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UnitOne,Mathematics,TextAGameTheory,2019/11/19,UnitOneMathematics,3,BackgroundInformation,TextOrganization,LanguageStudy,FurtherReadingandPractice,Interests,2019/11/19,UnitOneMathematics,4,BackgroundInformation,2019/11/19,UnitOneMathematics,5,AvinashDixitandBarryNalebuff,2019/11/19,UnitOneMathematics,6,AvinashDixitandBarryNalebuff,AvinashDixitistheJohnJ.SherredProfessorofEconomicsatPrincetonUniversity.BarryNalebuffisMiltonSteinbachProfessorofManagementatYaleUniversity,SchoolofOrganizationandManagement.,2019/11/19,UnitOneMathematics,7,GameTheory,Gametheoryisthemathematicalanalysisofanysituationinvolvingaconflictofinterest,withtheintentofindicatingtheoptimalchoicesthat,undergivenconditions,willleadtoadesiredoutcome.Althoughgametheoryhasrootsinthestudyofsuchwell-knownamusementsascheckers,tick-tack-toe,andpokerhencethenameitalsoinvolvesmuchmoreseriousconflictsofinterestarisinginsuchfieldsassociology,economics,andpolitical在博弈论和控制论,力学,经济学和计算机研制等领域做出了杰出的贡献.他同莫根施特恩合作,写出博弈论和经济行为(TheoryofGamesandEconomicBehavior,1947)一书,这是博弈论(又称对策论)中的经典著作,使他成为数理经济学的奠基人之一。,2019/11/19,UnitOneMathematics,18,tic-tac-toe,Tic-tac-toeisagameinwhichtwoplayersalternatelyputcrossesandcirclesinoneofthecompartmentsofasquaregridofninespaces;thegoalistogetarowofthreecrossesorthreecirclesbeforetheopponentdoes.井字棋,一种益智游戏。,2019/11/19,UnitOneMathematics,19,2019/11/19,UnitOneMathematics,20,JohnForbesNash,2019/11/19,UnitOneMathematics,21,JohnForbesNash,JohnForbesNash,Jr.(bornonJune13,1928)isanAmericanmathematicianwhoworksingametheoryanddifferentialgeometry.Hesharedthe1994NobelPrizeinEconomicswithtwoothergametheorists,ReinhardSeltenandJohnHarsanyi.,2019/11/19,UnitOneMathematics,22,JohnForbesNash,HeisbestknowninpopularcultureasthesubjectoftheHollywoodmovie,ABeautifulMind,abouthismathematicalgeniusandhisstruggleswithschizophrenia.,2019/11/19,UnitOneMathematics,23,Nashequilibrium,Nashequilibrium,hasbecomethecornerstoneofgametheory.Nashequilibriumabstractsthewaywereasonaboutstrategiesinacompetitivesituation:itcodifiesIthinkhewilldoXbecausehethinksIwilldoY,soIshoulddoZ.,2019/11/19,UnitOneMathematics,24,Nashequilibrium,纳什均衡,又称为非合作博弈均衡,是博弈论的一个重要术语,以约翰纳什命名。在一个博弈过程中,无论对方的策略选择如何,当事人一方都会选择某个确定的策略,则该策略被称作支配性策略。如果两个博弈的当事人的策略组合分别构成各自的支配性策略,那么这个组合就被定义为纳什均衡。一个策略组合被称为纳什均衡,当每个博弈者的均衡策略都是为了达到自己期望收益的最大值,与此同时,其他所有博弈者也遵循这样的策略。,2019/11/19,UnitOneMathematics,25,PrisonersDilemma,ThePrisonersDilemmaisoneofthebest-knownmodelsingametheory.Itillustratestheparadoxicalnatureofinteractionbetweenmutuallysuspiciousparticipantswithopposinginterests.,2019/11/19,UnitOneMathematics,26,PrisonersDilemma,囚徒困境,博弈论的经典案例。囚徒困境是博弈论的非零和博弈中具代表性的例子,反映个人最佳选择并非团体最佳选择。虽然困境本身只属模型性质,但现实中的价格竞争、环境保护等方面,也会频繁出现类似情况。单次发生的囚徒困境,和多次重复的囚徒困境结果不会一样。在重复的囚徒困境中,博弈被反复地进行。因而每个参与者都有机会去“惩罚”另一个参与者前一回合的不合作行为。这时,合作可能会作为均衡的结果出现。欺骗的动机这时可能被受到惩罚的威胁所克服,从而可能导向一个较好的、合作的结果。,2019/11/19,UnitOneMathematics,27,HernandoCorts,HewastheconquistadorwhobecamefamousforleadingthemilitaryexpeditionthatinitiatedtheSpanishConquestofMexico.CortswaspartofthegenerationofEuropeancolonizersthatbeganthefirstphaseoftheSpanishcolonizationoftheAmericas.,2019/11/19,UnitOneMathematics,28,HernandoCorts,2019/11/19,UnitOneMathematics,29,ThomasSchelling,2019/11/19,UnitOneMathematics,30,ThomasSchelling,2019/11/19,UnitOneMathematics,31,ThomasSchelling,ThomasCrombieSchelling(bornon14April1921)isanAmericaneconomistandprofessorofforeignaffairs,nationalsecurity,nuclearstrategy,andarmscontrolattheUniversityofMaryland,CollegeParkSchoolofPublicPolicy.Hewasawardedthe2005NobelPrizeinEconomics(sharedwithRobertAumann)for“havingenhancedourunderstandingofconflictandcooperationthroughgametheoryanalysis”.,2019/11/19,UnitOneMathematics,32,ThomasSchelling,SchellingreceivedhisbachelorsdegreeineconomicsfromtheUniversityofCalifornia,Berkeleyin1944.HereceivedhisPhDineconomicsfromHarvardUniversityin1951.Schellingsmostfamousbook,TheStrategyofConflict(1960),haspioneeredthestudyofbargainingandstrategicbehaviorandisconsideredoneofthehundredbooksthathavebeenmostinfluentialintheWestsince1945.Inthisbookheintroducedtheconceptofthefocalpoint,nowcommonlycalledtheSchellingpoint.SchellingseconomictheoriesaboutwarwereextendedinArmsandInfluence(1966).,2019/11/19,UnitOneMathematics,33,WinstonChurchill,2019/11/19,UnitOneMathematics,34,TheBigThree,2019/11/19,UnitOneMathematics,35,WinstonChurchill,HewastheEnglishstatesmanandauthor,bestknownasPrimeMinisteroftheUnitedKingdomduringtheSecondWorldWar.Well-knownasanorator,strategist,andpolitician,ChurchillwasoneofthemostimportantleadersinmodernBritishandworldhistory.Hewonthe1953NobelPrizeinLiteratureforhismanybooksonEnglishandworldhistory.SirWinstonChurchillwasvotedthegreatest-everBritoninthe2002BBCpollthe100GreatestBritons.,2019/11/19,UnitOneMathematics,36,TextOrganization,PartOne(Para.1-3)Gametheorycanbedefinedthescienceofstrategywhichstudiesbothpureconflicts(zero-sumgames)andconflictsincooperativeforms.PartTwo(Para.4-11)Therearetwodistincttypesofstrategicinterdependence:sequential-movegameandsimultaneous-movegame.,2019/11/19,UnitOneMathematics,37,TextOrganization,PartThree(Para.12-19)Thetypicalexamplesofgametheoryaregivenasbasicprinciplessuchasprisonersdilemma,mixingmoves,strategicmoves,bargaining,concealingandrevealinginformation.PartFour(Para.20)Theresearchofgametheoryhassucceededinillustratingstrategiesinsituationsofconflictandcooperationanditwillfocusonthedesignofsuccessfulstrategyinfuture.,2019/11/19,UnitOneMathematics,38,LanguageStudy,2019/11/19,UnitOneMathematics,39,range(para.1),varybetweenlimits,extend,runinalineThepricerangesfrom30$to80$.Theboundaryrangesfromnorthtosouth.takeovern.theactoraninstanceofassumingcontrolormanagementoforresponsibilityforsomethingTheeconomyofHongkonggoeswellafteritstakeover.,2019/11/19,UnitOneMathematics,40,GametheorywaspioneeredbyPrincetonmathematicianJohnvonNeumann.(para.2):,pioneern.originalinvestigatorofsubjectorexplorerorsettler;initiatorofenterpriseTheyounggenerationwasgreatlymotivatedbythepioneersexploits.ThepioneersofPuritanssettleddowninNewEngland.v.beapioneer;originate(courseofactionetc,followedlaterbyothers)Thenewtreatmentforcancerwaspioneeredbytheexpertsofstatehospital.,2019/11/19,UnitOneMathematics,41,Thatis,theparticipantsweresupposedtochooseandimplementtheiractionsjointly.(para.2):Thatis,theplayerswereexpectedtoselectandcarryouttheiractionstogether.,2019/11/19,UnitOneMathematics,42,hemustanticipateandovercomeresistancetohisplans.(para.3):,v.1)dealwithorusebeforepropertimeTedwasnotusedtosavingmonthlyandhewouldalwaysanticipatehisincome.2)toexpectorrealizebeforehand,foreseeTheexpertsareanticipatingthenegativeeffectsofairpollution.Thedirectorsanticipatedafallindemand/thatdemandwouldfall.,2019/11/19,UnitOneMathematics,43,Theessenceofagameistheinterdependenceofplayerstrategies.