．2010100022．2n．ESSU491.1A0254－0037201008－1077－072008-11-24．1959—．．1-4．fullrationality．boundedrationality．．．1973MaynardPrice5-6evolutionarystablestrategyESS．7．CheungFriedman8．hawkdovebuyersellermeanabsolutedeviation．．9．．10．Nash．．2．2010．．23．121.1．．．．O、D2ab1Ci=Ai+Bivii=ab1AiiBiiviiva+vbQ．12Fig．1ThetrafficnetworkoftwoindependentroutesbetweenOandDO、D2Q1Q2．．2abt2a、ba、bPatPbtaQ1Pat+Q2PatbQ1Pbt+Q2Pbta、bui=－Ai+BiQ1Pit+Q2Pit=－Ai+BiQPiti=ab222ab．2．．taQattaPat=Qat/Qa、buat、ubtutaPatPatdPatdt=dQatdtQ－QatdQdtQ2=dQat/dtQatQ－dQdtQ·QatQ=dQatdtQat－dQdtQPat3dQat/dtQat=uatdQ/dtQ=ut387018dPatdt=uat－utPat44aPatauat－uta．uatuta．dPat/dt=0asteadystate．2ut=Patuat+Pbtubt4dPatdt=uat－Patuat+PbtubtPat=Patuat－Patuat－1－Patubt=Pat1－Patuat－ubt55=0Pat=0Pat=1uat=ubt．uat=ubt1uat=ubtAa+BaQPat=Ab+BbQ1－PatPat=Ab－Aa+BbQ/Ba+BbQ．Pat=0Pat=1Pat=Ab－Aa+BbQ/Ba+BbQ2ab．1.25-7．1Y≠Xεy∈01uXεY+1－εX＞uYεY+1－εXε∈0εyX．1XESSuYX≤uXXYuYX=uXXuYY＜uXYY≠X1．PatP*atESSP*atPat＜P*atdPat/dt＞0PatP*atPat＞P*atdPat/dt＜0PatP*atd2Pat/dt2P*atdPat/dtP*at0．50＜Pat＜Ab－Aa+BbQ/Ba+BbQdPat/dt＞0Ab－Aa+BbQ/Ba+BbQ＜Pat＜1dPat/dt＜0．dPat/dt2．Pat3Ab－Aa+BbQ/Ba+BbQdPat/dt0．P*at=Ab－Aa+BbQ/Ba+BbQuat=ubtESSa．Pat=0Pat=12PatP*at=Ab－Aa+BbQ/Ba+BbQ．Pat=0Pat=1．9701201022dPat/dtFig．2ThecurveofdPat/dtfunctioninbinaryroutechoice1.3ESSWardrop．1Aa+Bav*a=Ab+Bbv*bv*a+v*b{=Q6v*a=Ab－Aa+BbQBa+Bbv*b=Aa－Ab+BaQBa+Bb7v*a=P*atQv*b=1－P*atQ=P*btQab．4．LogitPit=eλuit∑j∈Neλuitij∈N8Pittiuittiλ．22．8Pat－Pbt=eλuateλuat+eλubt－eλubteλuat+eλubt=e－λubt－uat－eλubt－uat1+eλubt－uat1+e－λubt－uat=1－e2λubt－uateλubt－uat1+eλubt－uat1+e－λubt－uat9Pat=Pbte2λubt－uat=1uat=ubtESS．2．22.133Fig．3ThetrafficnetworkofthreeindependentroutesbetweenOandD3．O、D3abc3．1Ci=Ai+Bivii=abcO、D2Q1Q2t2a、b、cPat、PbtPct．2a、b、cuit=－Ai+BiQPiti=abc10ut=Patuat+Pbtubt+Pctuct11080184dPatdt=Patuat－ut=Patuat－Patuat－Pbtubt－Pctuct=Pat1－Patuat－uct－Pbtubt－uct12dPbtdt=Pbt1－Pbtubt－uct－Patuat－uct13dPctdt=PctPatuct－uat－Pbtubt－uct1412、13、140Pat1－Patuat－uct－Pbtubt－uct=0Pbt1－Pbtubt－uct－Patuat－uct=0PctPatuct－uat－Pbtubt－uct{=015157Pat=1Pbt=1Pct=1Pat=0ubt=uctPbt=0uat=uctPct=0uat=ubtuat=ubt=uct．a、b、c、bc、ac、ababc．2.211YuYX≤uXX．XESSXX．12XYuYX=uXXuYY＜uXY．1AuYY=YTAYuXY=XTAY．uXY－uYY=XTAY－YTAY=XT－YTAY=XT－YTAY－X+X=XT－YTAY－X+XT－YTAX=－XT－YTAX－Y+XTAX－YTAX=－XT－YTAX－Y+uXX－uYX16uYX=uXXXT－YTAX－Y＜0uXY＞uYY．Pat=111abca．Pbt=1Pct=1Pat=0ubt=uctPbt=0uat=uctPct=0uat=ubt511．6．