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《博弈论的诡计全集》扫描版[PDF]
《博弈论的诡计全集》扫描版[PDF]http://www.xuexi111.com/book/shehui/63242.htmlhttp://i-7.vcimg.com/crop/f1cf57766d98072a808b730b1325e5e0145150(600x)/thumb.jpg内容提要 博弈论是讨论人们在博弈的交互作用中如何决策的学问。人生就是一个永不停息的博弈过程。在日常生活中，我们每个人的行为对他人的利益影响很大，每个人的利益又受到他人行为的很大影响。 《博弈论的诡计全集》摒弃了市面上大部分博弈书那种枯燥的说理和说教，通过精彩的故事和深刻的剖析来讲述那些能够带你走出迷津的博弈论的“诡计”，告诉读者怎样与他人相处、怎样适应并利用世界上的种种规则、怎样在这个过程中确立自己的人格和世界观，并因此改变对社会和生活的看法，使读者以理性的视角和思路看待问题和解决问题，从而在事业和人生的大博弈中取得真正的成功。 阅读《博弈论的诡计全集》，我们不仅可以了解到那些令人叹服的社会真实轨迹，还可以学到如何运用这些博弈论的“诡计”成为生活中的策略高手。内容截图http://i-7.vcimg.com/crop/85f003b1059e3a7f1a80575eb4d14de881329(600x)/thumb.jpg
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剑桥07新书《博弈论算法》(Algorithmic Game Theory)
见过别人发这本书，36金币，为了更好让大家共享资源，象征性收6币。希望大家多多支持！ContentsIntroduction,byNisan/Roughgarden/Tardos/Vazirani.(outline)PartI:ComputinginGamesChapter1:BasicSolutionConceptsandComputationalIssuesinGames,byTardos/Vazirani.(outline)Chapter2:AlgorithmsforEquilibria,byPapadimitriou.(outline)Chapter3:EquilibriumComputationforTwo-PlayerGamesinStrategicandExtensiveForm,byvonStengel.(outline)Chapter4:Learning,RegretMinimization,andEquilibria,byBlum/Mansour.(outline)Chapter5:CombinatorialAlgorithmsforMarketEquilibria,byVazirani.(outline)Chapter6:ComputationofMarketEquilibriabyConvexProgramming,byCodenotti/Varadarajan.(outline)Chapter7:GraphicalGames,byKearns.(outline)Chapter8:CryptographyandGameTheory,byDodis/Rabin.(outline)PartII:AlgorithmicMechanismDesignChapter9:IntroductiontoMechanismDesign(forComputerScientists),byNisan.(outline)Chapter10:MechanismDesignWithoutMoney,bySchummer/Vohra.(outline)Chapter11:CombinatorialAuctions,byBlumrosen/Nisan.(outline)Chapter12:ComputationallyEfficientApproximationMechanisms,byLavi.(outline)Chapter13:ProfitMaximizationinMechanismDesign,byHartline/Karlin.(outline)Chapter14:DistributedAlgorithmicMechanismDesign,byFeigenbaum/Schapira/Shenker.(outline)Chapter15:CostSharing,byJain/Mahdian.(outline)Chapter16:On-lineMechanisms,byParkes.(outline)AllPartIIOutlinesPartIII:QuantifyingtheInefficiencyofEquilibriaChapter17:IntroductiontotheInefficiencyofEquillibria,byRoughgarden/Tardos.(outline)Chapter18:RoutingGames,byRoughgarden.(outline)Chapter19:NetworkFormationGames,byTardosandWexler.(outline)Chapter20:SelfishLoadBalancing,byVoecking.(outline)Chapter21:ThePriceofAnarchyandtheDesignofScalableResourceAllocationMechanisms,byJohari.(outline)AllPartIIIOutlinesPartIV:AdditionalTopicsChapter22:IncentivesandPricinginCommunicationNetworks,byOzdaglar/Srikant.(outline)Chapter23:IncentivesinPeer-to-PeerSystems,byBabaioff/Chuang/Feldman.(outline)Chapter24:CascadingBehaviorinNetworks:AlgorithmicandEconomicIssues,byKleinberg.(outline)Chapter25:IncentivesandInformationSecurity,byAnderson/Moore/Nagaraja/Ozment.(outline)Chapter26:ComputationalAspectsofInformationMarkets,byPennock/Sami.(outline)Chapter27:Manipulation-ResistantReputationSystems,byFriedman/Resnick/Sami.(outline)Chapter28:SponsoredSearchAuctions,byLahaie/Pennock/Saberi/Vohra.(outline)Chapter29:ComputationalEvolutionaryGameTheory,bySuri.(outline)（原附件已被删除）
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[下载][分享]活学活用博弈论
【内容简介】我们常常被博弈论著作中大量的数学模型吓倒。其实，博弈论不是学者们用来唬人的把戏，而是一种一般性的分析方法。读过本书之后，相信你再也不会认为博弈论是一门远离自己生活的玄学，而会把它当成分析和描述自己身边事情的有效方法。本书用每个人都能理解的语言详细、准确且全面讲解了博弈论的分析方法及其在现实中的各种应用。对于2005年诺贝尔经济学奖得主奥曼和谢林的理论，本书也有详细的介绍。例如，对谢林在分析社会冲突时得出的一些有用的策略——加薪威胁、交出控制权以及切断联系等，本书用简明的语言进行了讲解，而对于奥曼的重复博弈，本书则是用通俗的例子加以说明。【编辑推荐】2005年诺贝尔经济授予奥曼和谢林两位博弈论学者，本书对其部分结论在现实中的应用进行了深入浅出的讲解。在我们身边常常会出现一些看似矛盾的现象： 在商战中，许多人展示的诚实，并不是基于道德，而是由于贪婪。 不为自己留退路的选择可以提高我们的收益。 企业烧钱可以增加财富。 进行短线投机的人也会关注股价的长期趋势。 要求加薪时，使自己陷入可能的难堪境地，能够增加自己的谈判力。 有精神问题的人比心智健全的同事更具谈判优势。 这些问题正是博弈论学者，包括２００５年诺贝尔经济学奖和主奥曼和谢林研究的问题。如果能抛开博弈论中艰深的数学分析，我们就可以很轻松地理解这些现象背后的博弈论原理，并将这些策略应用在我们的生活与工作中。 本书以通俗易懂的语言和大量实例讲解了博弈论的理论及其在日常生活和商业领域的应用，读者不需要研究晦涩的数学模型，就可以准确地把握博弈论的精髓，并利用这一工具使自己在竞争激烈的社会环境中立于不败之地。 与《孙子兵法》一样，博弈论的应用并不限于某一领域，只要是存在合作、竞争与对抗，博弈论方法就可以发挥效力。因而博弈论应该成为我们每个人在制定决策时的基本思考工具。【作译者介绍】本书提供作译者介绍米勒，史密斯学院经济学助理教授，获得芝加哥大学经济学博士学位、期坦福法学院法学博士学位。他运用博弈论写作了大量分析希腊神话、计算机加密、电子商务、投资、基因检测、网络侵权和彩票等问题的文章，其作品广泛刊载于大众与专业媒体上，包括《奥兰多前哨报》、《旗帜周刊》、《国际法律与经济学评论》、《信息、法律与技术学报》，以及《国家评论》、CNB和《福克斯新闻》的网站上。好书一起分享吧。5币也不贵。点一下每日红包就可兑换5币。
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考博题目，请博弈论高手的来看看
