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UnitOne Mathematics TextAGameTheory 23 04 2020 3 BackgroundInformation TextOrganization LanguageStudy FurtherReadingandPractice Interests 23 04 2020 4 BackgroundInformation 23 04 2020 5 AvinashDixitandBarryNalebuff 23 04 2020 6 AvinashDixitandBarryNalebuff AvinashDixitistheJohnJ SherredProfessorofEconomicsatPrincetonUniversity BarryNalebuffisMiltonSteinbachProfessorofManagementatYaleUniversity SchoolofOrganizationandManagement 23 04 2020 7 GameTheory Gametheoryisthemathematicalanalysisofanysituationinvolvingaconflictofinterest withtheintentofindicatingtheoptimalchoicesthat undergivenconditions willleadtoadesiredoutcome Althoughgametheoryhasrootsinthestudyofsuchwell knownamusementsascheckers tick tack toe andpoker hencethename italsoinvolvesmuchmoreseriousconflictsofinterestarisinginsuchfieldsassociology economics andpolitical militaryscience 23 04 2020 8 博弈论 博弈论有时也称为对策论是应用数学的一个分支 是研究具有斗争或竞争性质现象的数学理论和方法 也是运筹学的一个重要学科 目前在社会学 生物学 经济学 国际关系 计算机科学 政治学 军事战略和其他很多学科都有广泛的应用 23 04 2020 9 Princeton PrincetonisacityinGreenLakeCounty NJ UnitedStates 23 04 2020 10 Princeton 23 04 2020 11 PrincetonUniversity 23 04 2020 12 PrincetonUniversity 23 04 2020 13 PrincetonUniversity PrincetonUniversityisacoeducationalprivateuniversitylocatedinPrinceton NewJersey Itisthefourth oldestinstitutionofhighereducationintheU S andisoneoftheeightIvyLeagueuniversities Princetonhastraditionallyfocusedonundergraduateeducationandacademicresearch itnowoffersalargenumberoftop ratedprofessionalMaster sdegreesandPhDprogramsinarangeofsubjects 23 04 2020 14 JohnvonNeumann 23 04 2020 15 JohnvonNeumann HewasaHungarian bornAmericanmathematicianandwhomadecontributionstoquantumphysics functionalanalysis settheory economics computerscience topology numericalanalysis hydrodynamics ofexplosions statisticsandmanyothermathematicalfieldsasoneofworldhistory soutstandingmathematicians 23 04 2020 16 JohnvonNeumann Mostnotably vonNeumannwasapioneerofthemoderndigitalcomputerandtheapplicationofoperatortheorytoquantummechanics amemberoftheManhattanProjectandtheInstituteforAdvancedStudyatPrinceton andcreatorofgametheoryandtheconceptofcellularautomata AlongwithEdwardTellerandStanislawUlam vonNeumannworkedoutkeystepsinthenuclearphysicsinvolvedinthermonuclearreactionsandthehydrogenbomb 23 04 2020 17 约翰 冯 诺依曼 1903 1957 匈牙利裔美国数学家 普林斯顿大学和普林斯顿高等研究所教授 曾任研制原子弹的顾问 并参加研制计算机 被称为计算机之父 1954年成为美国原子能委员会委员 作为二十世纪最杰出的数学家之一 他在数理逻辑 测度论 格论和连续几何学方面都有开创性的成果 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 23 04 2020 18 tic tac toe Tic tac toeisagameinwhichtwoplayersalternatelyputcrossesandcirclesinoneofthecompartmentsofasquaregridofninespaces thegoalistogetarowofthreecrossesorthreecirclesbeforetheopponentdoes 井字棋 一种益智游戏 23 04 2020 19 23 04 2020 20 JohnForbesNash 23 04 2020 21 JohnForbesNash JohnForbesNash Jr bornonJune13 1928 isanAmericanmathematicianwhoworksingametheoryanddifferentialgeometry Hesharedthe1994NobelPrizeinEconomicswithtwoothergametheorists ReinhardSeltenandJohnHarsanyi 23 04 2020 22 JohnForbesNash HeisbestknowninpopularcultureasthesubjectoftheHollywoodmovie ABeautifulMind abouthismathematicalgeniusandhisstruggleswithschizophrenia 23 04 2020 23 Nashequilibrium Nashequilibrium hasbecomethecornerstoneofgametheory Nashequilibriumabstractsthewaywereasonaboutstrategiesinacompetitivesituation itcodifies IthinkhewilldoXbecausehethinksIwilldoY soIshoulddoZ 23 04 2020 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 23 04 2020 25 Prisoners Dilemma ThePrisoner