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首页 Advances in Dynamic Game Theory Numerical Metho…

Advances in Dynamic Game Theory Numerical Methods, Algorithms, and Applications.pdf

Advances in Dynamic Game Theory…

上传者: zhao_hailei 2010-12-07 评分 0 0 0 0 0 0 暂无简介 简介 举报

简介:本文档为《Advances in Dynamic Game Theory Numerical Methods, Algorithms, and Applicationspdf》,可适用于高等教育领域,主题内容包含AnnalsoftheInternationalSocietyofDynamicGamesVolumeSeriesEditorTamerBasarE符等。

AnnalsoftheInternationalSocietyofDynamicGamesVolumeSeriesEditorTamerBasarEditorialBoardTamerBasar,UniversityofIllinois,UrbanaPierreBernhard,ISCNRSandUniversityofNiceSophiaAntipolisMaurizioFalcone,UniversityofRome“LaSapienza”JerzyFilar,UniversityofSouthAustralia,AdelaideAlainHaurie,ORDECSYS,CheˆneBougeries,SwitzerlandArikAMelikyan,RussianAcademyofSciences,MoscowAndrzejSNowak,WroclawUniversityofTechnologyandUniversityofZielonaGoraLeonAPetrosjan,StPetersburgStateUniversityAlainRapaport,INRIA,MontpelierJosefShinar,Technion,HaifaAnnalsoftheInternationalSocietyofDynamicGamesAdvancesinDynamicGameTheoryNumericalMethods,Algorithms,andApplicationstoEcologyandEconomicsSteffenJørgensenMarcQuincampoixThomasLVincentEditorsBirkhauserBoston•Basel•BerlinSteffenJørgensenUniversityofSouthernDenmarkDepartmentofEconomicsandBusinessCampusvejDKOdenseDenmarkMarcQuincampoixUniversitedeBretagneOccidentaleLaboratoiredeMathematiquesAvenueLeGeorgeuBrestFranceThomasLVincentUniversityofArizonaDepartmentofAerospaceandMechanicalEngineeringTucson,AZUSAMathematicsSubjectClassification:Axx,A,A,A,A,A,A,A,A,A,A,A,ALibraryofCongressControlNumber:ISBN:eISBN:ISBN:eISBN:PrintedonacidfreepapercBirkhauserBostonAllrightsreservedThisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(BirkhauserBoston,coSpringerScienceBusinessMediaLLC,SpringStreet,NewYork,NY,,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysisUseinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbiddenTheuseinthispublicationoftradenames,trademarks,servicemarksandsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrightswwwbirkhausercom(LapSB)ContentsPrefaceixContributorsxviiPartIDynamicGameTheoryDifferentialGamesThroughViabilityTheory:OldandRecentResultsPierreCardaliaguet,MarcQuincampoixandPatrickSaintPierreDifferentialGameswithImpulseControlArkadiiAChikrii,IvanIMatychynandKirillAChikriiOntheInstabilityoftheFeedbackEquilibriumPayoffinaNonzeroSumDifferentialGameontheLinePierreCardaliaguetConstructingRobustControlinDifferentialGames:ApplicationtoAircraftControlDuringLandingSAGanebny,SSKumkov,VSPatskoandSGPyatkoGames,Incompetence,andTrainingJustinBeckandJerzyAFilar,StackelbergWellPosednessandHierarchicalPotentialGamesMarcoMargioccoandLuciaPusilloPartIIStochasticDifferentialGamesErgodicProblemsinDifferentialGamesOlivierAlvarezandMartinoBardiviContentsSubgameConsistentSolutionsforaClassofCooperativeStochasticDifferentialGameswithNontransferablePayoffsDavidWKYeung,LeonPetrosyanandPatriciaMelodyYeungPartIIIPursuitEvasionGamesGeometryofPursuitEvasionGamesonTwoDimensionalManifoldsArikMelikyanSolutionofaLinearPursuitEvasionGamewithVariableStructureandUncertainDynamicsJosefShinar,ValeryYGlizerandVladimirTuretskyPursuitEvasionGameswithImpulsiveDynamicsEvaCrück,MarcQuincampoixandPatrickSaintPierreApproachingCoalitionsofEvadersontheAverageIgorShevchenkoPartIVEvolutionaryGameTheoryandApplicationsAdaptiveDynamicsBasedonEcologicalStabilityJózsefGarayAdaptiveDynamics,ResourceConversionEfficiency,andSpeciesDiversityWilliamAMitchellEvolutionarilyStableRelativeAbundanceDistributionsTaniaLSVincentandThomasLVincentForagingUnderCompetition:EvolutionarilyStablePatchLeavingStrategieswithRandomArrivalTimesScrambleCompetitionFrédéricHamelin,PierreBernhard,PhilippeNainandÉricWajnbergForagingUnderCompetition:EvolutionarilyStablePatchLeavingStrategieswithRandomArrivalTimesInterferenceCompetitionFrédéricHamelin,PierreBernhard,AJShaijuandÉricWajnbergEvolutionofCornOilSensitivityintheFlourBeetleRCRael,TLVincent,RFCostantinoandJMCushingContentsviiTheEvolutionofGutModulationandDietSpecializationasaConsumerResourceGameChristopherJWhelan,JoelSBrownandJasonMollPartVApplicationsofDynamicGamestoEconomicsTimeConsistentFairWaterSharingAgreementsRodneyBeardandStuartMcDonaldAHybridNoncooperativeGameModelforWirelessCommunicationsTansuAlpcanandTamerBasarIncentiveBasedPricingforNetworkGameswithCompleteandIncompleteInformationHongxiaShenandTamerBasarIncentiveStackelbergStrategiesforaDynamicGameonTerrorismDorisABehrens,JonathanPCaulkins,GustavFeichtingerandGernotTraglerCapitalAccumulation,Mergers,andtheRamseyGoldenRuleRobertoCelliniandLucaLambertiniEconomicGrowthandProcessSpilloverswithStepbyStepInnovationShravanLuckrazSupplierManufacturerCollaborationonNewProductDevelopmentBowonKimandFouadElOuardighiADifferentialGameofaDualDistributionChannelOlivierRubelandGeorgesZaccourDesignImitationintheFashionIndustrySteffenJørgensenandAndreaDiLiddoFormulatingandSolvingServiceNetworkPricingandResourceAllocationGamesasDifferentialVariationalInequalitiesTLFriesz,RMookherjeeandMARigdonviiiContentsPartVINumericalMethodsandAlgorithmsinDynamicGamesNumericalMethodsforStochasticDifferentialGames:TheErgodicCostCriterionHaroldJKushnerGradientTransformationTrajectoryFollowingAlgorithmsforDeterminingStationaryMinMaxSaddlePointsWalterJGranthamSingularPerturbationTrajectoryFollowingAlgorithmsforMinMaxDifferentialGamesDaleBMcDonaldandWalterJGranthamMinMaxGuidanceLawIntegrationStéphaneLeMénecAgentBasedSimulationoftheNPersonChickenGameMiklosNSzilagyiTheOptimalTrajectoryinthePartialCooperativeGameOnikMikaelyanandRafikKhachaturyanPrefaceThetheoryofdynamicgamescontinuestoevolve,andonepurposeofthisvolumeistoreportanumberofrecenttheoreticaladvancesinthefield,whicharecoveredinPartsI,IIandIVAnotheraimofthisworkistopresentsomenewapplicationsofdynamicgamesinvariousareas,includingpursuitevasiongames(PartIII),ecology(PartIV),andeconomics(PartV)Thevolumeconcludeswithanumberofcontributionsinthefieldofnumericalmethodsandalgorithmsindynamicgames(PartVI)Withasingleexception,thecontributionsofthisvolumeareoutgrowthsoftalksthatwerepresentedattheEleventhInternationalSymposiumonDynamicGamesandApplications,heldinTucson,Arizona,USA,inDecember,andorganizedbytheInternationalSocietyofDynamicGamesThesymposiumwascosponsoredbytheUniversityofArizona,CollegeofEngineeringandAerospaceandMechanicalEngineering,aswellasGERAD,Montréal,Canada,andtheISDGOrganizingSocietyThevolumecontainsthirtyfivechaptersthathavebeenpeerreviewedaccordingtothestandardsofinternationaljournalsingametheoryandapplicationsPartIdealswiththetheoryofdynamicgamesandcontainssixchaptersCardaliaguet,Quincampoix,andSaintPierreprovideasurveyofthestateoftheartoftheuseofviabilitytheoryintheformulationandanalysisofdifferentialgames,inparticularzerosumgamesAnimportantresultofviabilitytheoryisthatmanyzerosumdifferentialgamescanbeformulatedasviabilityproblemsThemainachievementsofviabilitytheoryareassessedandanumberofrecentdevelopmentsareexplained,forinstance,theformulationofviabilityproblemsforhybriddifferentialgamesThechaptercontainsasubstantiallistofreferencesChikrii,Matychyn,andChikriiareconcernedwithdifferentialgamesofpursuitandevasioninwhichoneormoreplayerscanuseimpulsecontrolsThestatedynamicsareordinarydifferentialequationsthatareaffectedbyjumpsinthestateatdiscreteinstantsoftimeThemethodof“resolvingfunctions”providesageneralframeworkfortheanalysisofsuchproblemsandessentiallyemploysthetheoryofsetvaluedmappingsCardaliaguetinvestigatesanonzerosumdifferentialgameplayedbytowplayersonalineThedynamicsareverysimpleandplayerswishtomaximizetheirxPrefacerespectiveterminalpayoffsInthezerosumcase,thesituationiswellunderstoodHowever,thesituationinthenonzerosumgameiscompletelydifferentThefeedbackequilibriumpayoffs(FEP)areextremelyunstableandsmallperturbationsoftheterminalpayoffslead