各位兄弟姐妹：我在遇到一个练习题，挺有趣的但不知怎么做，请教大家，请高手赐教！某大学有n个学生，他们同时通过学校的数据网络发送数据，设xi>=0,表示学生i发送的数据量，每个学生i选择自己所需发送的数据量xi.网络传输速度与学生发送数据总量成反比，且设每个学生发送数据要花费xi*t(x1,x2,.....xn)分钟，其中t(x1,x2,....xn)=x1+x2+...+xn,这样，学生i发送数据量xi的支付水平（payoff)就为xi-xi*t(x1,x2,...xn).再假设学校给学生一笔一次性补助M，然后对学生发送数据每单位收取费用p。试计算：（1）在这种情况下的nash均衡。（2）如果我们要求在nash均衡时收支平衡，即M=p（x1(M,p)+...+xn(M,p))/n,其中xi（M，p）是学生i在均衡时发送的数据量，那么试计算使学生的均衡支付水平最大时的M和p的值。我的思路，（1）是求payoff的一阶偏导数，连立n个方程解出nash均衡的x1,x2...xn.（2）看到题目中说xi是M，p的函数，因为payoff中不涉及M，所以我就不知道xi为什么是M的函数了，是不是（1）的想法也是错的？请大家赐教，先谢过了！
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有几个关于博弈论的习题，大家帮忙啊...
大家能做几个就做几个，多谢大家啦！1．ABC三人通过考试竞争进入两校，每校只录取一人。进入较好的学校效用为H，进入较差的效用为L，而没有读书的效用为0，H〉L〉0。每个人的成绩都是私人信息，他们是在区间[0，1]上服从均匀分布的随机变量。三人考后正决定如何申报院校。申报方案是函数B：[0，1]映射到{好校，差校}，它是申请人在此不完全信息静态博弈下的一个策略。录取规则如下：（i）当某校有3个人申报时，取最高分，中等分转到另一院校，而最低分无书读。（ii）当某校有2个人申报时，申请另一个学校的人必然被录取，而申请该校的2人中取较高分，较低分者无书读。（iii）某校只有1人申报时，录取该人，另一学校的录取方法见（ii）。（4）某校无人申报时，所有人都申请另一院校，录取方法见（i）（1）写出每人的策略函数（2）以上博弈中是否存在一个对称的贝叶斯纳什均衡？如存在，请找出，否则，说明不存在的原因2卖方拥有一个成本为C的物品，买方对此物品的主观价值为V，V与C都是私人信息，他们相互独立且服从区间[0，1]上的均匀分布（i）设计一个事后有效（ExpostEfficient）分配此物品的机制（ii）证明不存在这样的激励相容事后有效机制，参与双方在观察到私人信息之后（Interim），其期望效用非负。3．一个地产商用Take-it-or-Leave-it-offer的方式来卖一套房，假设成本为0，定义Take-it-or-Leave-it-offer为：卖方出价P，买方接受则成交，否则一拍两散。有两个买房的，他们的私人主观价值x1,x2,服从[0，1]区间的i.i.d均匀分布，只要地产商的喊价P低于其主观价值，他们即接受，博弈随即结束。每个人的贴现系数为r,r属于[0，1]。（1）如果两买家等概率随机前来问价，地产商每次的最优叫价P*t，t=1,2是多少？（2）如果总是主观价值大的先来问价，地产商每次的最优叫价又是多少？（3）如果总共有10个买家，总是主观价值大的先来问价，地产商的最优叫价序列P*t，t=1,2,…10,是什么？4有两个买家参与一个物品的二价拍卖，假设卖方的成本为0，买家的私人主观价值x1,x2服从[0，1]上的i.i.d均匀分布，只要买家的出价大于等于0，卖家都卖（1）考虑一种合谋方式，即两买家商定均投标0，在获得物品后，应用抛硬币的方法来决定谁得到物品。问在在这种合谋方式，买家的exante(观测到私人主观价值xi之前)期望效用是多少？该期望效用是不合谋时的exante期望效用的百分之几？（2）如果进行着这种二价拍卖的无穷重复博弈，（1）中的合谋行为在贴现系数r,r属于[0，1]满足什么条件中，能被纳什回归所支持？
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请高手帮忙做一道博弈论的题！！！
一个静态博弈的定义见如下4条：a)自然决定收益情况由博弈1给出,或是由博弈2给出,选择每一博弈的概率相等；b）参与人1了解到自然是选择了博弈1，还是选择了博弈2，但参与人2不知道；c）参与人1选择T或B，同时参与人2选择L或R；d）根据自然选择的博弈，两人得到各自的收益。问题：写出参与人1和参与人2所有的纯战略；表4-1博弈1参与人2LR参与人1T1，10，0B0，00，0表4-2博弈2参与人2LR参与人1T0，00，0B0，02，2
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[耶鲁大学] 【视频】经济学：博弈论 01 绪论 Game Theory
Lecture1-Introduction:fivefirstlessonsOverview:WeintroduceGameTheorybyplayingagame.Weorganizethegameintoplayers,theirstrategies,andtheirgoalsorpayoffs;andwelearnthatweshoulddecidewhatourgoalsarebeforewemakechoices.Withsomeplausiblepayoffs,ourgameisaprisoners'dilemma.Welearnthatweshouldneverchooseadominatedstrategy;butthatrationalplaybyrationalplayerscanleadtobadoutcomes.Wediscusssomeprisoners'dilemmasintherealworldandsomepossiblereal-worldremedies.Withotherplausiblepayoffs,ourgameisacoordinationproblemandhasverydifferentoutcomes:sodifferentpayoffsmatter.Weoftenneedtothink,notonlyaboutourownpayoffs,butalsoothers'payoffs.Weshouldputourselvesinothers'shoesandtrytopredictwhattheywilldo.Thisistheessenceofstrategicthinking.Readingassignment:StrategiesandGames:TheoryAndPractice.(Dutta):Chapter1,Sections1-3Strategy:AnIntroductiontoGameTheory.(Watson):Chapter1http://www.tudou.com/v/6KiN6Y725pAGameTheory:Lecture1TranscriptSeptember5,2007ProfessorBenPolak:SothisisGameTheoryEconomics159.Ifyou'rehereforarthistory,you'reeitherinthewrongroomorstayanyway,maybethisistherightroom;butthisisGameTheory,okay.Youshouldhavefourhandouts;everyoneshouldhavefourhandouts.Thereisalegalreleaseform--we'lltalkaboutitinaminute--aboutthevideoing.Thereisasyllabus,whichisapreliminarysyllabus:it'salsoonline.AndtherearetwogameslabeledGame1andGame2.CanIgetyoualltolookatGame1andstartthinkingaboutit.Andwhileyou'rethinkingaboutit,Iamhopingyoucanmultitaskabit.I'lldescribeabitabouttheclassandwe'llgetabitofadminunderourbelts.Butpleasetryandlookat--somebody'snotlookingatit,becausethey'reusingitasafanhere--solookatGame1andfilloutthatformforme,okay?Sowhileyou'refillingthatout,letmetellyoualittlebitaboutwhatwe'regoingtobedoinghere.SowhatisGameTheory?GameTheoryisamethodofstudyingstrategicsituations.Sowhat'sastrategicsituation?Welllet'sstartoffwithwhat'snotastrategicsituation.InyourEconomics-inyourIntroEconomicsclassin115or110,yousawsomeprettygoodexamplesofsituationsthatwerenotstrategic.Yousawfirmsworkinginperfectcompetition.Firmsinperfectcompetitionarepricetakers:theydon'tparticularlyhavetoworryabouttheactionsoftheircompetitors.Youalsosawfirmsthatweremonopolistsandmonopolistsdon'thaveanycompetitorstoworryabout,sothat'snotaparticularlystrategicsituation.They'renotpricetakersbuttheytakethedemandcurve.Isthislookingfamiliarforsomeofyouwhocanrememberdoing115lastyearormaybetwoyearsagoforsomeofyou?Everythinginbetweenisstrategic.Soeverythingthatconstitutesimperfectcompetitionisastrategicsetting.Thinkaboutthemotorindustry,themotorcarindustry.FordhastoworryaboutwhatGMisdoingandwhatToyotaisdoing,andforthemomentatleastwhatChryslerisdoingbutperhapsnotforlong.Sothere'sasmallnumberoffirmsandtheiractionsaffecteachother.Soforaliteraldefinitionofwhatstrategicmeans:it'sasettingwheretheoutcomesthataffectyoudependonactions,notjustonyourownactions,butonactionsofothers.Allright,that'sasmuchasI'mgoingtosayforpreviewrightnow,we'regoingtocomebackandseeplentyofthisoverthecourseofthenextsemester.SowhatIwanttodoisgetontowherethisapplies.ItobviouslyappliesinEconomics,butitalsoappliesinpolitics,andinfact,thisclasswillcountasaPoliticalScienceclassifyou'reaPoliticalSciencemajor.YoushouldgocheckwiththeDUSinPoliticalScience.Itcount-GameTheoryisveryimportantinlawthesedays.Soforthoseofyou--forthehalfofyou--thataregoingtoendupinlawschool,thisisprettygoodtraining.GameTheoryisalsousedinbiologyandtowardsthemiddleofthesemesterwe'reactuallygoingtoseesomeexamplesofGameTheoryasappliedtoevolution.Andnotsurprisingly,GameTheoryappliestosport.Solet'stalkaboutabitofadmin.Howareyoudoingonfillingoutthosegames?Everyonemanagingtomultitask:fillinginGame1?Keepwriting.IwanttogetsomeadminoutofthewayandIwanttostartbygettingoutofthewaywhatisobviouslytheelephantintheroom.Someofyouwillhavenoticedthatthere'sacameracrewhere,okay.Soassomeofyouprobablyknow,Yaleisundergoinganopeneducationprojectandthey'revideoingseveralclasses,andtheideaofthis,istomakeeducationalmaterialsavailablebeyondthewallsofYale.Infact,ontheweb,internationally,sopeopleinplaces,maybeplacesintheU.S.orplacesmilesaway,maybeinTimbuktuorwhatever,whofinditdifficulttogeteducationalmaterialsfromthelocaluniversityorwhatever,canwatchcertainlecturesfromYaleontheweb.Someofyouwouldhavebeeninclassesthatdothatbefore.What'sgoingtodifferentaboutthisclassisthatyou'regoingtobeparticipatinginit.Thewayweteachthisclassiswe'regoingtoplaygames,we'regoingtohavediscussions,we'regoingtotalkamongtheclass,andyou'regoingtobelearningfromeachother,andIwantyoutohelppeoplewatchingathometobeabletolearntoo.Andthatmeansyou'regoingtobeonfilm,attheveryleastonmike.Sohow'sthatgoingtowork?AroundtheroomarethreeT.A.sholdingmikes.Letmeshowyouwheretheyare:onehere,onehere,andonehere.WhenIaskforclassroomdiscussions,I'mgoingtohaveoneoftheT.A.sgotoyouwithamicrophonemuchlikein"Donahue"orsomething,okay.Atcertaintimes,you'regoingtobeseenonfilm,sothecameraisactuallygoingtocomearoundandpointinyourdirection.NowIreallywantthistohappen.Ihadtoargueforthistohappen,causeIreallyfeelthatthisclassisn'taboutme.I'mpartoftheclassobviously,butit'saboutyouteachingeachotherandparticipating.Butthere'sacatch,thecatchis,thatthatmeansyouhavetosignthatlegalreleaseform.Soyou'llseethatyouhaveinfrontofyoualegalreleaseform,youhavetobeabletosignit,andwhatthatsaysisthatwecanuseyoubeingshowninclass.Thinkofthisasabadhairdayreleaseform.Allright,youcan'tsueYalelaterifyouhadabadhairday.ForthoseofyouwhoareontherunfromtheFBI,yourVisahasrunout,oryou'resittingnexttoyourex-girlfriend,nowwouldbeagoodtimetoputapaperbagoveryourhead.Allright,nowjusttogetyouusedtotheidea,ineveryclasswe'regoingtohaveIthinkthesametwopeople,soJudeisthecameraman;whydon'tyouallwavetoJude:thisisJudeokay.AndWesisouraudioguy:thisisWes.AndIwilltryandremembernottoincludeJudeandWesintheclassroomdiscussions,butyoushouldbeawarethatthey'rethere.Now,ifthisismakingyounervous,ifit'sanyconsolation,it'smakingmeverynervous.So,allright,we'lltryandmakethisclassworkassmoothlyaswecan,allowingforthisextrathing.Letmejustsay,noone'smakinganymoneyoffthis--atleastI'mhopingtheseguysarebeingpaid--butmeandtheT.A.sarenotbeingpaid.Theaimofthis,thatIthinkisagoodaim,it'saneducationalproject,andI'mhopingyou'llhelpuswithit.Theonedifferenceitisgoingtomean,isthatattimesImightholdsomeofthediscussionsfortheclass,comingdownintothispartoftheroom,here,tomakeitalittleeasierforJude.Allright,howarewedoingnowonfillingoutthoseforms?Haseveryonefilledintheirstrategyforthefirstgame?Notyet.Okay,let'sgoondoingabitmoreadmin.ThethingyoumostlycareaboutI'mguessing,isthegrades.Allright,sohowisthegradegoingtoworkforthisclass?30%oftheclasswillbeonproblemsets,30%ofthegrade;30%onthemid-term,and40%onthefinal;so30/30/40.Themid-termwillbeheldinclassonOctober17th;thatisalsoinyoursyllabus.Pleasedon'tanybodytellmelate-anytimeaftertodayyoudidn'tknowwhenthemid-termwasandthereforeitclasheswith17differentthings.Themid-termisonOctober17th,whichisaWednesday,inclass.Allright,theproblemsets:therewillberoughlytenproblemsetsandI'lltalkaboutthemmorelateronwhenIhandthemout.ThefirstonewillgooutonMondaybutitwillbeduetendayslater.Roughlyspeakingthey'llbeeveryweek.Thegradedistribution:allright,sothisistheroughgradedistribution.Roughlyspeaking,asixthoftheclassaregoingtoendupwithA's,asixtharegoingtoendupwithA-,asixtharegoingtoendupwithB+,asixtharegoingtoendupwithB,asixtharegoingtoendupwithB-,andtheremainingsixth,ifIaddedthatupright,aregoingtoendupwithwhatIguesswe'renowcallingthepresidentialgrade,isthatright?That'snotliterallytrue.I'mgoingtosqueezeitabit,I'mgoingtocurveitabit,soactuallyslightlyfewerthanasixthwillgetstraightA's,andfewerthanasixthwillgetC'sandbelow.We'llsqueezethemiddletomakethembemoreB's.OnethingIcanguaranteefrompastexperienceinthisclass,isthatthemediangradewillbeaB+.ThemedianwillfallsomewhereintheB+'s.Justasforewarningforpeoplewhohaveforgottenwhatamedianis,thatmeanshalfofyou--notapproximatelyhalf,itmeansexactlyhalfofyou--willbegettingsomethinglikeB+andbelowandhalfwillgetsomethinglikeB+andabove.Now,howareyoudoinginfillingintheforms?Everyonefilledtheminyet?Surelymustbeprettyclosetogettingeveryonefilledin.Allright,solastthingstotalkaboutbeforeIactuallycollectthemin-textbooks.Therearetextbooksforthisclass.Themaintextbookisthisone,Dutta'sbookStrategyandGames.Ifyouwantaslightlytougherbook,morerigorousbook,tryJoelWatson'sbook,Strategies.Bothofthosebooksareavailableatthebookstore.ButIwanttowarneverybodyaheadoftime,Iwillnotbefollowingthetextbook.Iregardthesebooksassafetynets.Ifyoudon'tunderstandsomethingthathappenedinclass,youwanttoreinforceanideathatcameupinclass,thenyoushouldreadtherelevantchaptersinthebookandthesyllabuswilltellyouwhichchapterstoreadforeachclass,orforeachweekofclass,allright.ButIwillnotbefollowingthesebooksreligiouslyatall.Infact,they'rejustthereasbackup.Inaddition,Istronglyrecommendpeopleread,ThinkingStrategically.Thisisgoodbedtimereading.Doanyofyousufferfrominsomnia?It'sverygoodbedtimereadingifyousufferfrominsomnia.It'sagoodbookandwhat'smorethere'sgoingtobeaneweditionofthisbookthisyearandNortonhaveallowedustogetadvancecopiesofit.Soifyoudon'tbuythisbookthisweek,Imaybeabletomaketheadvancecopyoftheneweditionavailableforsomeofyounextweek.I'mnottakingacutonthateither,allright,there'snomoneychanginghands.Allright,sectionsareonthesyllabussignup-sorryonthewebsite,signupasusual.Putyourselfdownonthewaitlistifyoudon'tgetintothesectionyouwant.Youprobablywillgetintothesectionyouwantoncewe'redone.Allright,nowwemustbedonewiththeforms.Arewedonewiththeforms?Allright,sowhydon'twesendtheT.A.s,withorwithoutmikes,upanddowntheaislesandcollectinyourGame#1;notGame#2,justGame#1.Justwhilewe'redoingthat,Ithinkthereputationofthisclass--Ithink--ifyoulookatthecourseevaluationsonlineorwhatever,isthatthisclassisreasonablyhardbutreasonablyfun.SoI'mhopingthat'swhatthereputationoftheclassis.Ifyouthinkthisclassisgoingtobeeasy,Ithinkitisn'tactuallyaneasyclass.It'sactuallyquiteahardclass,butIthinkIcanguaranteeit'sgoingtobeafunclass.Nowonereasonit'safunclass,isthenicethingaboutteachingGameTheory-quietendownfolks--onethingaboutteachingGameTheoryis,yougettoplaygames,andthat'sexactlywhatwe'vejustbeendoingnow.Thisisourfirstgameandwe'regoingtoplaygamesthroughoutthecourse,sometimesseveraltimesaweek,sometimesjustonceaweek.Wegotallthesethingsin?Everyonehandedthemin?SoIneedtogetthosecounted.HasanyonetakentheYaleAccountingclass?Noonewantsto-hasaspirationstobe-onepersonhas.I'llhaveaT.A.doit,it'sallright,we'llhaveaT.A.doit.SoKaj,canyoucountthoseforme?Isthatright?Letmereadoutthegameyou'vejustplayed."Game1,asimplegradeschemefortheclass.Readthefollowingcarefully.Withoutshowingyourneighborwhatyouaredoing,putitintheboxbeloweithertheletterAlphaortheletterBeta.Thinkofthisasagradebid.Iwillrandomlypairyourformwithanotherformandneitheryounoryourpairwilleverknowwithwhomyouwerepaired.Here'showthegradesmaybeassignedfortheclass.