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1、GameTheoryBasicsBernhardvonStengelDepartmentofMathematics,LondonSchoolofEconomics,HoughtonSt,LondonWC2A2AE,UnitedKingdomemail:stengel@maths.lse.ac.ukOctober6,2008iiThematerialinthisbookhasbeenadaptedanddevelopedfrommaterialoriginallyproducedfortheBScMathematicsan
2、dEconomicsbydistancelearningofferedbytheUniversityofLondonExternalProgramme(www.londonexternal.ac.uk).IamgratefultoGeorgeZourosforhisvaluablecomments,andtoRahulSavaniforhiscontinuinginterestinthisproject,histhoroughreadingofearlierdrafts,andthefunwehaveinjointres
3、earchandwritingongametheory.PrefaceGametheoryistheformalstudyofconflictandcooperation.Itisconcernedwithsitua-tionswhere“players”interact,sothatitmatterstoeachplayerwhattheotherplayersdo.Gametheoryprovidesmathematicaltoolstomodel,structureandanalysesuchinterac-tive
4、scenarios.Theplayersmaybe,forexample,competingfirms,politicalvoters,matinganimals,orbuyersandsellersontheinternet.Thelanguageandconceptsofgametheoryarewidelyusedineconomics,politicalscience,biology,andcomputerscience,tonamejustafewdisciplines.Gametheoryhelpstounde
5、rstandeffectsofinteractionthatseempuzzlingatfirst.Forexample,thefamous“prisoners’dilemma”explainswhyfisherscanexhausttheirresourcesbyover-fishing:theyhurtthemselvescollectively,buteachfisheronhisowncannotreallychangethisandstillprofitsbyfishingasmuchaspossible.Otherins
6、ightscomefromthewayoflookingatinteractivesituations.Gametheorytreatsplayersequallyandrecommendstoeachplayerhowtoplaywell,givenwhattheotherplayersdo.Thismindsetisusefulinstrategicquestionsofmanagement,because“youputyourselfinyouropponent’sshoes”.Gametheoryisfascin
7、atingasatopicbecauseofitsdiverseapplications.Theideasofgametheorystartedwithmathematicians,mostnotablytheoutstandingmathematicianJohnvonNeumann(1903–1957).Inthe1950s,agroupofyoungresearchersinmathe-maticsatPrincetondevelopedgametheoryfurther,amongthemJohnNash,Har
8、oldKuhnandLloydShapley,andthesepioneerscanstill,over50yearslater,bemetatconferencesongametheory.Mostresearchingametheoryisnowdonebyeconomistsandothersocialscie
