[博弈论书籍].game.theory.lecture.notes.introduction,muhamet yildiz

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1、14.12GameTheoryLectureNotesIntroductionMuhametYildiz(Lecture1)GameTheoryisamisnomerforMultipersonDecisionTheory,analyzingthedecision-makingprocesswhentherearemorethanonedecision-makerswhereeachagent’spayoffpossiblydependsontheactionstakenbytheotheragents.Sinceanagent’spreferencesonhisactionsdependonw

2、hichactionstheotherpartiestake,hisactiondependsonhisbeliefsaboutwhattheothersdo.Ofcourse,whattheothersdodependsontheirbeliefsaboutwhateachagentdoes.Inthisway,aplayer’saction,inprinciple,dependsontheactionsavailabletoeachagent,eachagent’spreferencesontheoutcomes,eachplayer’sbeliefsaboutwhichactionsar

3、eavailabletoeachplayerandhoweachplayerrankstheoutcomes,andfurtherhisbeliefsabouteachplayer’sbeliefs,adinfinitum.Underperfectcompetition,therearealsomorethanone(infact,infinitelymany)decisionmakers.Yet,theirdecisionsareassumedtobedecentralized.Aconsumertriestochoosethebestconsumptionbundlethathecanaffor

4、d,giventheprices—withoutpayingattentionwhattheotherconsumersdo.Inreality,thefuturepricesarenotknown.Consumers’decisionsdependontheirexpectationsaboutthefutureprices.Andthefuturepricesdependonconsumers’decisionstoday.Onceagain,eveninperfectlycompetitiveenvironments,aconsumer’sdecisionsareaffectedbythe

5、irbeliefsaboutwhatotherconsumersdo—inanaggregatelevel.Whenagentsthinkthroughwhattheotherplayerswilldo,takingwhattheotherplayersthinkaboutthemintoaccount,theymayfindaclearwaytoplaythegame.Considerthefollowing“game”:112LmRT(1,1)(0,2)(2,1)M(2,2)(1,1)(0,0)B(1,0)(0,0)(−1,1)Here,Players1hasstrategies,T,M,

6、BandPlayer2hasstrategiesL,m,R.(Theypicktheirstrategiessimultaneously.)Thepayoffsforplayers1and2areindicatedbythenumbersinparentheses,thefirstoneforplayer1andthesecondoneforplayer2.Forinstance,ifPlayer1playsTandPlayer2playsR,thenPlayer1getsapayoffof2andPlayer2gets1.Let’sassumethateachplayerknowsthatthes

7、earethestrategiesandthepayoffs,eachplayerknowsthateachplayerknowsthis,eachplayerknowsthateachplayerknowsthateachplayerknowsthis,...adinfinitum.Now,player1looksathispayoffs,andrealizesthat,nomatterwhatthe