[Welltheywon'tbe,butwecanpretend.]IfyouputAlphaandyou'repairedwithBeta,thenyouwillgetanAandyourpairaC.IfyouandyourpairbothputAlpha,you'llbothgetB-.IfyouputBetaandyou'repairedwithAlpha,you'llgetaCandyourpairanA.IfyouandyourpairbothputBeta,thenyou'llbothgetB+."Sothat'sthethingyoujustfilledin.Nowbeforewetalkaboutthis,let'sjustcollectthisinformationinamoreusefulway.SoI'mgoingtoremovethisfornow.We'lldiscussthisinasecond,butwhydon'tweactuallyrecordwhatthegameis,thatwe'replaying,first.Sothisisourgradegame,andwhatI'mgoingtodo,sinceit'skindofhardtoabsorballtheinformationjustbyreadingaparagraphoftext,I'mgoingtomakeatabletorecordtheinformation.SowhatI'mgoingtodoisI'mgoingtoputmehere,andmypair,thepersonI'mrandomlypairedwithhere,andAlphaandBeta,whicharethechoicesI'mgoingtomakehereandonthecolumnsAlphaandBeta,thechoicesmypairismaking.Inthistable,I'mgoingtoputmygrades.SomygradeifwebothputAlphaisB-,ifwebothputBeta,wasB+.IfIputAlphaandsheputaBeta,IgotanA,andifIputBetaandsheputanAlpha,IgotaC.Isthatcorrect?That'smoreorlessright?Yeah,okaywhilewe'rehere,whydon'twedothesameformypair?Sothisismygradesonthelefthandtable,butnowlet'slookatwhatmypairwilldo,whatmypairwillget.SoIshouldwarnthepeoplesittingatthebackthatmyhandwritingisprettybad,that'sonereasonformovingforward.TheotherthingIshouldapologizeatthisstageoftheclassismyaccent.Iwilltryandimprovethehandwriting,there'snotmuchIcandoabouttheaccentatthisstage.SoonceagainifyoubothputAlphathenmypairgetsaB-.IfwebothputBeta,thenwebothgetaB+;inparticular,mypairgetsaB+.IfIputAlphaandmypairputsBeta,thenshegetsaC.AndifIputBetaandsheputsAlpha,thenshegetsanA.SoInowhavealltheinformationthatwasonthesheetofpaperthatyoujusthandedin.Nowthere'sanotherwayoforganizingthisthat'sstandardinGameTheory,sowemayaswellgetusedtoitnowonthefirstday.Ratherthendrawingtwodifferenttableslikethis,whatI'mgoingtodoisI'mgoingtotakethesecondtableandsuper-imposeitontopofthefirsttable.Okay,soletmedothatandyou'llseewhatImean.WhatI'mgoingtodoisdrawalargertable,thesamebasicstructure:I'mchoosingAlphaandBetaontherows,mypairischoosingAlphaandBetaonthecolumns,butnowI'mgoingtoputbothgradesin.Sotheeasyonesareonthediagonal:youbothgetB-ifwebothchooseAlpha;webothgetB+ifwebothchooseBeta.ButifIchooseAlphaandmypairchoosesBeta,IgetanAandshegetsaC.AndifIchooseBetaandshechoosesAlpha,thenit'smewhogetstheCandit'sherwhogetstheA.SonoticewhatIdidhere.Thefirstgradecorrespondstotherowplayer,meinthiscase,andthesecondgradeineachboxcorrespondstothecolumnplayer,mypairinthiscase.Sothisisanicesuccinctwayofrecordingwhatwasintheprevioustwotables.Thisisanoutcomematrix;thistellsuseverythingthatwasinthegame.Okay,sonowseemsagoodtimetostarttalkingaboutwhatpeopledid.Solet'sjusthaveashowofhands.HowmanyofyouchoseAlpha?LeaveyourhandsupsothatJudecancatchthat,sopeoplecanseeathome,okay.AllrightandhowmanyofyouchoseBeta?There'sfarmoreAlphas-waveyourhandstheBeta'sokay.Allright,there'saBetahere,okay.Soitlookslikealotof-wellwe'regoingtofindout,we'regoingtocount--butalotmoreAlpha'sthanBeta's.Letmetryandfindoutsomereasonswhypeoplechose.SoletmehavetheAlpha'supagain.So,thewomanwho'sinredhere,canwegetamiketothe-yeah,isitokayifweaskyou?You'renotontherunfromtheFBI?Wecanaskyouwhy?Okay,soyouchoseAlpharight?SowhydidyouchooseAlpha?Student:[inaudible]realizedthatmypartnerchoseAlpha,thereforeIchose[inaudible].ProfessorBenPolak:Allright,soyouwroteoutthesesquares,yourealizedwhatyourpartnerwasgoingtodo,andrespondedtothat.AnyotherreasonsforchoosingAlphaaroundtheroom?Canwegetthewomanhere?Trynottobeintimidatedbythesemicrophones,they'rejustmikes.It'sokay.Student:ThereasonIchoseAlpha,regardlessofwhatmypartnerchose,IthinktherewouldbebetteroutcomesthanchoosingBeta.ProfessorBenPolak:Allright,soletmeaskyournamesforasecond-soyournamewas?Student:Courtney.ProfessorBenPolak:Courtneyandyournamewas?Student:ClaraElise.ProfessorBenPolak:ClaraElise.Soslightlydifferentreasons,samechoiceAlpha.ClaraElise'sreason-whatdidClaraElisesay?Shesaid,nomatterwhattheotherpersondoes,shereckonsshe'dgetabettergradeifshechoseAlpha.Soholdthatthoughtasecond,we'llcomebackto-isitClaraElise,isthatright?We'llcomebacktoClaraEliseinasecond.Let'stalktotheBeta'sasecond;letmejustemphasizeatthisstagetherearenowronganswers.Lateronintheclassthere'llbesomequestionsthathavewronganswers.Rightnowthere'snowronganswers.Theremaybebadreasonsbutthere'snowronganswers.Solet'shavetheBeta'supagain.Let'sseetheBeta's.Ohcomeon!TherewasaBetarighthere.YouwereaBetaright?YoubackedofftheBeta,okay.SohowcanIgetamikeintoaBeta?Let'sstickinthisaisleabit.IsthataBetarightthere?AreyouaBetarightthere?CanIgettheBetainhere?WhowastheBetainhere?Canwegetthemikeinthere?Isthatpossible?Inhere-youcanleaveyourhandsothat-therewego.Justpointtowards-that'sfine,justspeakintoit,that'sfine.Student:Sothereasonright?ProfessorBenPolak:Yeah,goahead.Student:Ipersonallydon'tlikeswingsthatmuchandit'stheB-/B+range,soI'dmuchratherpreferthattoaswingfromAtoC,andthat'smyreason.ProfessorBenPolak:Allright,soyou'resayingitcompressestherange.I'mnotsureitdoescompresstherange.ImeanifyouchoseAlpha,you'reswingingfromAtoB-;andfromBeta,swingingfromB+toC.Imeanthosearesimilarkindofrangesbutitcertainlyisareason.Otherreasonsforchoosing?Yeah,theguyinbluehere,yep,good.That'sallright.Don'tholdthemike;justletitpointatyou,that'sfine.Student:WellIguessIthoughtwecouldbemorecollusiveandkindofworktogether,butIguessnot.SoIchoseBeta.ProfessorBenPolak:There'sasireninthebackgroundsoImissedtheanswer.Standupasecond,sowecanjusthearyou.Student:Sure.ProfessorBenPolak:Sorry,sayagain.Student:Sure.MynameisTravis.Ithoughtwecouldworktogether,butIguessnot.ProfessorBenPolak:Allrightgood.That'saprettygoodreason.Student:IfyouhadchosenBetawewouldhaveallgottenB+'sbutIguessnot.ProfessorBenPolak:Good,soTravisisgivingusadifferentreason,right?He'ssayingthatmaybe,someofyouintheroommightactuallycareabouteachother'sgrades,right?Imeanyouallknoweachotherinclass.Youallgotothesamecollege.Forexample,ifweplayedthisgameupinthebusinessschool--arethereanyMBAstudentsheretoday?Oneortwo.Ifweplaythisgameupinthebusinessschool,Ithinkit'squitelikelywe'regoingtogetalotofAlpha'schosen,right?Butifweplayedthisgameupinlet'ssaytheDivinitySchool,allrightandI'mguessingthatTravis'answerisreflectingwhatyouguysarereasoninghere.IfyouplayedintheDivinitySchool,youmightthinkthatpeopleintheDivinitySchoolmightcareaboutotherpeople'sgrades,right?Theremightbeethicalreasons--perfectlygood,sensible,ethicalreasons--forchoosingBetainthisgame.Theremightbeotherreasonsaswell,butthat'sperhapsthereasontofocuson.Andperhaps,thelessonIwanttodrawoutofthisisthatrightnowthisisnotagame.Rightnowwehaveactions,strategiesforpeopletotake,andweknowwhattheoutcomesare,butwe'remissingsomethingthatwillmakethisagame.Whatarewemissinghere?Student:Objectives.ProfessorBenPolak:We'remissingobjectives.We'remissingpayoffs.We'remissingwhatpeoplecareabout,allright.Sowecan'treallystartanalyzingagameuntilweknowwhatpeoplecareabout,anduntilweknowwhatthepayoffsare.Nowlet'sjustsaysomethingnow,whichI'llprobablyforgettosayinanyothermomentoftheclass,buttodayit'srelevant.GameTheory,me,professorsatYale,cannottellyouwhatyourpayoffshouldbe.Ican'ttellyouinausefulwaywhatitisthatyourgoalsinlifeshouldbeorwhatever.That'snotwhatGameTheoryisabout.However,onceweknowwhatyourpayoffsare,onceweknowwhatyourgoalsare,perhapsGameTheorycanyouhelpyougetthere.Sowe'vehadtwodifferentkindsofpayoffsmentionedhere.Wehadthekindofpayoffwherewecareaboutourowngrade,andTravishasmentionedthekindofpayoffwhereyoumightcareaboutotherpeople'sgrades.Andwhatwe'regoingtodotodayisanalyzethisgameunderboththosepossiblepayoffs.Tostartthatoff,let'sputupsomepossiblepayoffsforthegame.AndIpromisewe'llcomebackandlookatsomeotherpayoffslater.We'llrevisittheDivinitySchoollater.Allright,sohereonceagainisoursamematrixwithmeandmypair,choosingactionsAlphaandBeta,butthistimeI'mgoingtoputnumbersinhere.Andsomeofyouwillperhapsrecognizethesenumbers,butthat'snotreallyrelevantfornow.Allright,sowhat'stheideahere?Wellthefirstideaisthatthesenumbersrepresentutilesorutilities.Theyrepresentwhatthesepeoplearetryingtomaximize,whatthey'retoachieve,theirgoals.Theideais-justtocomparethistotheoutcomematrix-forthepersonwho'smehere,(A,C)yieldsapayoffof--(A,C)isthisbox--so(A,C)yieldsapayoffofthree,whereas(B-,B-)yieldsapayoffof0,andsoon.Sowhat'stheinterpretation?It'sthefirstinterpretation:thenaturalinterpretationthatalotofyoujumpedtostraightaway.Thesearepeople--peoplewiththesepayoffsarepeople--whoonlycareabouttheirowngrades.TheypreferanAtoaB+,theypreferaB+toaB-,andtheypreferaB-toaC.Right,I'mhopingIthegradesinorder,otherwiseit'sgoingtoruinmycurveattheendoftheyear.Sothesepeopleonlycareabouttheirowngrades.Theyonlycareabouttheirowngrades.Whatdowecallpeoplewhoonlycareabouttheirowngrades?What'sagoodtechnicaltermforthem?InEngland,Ithinkwerefertotheseguys-whetherit'stechnicalornot-as"evilgits."Thesearenotperhapsthemostmoralpeopleintheuniverse.Sonowwecanaskadifferentquestion.Suppose,whethertheseareactuallyyourpayoffsornot,pretendtheyarefornow.Supposetheseareallpayoffs.Nowwecanask,notwhatdidyoudo,butwhatshouldyoudo?Nowwehavepayoffsthatcanreallyswitchthequestiontoanormativequestion:whatshouldyoudo?Let'scomebackto-wasitClaraElise--wherewasClaraElisebefore?Let'sgetthemikeonyouagain.Sojustexplainwhatyoudidandwhyagain.Student:WhyIchoseAlpha?ProfessorBenPolak:Yeah,standupasecond,ifthat'sokay.Student:Okay.ProfessorBenPolak:YouchoseAlpha;I'massumingthesewereroughlyyourpayoffs,moreorless,youwerecaringaboutyourgrades.Student:Yeah,Iwasthinking-ProfessorBenPolak:WhydidyouchooseAlpha?Student:I'msorry?ProfessorBenPolak:WhydidyouchooseAlpha?Justrepeatwhatyousaidbefore.Student:BecauseIthoughtthepayoffs-thetwodifferentpayoffsthatIcouldhavegotten--werehighestifIchoseAlpha.ProfessorBenPolak:Good;sowhatClaraEliseissaying--it'sanimportantidea--isthis(andtellmeifI'mparaphrasingyouincorrectlybutIthinkthisismoreorlesswhatyou'resaying):isnomatterwhattheotherpersondoes,nomatterwhatthepairdoes,sheobtainsahigherpayoffbychoosingAlpha.Let'sjustseethat.IfthepairchoosesAlphaandshechoosesAlpha,thenshegets0.IfthepairchoosesAlphaandshechoseBeta,shegets-1.0isbiggerthan-1.IfthepairchoosesBeta,thenifshechoosesAlphashegets3,Betashegets1,and3isbiggerthan1.Soinbothcases,nomatterwhattheotherpersondoes,shereceivesahigherpayofffromchoosingAlpha,sosheshouldchooseAlpha.Doeseveryonefollowthatlineofreasoning?That'sastrongerlineofreasoningthenthereasoningwehadearlier.Sothewoman,Ihaveimmediatelyforgottenthenameof,intheredshirt,whosenamewas-Student:Courtney.ProfessorBenPolak:Courtney,soCourtneyalsogaveareasonforchoosingAlpha,anditwasaperfectlygoodreasonforchoosingAlpha,nothingwrongwithit,butnoticethatthisreason'sastrongerreason.Itkindofimpliesyourreason.Solet'sgetsomedefinitionsdownhere.IthinkIcanfititinhere.Let'stryandfititinhere.Definition:WesaythatmystrategyAlphastrictlydominatesmystrategyBeta,ifmypayofffromAlphaisstrictlygreaterthanthatfromBeta,[andthisisthekeypartofthedefinition],regardlessofwhatothersdo.Shallwejustreadthatback?"WesaythatmystrategyAlphastrictlydominatesmystrategyBeta,ifmypayofffromAlphaisstrictlygreaterthanthatfromBeta,regardlessofwhatothersdo."Nowit'sbynomeansmymainaiminthisclasstoteachyoujargon.Butafewbitsofjargonaregoingtobehelpfulinallowingtheconversationtomoveforwardandthisiscertainlyone."Evilgits"ismaybeonetoo,butthisiscertainlyone.Let'sdrawoutsomelessonsfromthis.Actually,soyoucanstillreadthat,letmebringdownandcleanthisboard.Sothefirstlessonoftheclass,andtherearegoingtobelotsoflessons,isalessonthatemergesimmediatelyfromthedefinitionofadominatedstrategyandit'sthis.SoLessonOneofthecourseis:donotplayastrictlydominatedstrategy.SowithapologiestoStrunkandWhite,thisisinthepassiveform,that'sdominated,passivevoice.Donotplayastrictlydominatedstrategy.Why?Somebodywanttotellmewhy?Doyouwanttogetthisguy?Standup-yeah.Student:Becauseeveryone'sgoingtopickthedominantoutcomeandtheneveryone'sgoingtogettheworstresult-thecollectivelyworstresult.ProfessorBenPolak:Yeah,that'sapossibleanswer.I'mlookingforsomethingmoredirecthere.Sowelookatthedefinitionofastrictlydominatedstrategy.I'msayingneverplayone.What'sapossiblereasonforthat?Let's-canwegetthewomanthere?Student:[inaudible]ProfessorBenPolak:"You'llalwayslose."Well,Idon'tknow:it'snotaboutwinningandlosing.Whatelsecouldwehave?Couldwegetthisguyinthepinkdownhere?Student:Well,thepayoffsarelower.ProfessorBenPolak:Thepayoffsarelower,okay.Sohere'sanabbreviatedversionofthat,Imeanit'sperhapsalittlebitlonger.ThereasonIdon'twanttoplayastrictlydominatedstrategyis,ifinstead,Iplaythestrategythatdominatesit,Idobetterineverycase.ThereasonIneverwanttoplayastrictlydominatedstrategyis,ifinsteadIplaythestrategythatdominatesit,whateveranyoneelsedoesI'mdoingbetterthanIwouldhavedone.Nowthat'saprettyconvincingargument.Thatsoundslikeaconvincingargument.Itsoundsliketooobviouseventobeworthstatinginclass,soletmenowtryandshakeyourfaithalittlebitinthisanswer.You'resomebodywho'swantedbytheFBI,right?Okay,sohowaboutthefollowingargument?LookatthepayoffmatrixagainandsupposeIreasonasfollows.SupposeIreasonandsayifwe,meandmypair,bothreasonthiswayandchooseAlphathenwe'llbothget0.ButifwebothreasonedadifferentwayandchoseBeta,thenwe'llbothget1.SoIshouldchooseBeta:1isbiggerthan0,IshouldchooseBeta.What'swrongwiththatargument?Myargumentmustbewrongbecauseitgoesagainstthelessonoftheclassandthelessonsoftheclassaregospelright,they'renotwrongever