a course in game theory

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1、1Introduction1.1GameTheoryGametheoryisabagofanalyticaltoolsdesignedtohelpusunderstandthephenomenathatweobservewhendecision-makersinteract.Theba-sicassumptionsthatunderliethetheoryarethatdecision-makerspursuewell-denedexogenousobjectives(theyarerational)andtakeintoac-countthei

2、rknowledgeorexpectationsofotherdecision-makers'behavior(theyreasonstrategically).Themodelsofgametheoryarehighlyabstractrepresentationsofclassesofreal-lifesituations.Theirabstractnessallowsthemtobeusedtostudyawiderangeofphenomena.Forexample,thetheoryofNashequilibrium(Chapter2)h

3、asbeenusedtostudyoligopolisticandpoliti-calcompetition.Thetheoryofmixedstrategyequilibrium(Chapter3)hasbeenusedtoexplainthedistributionsoftonguelengthinbeesandtubelengthin owers.Thetheoryofrepeatedgames(Chapter8)hasbeenusedtoilluminatesocialphenomenalikethreatsandpromises.Thet

4、heoryofthecore(Chapter13)revealsasenseinwhichtheoutcomeoftradingunderapricesystemisstableinaneconomythatcontainsmanyagents.Theboundarybetweenpureandappliedgametheoryisvague;somedevelopmentsinthepuretheoryweremotivatedbyissuesthataroseinapplications.Neverthelesswebelievethatsuc

5、halinecanbedrawn.Thoughwehopethatthisbookappealstothosewhoareinterestedinapplications,westayalmostentirelyintheterritoryofpure"theory.Theartofapplyinganabstractmodeltoareal-lifesituationshouldbethesubjectofanothertome.Gametheoryusesmathematicstoexpressitsideasformally.However

6、,thegametheoreticalideasthatwediscussarenotinherentlymathemat-2Chapter1.Introductionical;inprincipleabookcouldbewrittenthathadessentiallythesamecontentasthisoneandwasdevoidofmathematics.Amathematicalformulationmakesiteasytodeneconceptsprecisely,toverifythecon-sistencyofideas,

7、andtoexploretheimplicationsofassumptions.Con-sequentlyourstyleisformal:westatedenitionsandresultsprecisely,interspersingthemwithmotivationsandinterpretationsoftheconcepts.Theuseofmathematicalmodelscreatesindependentmathematicalinterest.Inthisbook,however,wetreatgametheorynota

8、sabranchofmathematicsbutasasocialsciencewhoseaimistounderstan