,ingeneral,tolargechangesintheFEPsGanebny,Kumkov,Patsko,andPyatkosuggestamethodforconstructingrobustfeedbackcontrollersfordifferentialgamesthathavelineardynamicswithdisturbancesThemethodisbasedonresultsfromthetheoryofdifferentialgameswithgeometricconstraintsonplayers’controlsTheauthorsalsoprovideanalgorithmforconstructingarobustcontrolandpresentsimulationresultsforthepracticalcaseoflateralmotioncontrolofanaircraftduringlandingunderwinddisturbancesBeckandFilarquestionastandardassumptionofgametheorythatpayoffsinnoncooperativematrixgamesaredetermineddirectlybytheplayers’choiceofstrategiesInreallife,palyersmayforseveralreasonsbeunabletoexecutetheirchosenstrategiesSuchinabilityisreferredtoas“incompetence”Amethodforanalyzingincompetenceinmatrixgamesissuggested,assessed,anddemonstratedThemethodismotivatedbyapplicationswhereinvestmentsineffortsthatwilldecreaseincompetencecanbemadeMargioccoandPusillostudytheclassicalStackelberggameinwhichthefirstplayeristheleaderandthesecondplayeristhefollowerBywellposednessitismeantthatthesolutionexists,isunique,andtheapproachof“maximizingsequences”isvalidVariousgeneralcharacterizationsofStackelbergwellposednessareprovidedFurthermore,hierarchicalpotentialgamesareconsidered,anditisprovedthatsomepropertiesofwellposednessareequivalenttotheTikhonovwellposednessofamaximumproblemofthepotentialfunctionPartIIcontainstwochaptersdealingwiththetheoryofstochasticdifferentialgamesAlvarézandBardiproposeandstudyanotionofergodicityfordeterministic,zerosumdifferentialgamesthatextendstheoneinclassicalergodiccontroltheoryofsystemswithtwoopponentcontrollersTheconnectionstotheexistenceofaconstantanduniformlongtimelimitofthevalueoffinitehorizongamesareestablishedMoreover,aseriesofconditionsforergodicityarestatedandsomeextensionstostochasticdifferentialgamesareprovidedYeung,Petrosyan,andYeungaddresstheproblemofdesigningmechanismsthatguaranteesubgameconsistencyintheframeworkofcooperativestochasticdifferentialgameswithwhitenoiseRecentresultsoftheauthorsforthecaseoftransferablepayoffs(utility)areextendedtothehighlyintractablecasewherepayoffcannotbetransferredamongplayersPrefacexiPartIIIisdevotedtopursuitevasiongamesandcontainsfourchaptersMelikyanstudiesthegeometryofpursuitevasiongamesonDmanifoldsTheanalysisisdoneforavarietyofgamespacesBecauseoftheirsimplemotion,optimaltrajectoriesare,ingeneral,geodesiclinesofthegamespacemanifoldsInsomecasesthereisasingularsurfaceconsistingtrajectoriesthatareenvelopesoffamilyofgeodesicsNecessaryandsufficientconditionsforsuchsingularitiesarestatedTheanalysisisbaseduponviscositysolutionstotheIsaacsequations,variationalcalculus,andgeometricalmethodsShinar,Glizer,andTuretskyproposeaclassofpursuitevasiondifferentialgamesinwhichtwofinitesetsofpossibledynamicsofthepursuerandtheevader,respectively,aregiveThesesetsareknownbybothplayersTheevaderchoosesherdynamicsoncebeforethegamestarts,andthischoiceisunobservedbythepursuerThelattercanchangehisdynamicsafinitenumberoftimesduringthecourseofthegameOptimalstrategiesoftheplayersarecharacterized,andtheexistenceofasaddlepointisestablishedCrück,Quincampoix,andSaintPierreareconcernedwithpursuitevasiongameswithimpulsivedynamics(seealsoChikrii,Matychyn,andChikriiinPartI)Thesystemcontrolledbyaplayerconsistsofanordinarydifferentialequation,describingcontinuousevolution,andadiscreteequationthataccountsforjumpsinthestateForqualitativegames,ageometriccharacterizationofthevictory(capture)domainsaregivenForquantitativegames,valuefunctionsaredeterminedusingtheIsaacspartialdifferentialinequalitiesShevchenkostudiesagamewithsimplemotioninwhichapursuerandcoalitionofevadersmovewithconstantspeedsinaplaneThepursuerwishestominimizethedistancetothecoalition(definedinaparticularway)andterminatesthegamewhendistancereductionnolongerisguaranteedThegamewithtwoevaders,whichcanbecalledagameofalternativepursuit,isstudiesindetailPartIVisdevotedtoevolutionarygametheoryandapplicationsItcontainssevenchaptersGarayexaminesasituationinwhicharesidentpopulationofinteractingindividualsisdescribedbyalogisticmodelinwhichinteractionparametersdependonthephenotypesoftheindividualsAnewmutantclonearisesinthepopulationAmongthequestionsaddressedare:whatkindofmutuantcan(cannot)invadethepopulation,and,ifinvasionoccurs,whendoesstablecoexistenceariseTheworkestablishesaconnectionbetweenadaptivedynamicsanddynamicevolutionarystabilityMitchellpresentsananalysisofaresourceconsumermodelinwhichindividualsareallowedtoadaptivelyvarytheirresourceuseasafunctionofcompetitordensityandstrategyItisdemonstratedthathabitatspecialization,stableminima,xiiPrefacecommunityinvasibility,andsympatricspeciationaremorelikelywhenindividualsaremoreefficientatconvertingresourcesintoviableoffspringTheworksuggestspossiblelinksbetweenspeciesdiversityandfactorsinfluencingresourceconversionefficiency(climate,habitatfragmentation,environmentaltoxins)VincentandVincentsuggestaseriesofmodificationsofawellknownmodelforcoexistenceTheirstartingpointisaclassicalversionoftheLotkaVolterracompetitionequation,whichsubsequentlyismadefrequencydependentinthreedifferentwaysandallowsthemodelingofrelativeabundanceThepurposeistoexaminetheconditionsthatdeterminetherelativeabundanceofspecieswhichareinanevolutionarystablestateItisassumedthattheecosystemisatornearanevolutionaryequilibrium,andtheauthorsseekevolutionarystablestrategiestoidentifyacoalitionofindividualspeciesHamelin,Bernhard,Nain,andWajnberg,andHamelin,Bernhard,Shaiju,andWajnbergareconcernedwiththeoptimalbehaviorofforagersthatreachapatchatrandomarrivaltimesInthefirstchapter,competitionislimitedtosharingacommonresourceInthiscase,optimalbehaviorcanbecharacterizedbyusingaCharnovrulewith“carefullychosen”parametersThesecondchapterdealswiththecaseofinterferencecompetitionHere,anearlierresultintheliteratureisextendedtoasynchronousarrivalsTheresultingproblemrequiresthesolutionofawarofattritiongamewithrandomterminaltimeInbothchapters,theanalysisisvalidnomatterthearrivallaw,providedthatitisMarkovianRael,Vincent,Costantino,andCushingexplorethepersistenceofcornoilsensitivityinapopulationofoneparticularflourbeetleTheauthorsuseevolutionarygametheorytomodelandanalyzepopulationdynamicsandchangesinthemeanstrategyofapopulationovertimeCornoilsensitivityisastrategyoftheflourbeetleandisatraitinanevolutionarygamethataffectsthefitnessoftheorganismsEquilibriumallelefrequenciesresultingfromthegameareevolutionarystablestrategiesandcomparefavorablywiththoseobtainedfromexperimentaldataWhelan,Brown,andMollproposeagameofresourcecompetition(seealsothechaptersbyHamelin,etal)Toaforager,fooditemshavethreepropertiesthatrelatetothevalueofaparticularstrategy:profitability,richness,andeaseofdigestionWhenforagingonfoodsthatdifferwithrespecttotheseproperties,adjustment(modulation)ofgutsizeandthroughputrateleadstoaspecializationofthedigestivesystemModulationofdigestivephysiologytoaparticularfoodtypecausesdifferentfoodtypestobeantagonisticresourcesAdjustmentofgutvolumeandprocessingmaypromotenichediversificationand,inturn,sympatricspeciationPartVcontainstenchaptersdealingwiththeapplicationofdynamicgametheorytovariousbranchesofeconomicsBeardandMcDonaldexaminetheissueofimprovingtheefficiencyofwaterusageOneparticularinstrumenthereisthetradingofwaterrightsAnimportantPrefacexiiiproblemishowtodesignanallocationsystemforalongperiodoftimesuchthatthedesirablepropertiesofthesystemaresustainedateachpointoftimeThisinvolvesthequestionoftimeconsistencyofthewatertradingcontract(seealsothechapterbyYeung,etalinPartII)AmodelofdynamicrecontractingofwaterrightsisdevelopedanditstimeconsistencypropertiesareassessedAlpcanandBassarinvestigatea(hybrid)noncooperativegamethatismotivatedbythepracticalproblemofjointpowercontrolandbasestationassignmentincodedivision,multipleaccesswirelessadatanetworksEachmobil

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