uat=ubt=uct1P'at、P'btP'ctP'at=BbAc+BcAb－Bb+BcAa+BbBcQBaBb+BbBc+BaBcQP'bt=BcAa+BaAc－Ba+BcAb+BaBcQBaBb+BbBc+BaBcQP'ct=BbAa+BaAb－Ba+BbAc+BaBbQBaBb+BbBc+BaBcQ17P'at、P'btP'cta、bcP'at、P'btP'ctuat=ubt=uct11．101A12a、b、c1A=－Aa+BaQPat－Aa+BaQPat－Aa+BaQPat－Ab+BbQPbt－Ab+BbQPbt－Ab+BbQPbt－Ac+BcQPct－Ac+BcQPct－Ac+BcQPct18180120102218．X=P'atP'btP'ctYX－Y=αβγαβγX－Ya、b、cXT－YTAX－Y=－αAa+BaQα+βAb+BbQβ+γAc+BcQγα+β+γα+β+γ=1αβγ0XT－YTAX－Y＜0uat=ubt=uct12XESS．43Pat、PbtPctFig．4TheevolutionarylocusofPat、PbtandPct23Pat、Pbt、Pct14．A、B、Ca、b、cBC、ACABPat、PbtPct．42ubt=uct、uat=ubtuat=uct32a、b、cuat=ubt=uct3ESS．19uat=ubt=uct．P'at、P'bt、P'ct、．n．n1n2n－12n－11C1n2C2n…n－1Cn－1nnCnnC1n+C2n+…+Cn－1n+Cnn=2n－C0n=2n－1n．12uat=ubt=…=unt．2．32、3n．280181．M．2001．2．M．2004．3．M．2．2006．4．M．2004．5MAYNARDSMITHJPRICEGR．ThelogicofanimalconflictJ．Nature197324615-18．6MAYNARDSMITHJ．ThetheoryofgamesandtheevolutionofanimalconflictJ．JournalofTheoreticalBiology197447209-21．7·W·．M．200640-56．8CHEUNGYWFRIEDMAND．AcomparisonoflearningandreplicatordynamicsusingexperimentdataJ．JournalofEconomicBehaviorandOrganization199835263-280．9．J．20033223-27．LIZhen-long．AstudyofroutechoicebehaviorofdriversbasedontheevolutionarygameundertheconditionoftrafficflowguidanceJ．JournalofTransportationSystemEngineeringandInformationTechnology20033223-27．inChinese10．J．2006193106-110．WUBingLILin-bo．EvolutionarydynamicanalysisoftrafficcongestionJ．ChinaJournalofHighwayandTransport2006193106-110．inChineseADrivers'ChoiceBehaviorModelBasedonEvolutionaryGameTheoryGUANHong-zhiPULiangTransportationResearchCenterBeijingUniversityofTechnologyBeijing100124ChinaAbstractItisessentialtoknowdrivers'learningprocessesanddecisionrulesinactualconditionssoastounderstandtheirchoicebehaviorandtrafficphenomenon．Thispaperassumesthatthedriversareinfluencedbyincompletetrafficinformationinadditiontotheirboundedrationality．Undersuchassumptionthispaperproceedstoconstructamodelofthedrivers'choicebehavioronthebasisoftheevolutionarygametheory．Withmathematicalinductionasatoolthispaperprovesthesuitabilityofevolutionaryapproachfortheanalysisofdrivers'routechoicebehavior．It'sfoundthatfortwoanduptonroutestheevolutionarystablestatederivedfromtheabove-mentionedapproachisexactlyequivalenttoequilibriumderivedfromtrafficassignmenttheoryandstochasticutilitytheorem．KeywordsroutechoicebehaviorevolutionarygamestablestateevolutionarystablestrategyESS3801