博弈論發(fā)展綜述與泛函分析在博弈論中的應(yīng)用.pdf

1、四川大學(xué)碩士學(xué)位論文博弈論發(fā)展綜述與泛函分析在博弈論中的應(yīng)用姓名：曹志平申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：運(yùn)籌學(xué)與控制論指導(dǎo)教師：曹廣福20030320SummarizationofGameTheory’SDevelopmentsandFunctionalAnalysis’ApplicationsinGameTheoryMajor：OperationalResearchandCybemeticsGraduateStudent：CaoZhiping

2、Supervisor：CaoGuangfuItiSmadeuDofthedevelopmentsoffunctionalanalysisingametheoryintheChapter1TheresearchaboutgamesinwhicheachplayershasanumberofpurestrategiesandmixedstrategieshavecomeintobeinggrownuptheoriesandmethodsPe

3、oplehavegotmanyresults訕tll也emixedgamewithinfinitepurestrategysetsForinstanceItiSwell—knownthatthereexistsoptimalmixedstrategiesingameswhicheachplayerhasapayofffunctionwithacontinualpurestrategysetontheunitsquare(consult『

4、101『11])GowenhasalsodiscussedtheexistenceofoptimalmixedstrategiesinwhicheachplayerhasapayofffunctionwithadiscontinuouspurestrategiesHowevercomparedwithfinitepurestrategyset，thereremainsanumberofunsolvablequestionsofgames

5、inwhicheachplayershasaninfinitepurestrategysetandfixedstrategiesIntheChapter1，amax—mintheoremandamaxtheoremareprovedonlocalconvextopologicallinearspacesasanapplication，itiSobtainedthatthereexistsoptimalmixedstrategiesina

6、gamewithallinfinitepurestrategysetonacompactHausdorffspaceonthebasisofanalyticmethodsweconcemthedevelopmentsofgametheoryinthechapter2Atfirstitintroducesthegeneralsituation，thehistoricalstagesandmainachievementsofgametheo

7、ry’SdevelopmentsInthesecondpart，itgoesonwithstaticgameofperfectinformationandbringsinNashEquilibriumWjanalyzeNashEquilibriumoftheclassicaltheorygameofPrisoner’sDilemmaandpointoutthesolutionunpracticalaithou曲ithasthechanc

8、etooptimizetheoreticallyAsanapplication，weexplaintheexistnecessityofmanyenvironmentproblemsbythecaseof“sheepeatgrass”DuringthethirdpartweintroducesubgameperfectNashEquilibrium，whichiStherationalequilibriumsolutionofdynam

9、icgameofperfectinformationWeuse也ebackwardinductiontoWOrkouttheoptimalequilibdumsolutionofoptimaltaftfrgame，atthesametime，explaintheimportanceoftaftffamongtheintcreationalcompetitionandtradepunishmentIntllefourthpart，itgi

10、vesthedefinitionofBayesianNashEquilibriuminthestaticgameofincompleteinformationanddiscussesthegameofsealedauctionanddrawssomeconclusionsaccordingtoitDuringthetiP&part，weintroduceperfectBayesianNashEquilibrium，whichiStheo

11、ptimalSOlutionofdynamicgameofincompleteinformation，meanwhile，analyzethereasonofanabnormalphenomenoninChineseStoekMarketsFinallycombinedwiththereformofeconomicconstructionandthebuildingofmarketeconomics，itopensup肌applying