sDilemmaisoneofthebest knownmodelsingametheory Itillustratestheparadoxicalnatureofinteractionbetweenmutuallysuspiciousparticipantswithopposinginterests 23 04 2020 26 Prisoners Dilemma 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 23 04 2020 27 HernandoCort s HewastheconquistadorwhobecamefamousforleadingthemilitaryexpeditionthatinitiatedtheSpanishConquestofMexico Cort swaspartofthegenerationofEuropeancolonizersthatbeganthefirstphaseoftheSpanishcolonizationoftheAmericas 23 04 2020 28 HernandoCort s 23 04 2020 29 ThomasSchelling 23 04 2020 30 ThomasSchelling 23 04 2020 31 ThomasSchelling ThomasCrombieSchelling bornon14April1921 isanAmericaneconomistandprofessorofforeignaffairs nationalsecurity nuclearstrategy andarmscontrolattheUniversityofMaryland CollegeParkSchoolofPublicPolicy Hewasawardedthe2005NobelPrizeinEconomics sharedwithRobertAumann for havingenhancedourunderstandingofconflictandcooperationthroughgametheoryanalysis 23 04 2020 32 ThomasSchelling Schellingreceivedhisbachelor sdegreeineconomicsfromtheUniversityofCalifornia Berkeleyin1944 HereceivedhisPhDineconomicsfromHarvardUniversityin1951 Schelling smostfamousbook TheStrategyofConflict 1960 haspioneeredthestudyofbargainingandstrategicbehaviorandisconsideredoneofthehundredbooksthathavebeenmostinfluentialintheWestsince1945 Inthisbookheintroducedtheconceptofthefocalpoint nowcommonlycalledtheSchellingpoint Schelling seconomictheoriesaboutwarwereextendedinArmsandInfluence 1966 23 04 2020 33 WinstonChurchill 23 04 2020 34 TheBigThree 23 04 2020 35 WinstonChurchill HewastheEnglishstatesmanandauthor bestknownasPrimeMinisteroftheUnitedKingdomduringtheSecondWorldWar Well knownasanorator strategist andpolitician ChurchillwasoneofthemostimportantleadersinmodernBritishandworldhistory Hewonthe1953NobelPrizeinLiteratureforhismanybooksonEnglishandworldhistory SirWinstonChurchillwasvotedthegreatest everBritoninthe2002BBCpollthe100GreatestBritons 23 04 2020 36 TextOrganization PartOne Para 1 3 Gametheorycanbedefinedthescienceofstrategywhichstudiesbothpureconflicts zero sumgames andconflictsincooperativeforms PartTwo Para 4 11 Therearetwodistincttypesofstrategicinterdependence sequential movegameandsimultaneous movegame 23 04 2020 37 TextOrganization PartThree Para 12 19 Thetypicalexamplesofgametheoryaregivenasbasicprinciplessuchasprisoners dilemma mixingmoves strategicmoves bargaining concealingandrevealinginformation PartFour Para 20 Theresearchofgametheoryhassucceededinillustratingstrategiesinsituationsofconflictandcooperationanditwillfocusonthedesignofsuccessfulstrategyinfuture 23 04 2020 38 LanguageStudy 23 04 2020 39 range para 1 varybetweenlimits extend runinalineThepricerangesfrom30 to80 Theboundaryrangesfromnorthtosouth takeovern theactoraninstanceofassumingcontrolormanagementoforresponsibilityforsomethingTheeconomyofHongkonggoeswellafteritstakeover 23 04 2020 40 GametheorywaspioneeredbyPrincetonmathematicianJohnvonNeumann para 2 pioneern originalinvestigatorofsubjectorexplorerorsettler initiatorofenterpriseTheyounggenerationwasgreatlymotivatedbythepioneers exploits ThepioneersofPuritanssettleddowninNewEngland v beapioneer originate courseofactionetc followedlaterbyothers Thenewtreatmentforcancerwaspioneeredbytheexpertsofstatehospital 23 04 2020 41 Thatis theparticipantsweresupposedtochooseandimplementtheiractionsjointly para 2 Thatis theplayerswereexpectedtoselectandcarryouttheiractionstogether 23 04 2020 42 hemustanticipateandovercomeresistancetohisplans para 3 v 1 