(para.4),essencen1)thequalitywhichmakesathingwhatitis;theinnernatureormostimportantqualityofathingIstheessenceofmoralityrightintention?Thetwothingsarethesameinoutwardformbutdifferentinessence.,2019/11/19,UnitOneMathematics,44,2)extractobtainedfromasubstancebytakingoutasmuchofthemassaspossiblemilkessence,essenceofpeppermintessentialadj.necessary:indispensable,mostimportant;fundamentalExercise,freshairandsleepareessentialforthepreservationofhealth.LoveoffairplayissaidtobeanessentialpartoftheEnglishcharacter.,2019/11/19,UnitOneMathematics,45,interdependence,n.thequalityorfactofdependingoneachotherinterdependentadjinter-前缀betweeneachother,类似的词还有interchange,intermarry,international,interview,etc.,2019/11/19,UnitOneMathematics,46,Inprinciple,anysequentialgamethatendsafterafinitesequenceofmoves(para.6):,finiteadj.limited;havingboundsThepetroleumsupplyisfiniteforhumankind.infiniteadj.withoutlimits;havingnobounds;(number)thatcannotbecalculatedinfinitespaceAtomsandmoleculesareinfinitelysmall.,2019/11/19,UnitOneMathematics,47,Incontrasttothelinearchainofreasoningforsequentialgames,agamewithsimultaneousmovesinvolvesalogicalcircle.(para.7):Agamewithsimultaneousmoverequiresalogicalcircularthinking,whichistotallydifferentfromthelinearchainofreasoningforsequentialgames.,2019/11/19,UnitOneMathematics,48,inignoranceoftheotherscurrentactions(para.7):,ignorancen.beinglackingofknowledgeoruninformedThemanagerwasoffendedbytheignoranceofhisplans.ignorev.refusetotakenoticeof;intentionallydisregardThepresidentignoredtherisingobjectionagainstnucleartestsandinsistedoncarryingouttheoriginalplan.Histheorycontainedsomethingthatwasignoredinpractice.,2019/11/19,UnitOneMathematics,49,Gametheoryquantifiesthisinsightanddetailstherightproportionsofsuchmixtures.(para.14):,insightn.pieceofknowledgeobtained,understanding;powerofseeingintosth.withthemindamanofdeepinsightGoodteachershaveinsightintotheproblemsofstudents.。showinsightintohumancharacter,2019/11/19,UnitOneMathematics,50,RecallWinstonChurchillsdictumofhidingthetruthina“bodyguardoflies”.(para.19):,recallv.1)bringbacktomind,remembersomethingTwentyyearslaterhecouldstillclearlyrecalltheevent.Iseemtorecallseeingthedocument.2)toorderthereturnofapersonwhobelongstoanorganizationTheambassadorwasrecalledwhenwarbrokeout.,2019/11/19,UnitOneMathematics,51,Toconveyinformation,useanactionthatisacredible“signal”(para.19):,v.make(ideas,feelings,etc.)knowntoanotherLanguageconveysmessage.WordscannotconveyhowdelightedIamthatIhaveacceptedbyYaleUniversity.,2019/11/19,UnitOneMathematics,52,FurtherReading,2019/11/19,UnitOneMathematics,53,FurtherReading,IntroductoryAnkeny,Nesmith.PokerStrategy:WinningwithGameTheory.1981.Brams,Steven.GameTheoryandPolitics.1979.Dixit,Avinash,andBarryNalebuff.ThinkingStrategically:ACompetitiveEdgeinBusiness,Politics,andEverydayLife.1991.McDonald,John.StrategyinPoker,BusinessandWar.1950.Porter,Michael.CompetitiveStrategy.1982.Riker,William.TheArtofPoliticalManipulation.1986.Schelling,Thomas.TheStrategyofConflict.1960.,2019/11/19,UnitOneMathematics,54,FurtherReading,AdvancedNeumann,Johnvon,andOskarMorgenstern.TheoryofGamesandEconomicBehavior.1947.Ordeshook,Peter.GameTheoryandPoliticalTheory.1986.Shubik,Martin.GameTheoryintheSocialSciences.1982.,2019/11/19,UnitOneMathematics,55,Interests,2019/11/19,UnitOneMathematics,56,WhatisGameTheory?(definition),Gametheoryistheformalstudyofconflictandcooperation.Gametheoreticconceptsapplywhenevertheactionsofseveralagentsareinterdependent.Theseagentsmaybeindividuals,groups,firms,oranycombinationofthese.Theconceptsofgametheoryprovidealanguagetoformulate,structure,analyze,andunderstandstrategicscenarios.,2019/11/19,UnitOneMathematics,57,HistoryofGameTheory,AntoineCournot-thestudyofaduopoly(1838)EmileBorel-suggestedaformaltheoryofgames(1921)JohnvonNeumann-publicationofthemonumentalvolumeTheoryofGamesandEconomicBehaviorbyJohnvonNeumannandtheeconomistOskarMorgenstern(1944),2019/11/19,UnitOneMathematics,58,HistoryofGameTheory,J
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