dealwithorusebeforepropertimeTedwasnotusedtosavingmonthlyandhewouldalwaysanticipatehisincome 2 toexpectorrealizebeforehand foreseeTheexpertsareanticipatingthenegativeeffectsofairpollution Thedirectorsanticipatedafallindemand thatdemandwouldfall 23 04 2020 43 Theessenceofagameistheinterdependenceofplayerstrategies para 4 essencen1 thequalitywhichmakesathingwhatitis theinnernatureormostimportantqualityofathingIstheessenceofmoralityrightintention Thetwothingsarethesameinoutwardformbutdifferentinessence 23 04 2020 44 2 extractobtainedfromasubstancebytakingoutasmuchofthemassaspossiblemilkessence essenceofpeppermintessentialadj necessary indispensable mostimportant fundamentalExercise freshairandsleepareessentialforthepreservationofhealth LoveoffairplayissaidtobeanessentialpartoftheEnglishcharacter 23 04 2020 45 interdependence n thequalityorfactofdependingoneachotherinterdependentadjinter 前缀betweeneachother 类似的词还有interchange intermarry international interview etc 23 04 2020 46 Inprinciple anysequentialgamethatendsafterafinitesequenceofmoves para 6 finiteadj limited havingboundsThepetroleumsupplyisfiniteforhumankind infiniteadj withoutlimits havingnobounds number thatcannotbecalculatedinfinitespaceAtomsandmoleculesareinfinitelysmall 23 04 2020 47 Incontrasttothelinearchainofreasoningforsequentialgames agamewithsimultaneousmovesinvolvesalogicalcircle para 7 Agamewithsimultaneousmoverequiresalogicalcircularthinking whichistotallydifferentfromthelinearchainofreasoningforsequentialgames 23 04 2020 48 inignoranceoftheothers currentactions para 7 ignorancen beinglackingofknowledgeoruninformedThemanagerwasoffendedbytheignoranceofhisplans ignorev refusetotakenoticeof intentionallydisregardThepresidentignoredtherisingobjectionagainstnucleartestsandinsistedoncarryingouttheoriginalplan Histheorycontainedsomethingthatwasignoredinpractice 23 04 2020 49 Gametheoryquantifiesthisinsightanddetailstherightproportionsofsuchmixtures para 14 insightn pieceofknowledgeobtained understanding powerofseeingintosth withthemindamanofdeepinsightGoodteachershaveinsightintotheproblemsofstudents showinsightintohumancharacter 23 04 2020 50 RecallWinstonChurchill sdictumofhidingthetruthina bodyguardoflies para 19 recallv 1 bringbacktomind remembersomethingTwentyyearslaterhecouldstillclearlyrecalltheevent Iseemtorecallseeingthedocument 2 toorderthereturnofapersonwhobelongstoanorganizationTheambassadorwasrecalledwhenwarbrokeout 23 04 2020 51 Toconveyinformation useanactionthatisacredible signal para 19 v make ideas feelings etc knowntoanotherLanguageconveysmessage WordscannotconveyhowdelightedIamthatIhaveacceptedbyYaleUniversity 23 04 2020 52 FurtherReading 23 04 2020 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 23 04 2020 54 FurtherReading AdvancedNeumann Johnvon andOskarMorgenstern TheoryofGamesandEconomicBehavior 1947 Ordeshook Peter GameTheoryandPoliticalTheory 1986 Shubik Martin GameTheoryintheSocialSciences 1982 23 04 2020 55 Interests 23 04 2020 56 WhatisGameTheory definition Gametheoryistheformalstudyofconflictandcooperation Gametheoreticconceptsapplywhenevertheactionsofseveralagentsareinterdependent Theseagentsmaybeindividuals groups firms oranycombinationofthese Theconceptsofgametheoryprovidealanguagetoformulate structure analyze andunderstandstrategicscenarios 23 04 2020 57 HistoryofGameTheory AntoineCournot thestudyofaduopoly 1838 EmileBorel suggestedaformaltheoryofgames 1921 JohnvonNeumann publicationofthemonumentalvolume

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