,sowhat'swrongwiththatargument?Yes,Ale-yeahgood.Student:Wellbecauseyouhavetobeabletoagree,youhavetobeabletospeaktothembutwearen'tallowedtoshowourpartnerswhatwewrote.ProfessorBenPolak:Allright,soitinvolvessomenotionofagreeing.Socertainlypartoftheproblemhere,withthereasoningIjustgaveyou--thereasoningthatsaidIshouldchooseBeta,becauseifwebothreasonthesameway,webothdobetterthatway--involvessomekindofmagicalreasoning.It'sasifI'marguingthatifIreasonthiswayandreasonmyselftochoosingBeta,somehowI'mgoingtomaketherestofyoureasonthesamewaytoo.It'slikeI'vegotESPorI'msomecharacteroutoftheX-Men,isthatwhatit'scalled?TheX-Menright?Nowinfact,thismaycomeasasurprisetoyou,Idon'thaveESP,I'mnotacharacteroutoftheX-Men,andsoyoucan'tactuallyseebrainwavesemittingfrommyhead,andmyreasoningdoesn'taffectyourreasoning.SoifIdidreasonthatway,andchoseBeta,I'mnotgoingtoaffectyourchoiceonewayortheother.That'sthefirstthingthat'swrongwiththatreasoning.Whatelseiswrongwiththatreasoning?Yeah,thatguydownhere.Student:Well,thesecondthatyouchooseBetathensomeone'sgoing-it'sinsomeone'sbestinteresttotakeadvantageofit.ProfessorBenPolak:Allright,sosomeone'sgoingtotakeadvantageofme,butevenmorethanthat,anevenstrongerargument:that'strue,butevenastrongerargument.Wellhowaboutthis?EvenifIwasthatguyintheX-MenortheMatrixorwhateveritwas,whocouldreasonhiswayintomakingpeopledothings.EvenifIcouldmakeeveryoneintheroomchooseBetabytheforceofmybrainwaves,whatshouldIthendo?IshouldchooseAlpha.IfthesearemypayoffsIshouldgoaheadandchooseAlphabecausethatwayIendupgetting3.Sothere'stwothingswrongwiththeargument.One,there'sthismagicalreasoningaspect,myreasoningiscontrollingyouractions.Thatdoesn'thappenintherealworld.Andtwo,evenifthatwasthecaseI'ddobettertomyselfchooseAlpha.So,nevertheless,there'sanelementoftruthinwhatIjustsaid.It'sthefactthatthere'sanelementoftruthinitthatmakesitseemlikeagoodargument.Theelementoftruthisthis.ItistruethatbybothchoosingAlphawebothendedupwithB-'s.Webothendupwithpayoffsof0,ratherthanpayoffsof1.Itistruethatbybothchoosing,bybothfollowingthislessonandnotchoosingthedominatedstrategyBeta,weendedupwithpayoffs,(0,0),thatwerebad.Andthat'sprobablythesecondlessonoftheclass.SoLesson2,andthislessonprobablywouldn'tbeworthstating,ifitwasn'tforsortofacenturyofthoughtandeconomicsthatsaidtheopposite.Sorationalchoice[inthiscase,peoplenotchoosingadominatedstrategy;peoplechoosingadominantstrategy]rationalchoicecanleadtooutcomesthat-whatdoAmericanscallthis?--that"suck."Ifyouwantamoretechnicaltermforthat(andyourememberthisfromEconomics115),itcanleadtooutcomesthatare"inefficient,"thatare"Paretoinefficient,"but"suck"willdofortoday.Rationalchoicesbyrationalplayers,canleadtobadoutcomes.Sothisisafamousexampleforthisreason.It'sagoodillustrationofthispoint.It'safamousexample.What'sthenameofthisexample,somebody?ThisiscalledPrisoner'sDilemma.HowmanyofyouhaveheardofthePrisoner'sDilemmabefore?Mostofyousawitin115,whyisitcalledthePrisoner'sDilemma?Yes,theguyhereinorange.That'sokay;hecanjustpointatyouthat'sfine.Student:Ithinkit'swhetherornottheprisoner'scooperateinthesentencetheyhave,andiftheykindofratouttheotherperson,thentheycanhaveless;butifbothratout,thentheylikeenduplosinglargescale.ProfessorBenPolak:Good,sointhestandardstoryyou'vegotthesetwocrooks,ortwoaccusedcrooks,andthey'reinseparatecellsandthey'rebeinginterviewedseparately--keptapart--andthey'rebothtoldthatifneitherofthemratstheotherguyout,they'llgotojailforsayayear.Iftheybothrateachotherout,they'llendupinjailfortwoyears,Butifyourattheotherguyoutandhedoesn'tratyouout,thenyouwillgohomefreeandhe'llgotojailforfiveyears.Putthatalldownandyouprettyquicklyseethat,regardlesswhethertheotherguyratsyouornot,you'rebetteroffrattinghimout.Now,ifyouhaveneverseenthatPrisoner'sDilemma,youcanseeitprettymucheverynightonashowcalledLaw&Order.HowmanyofyouhaveseenLaw&Order?Ifyouhaven'tseenLaw&Order,thewaytoseeLaw&OrderistogotoarandomTVset,atarandomtime,andturnonarandomchannel.Thishappensineverysingleepisode,somuchsothatifanyofyouactually-ImeanthismightactuallybetrueatYale--butifyouanyofyouortheTVguys:ifanyofyouknowtheguywhowritestheplotsforthis,havehimcometotheclass(soIguesstoseethevideonow)andwegetsomebetterplotlinesinthere.But,ofcourse,that'snottheonlyexample.Thegradegameandthisisnottheonlyexample.TherearelotsofexamplesofPrisoner'sDilemmasoutthere.Let'stryandfindsomeotherones.Sohowmanyofyouhaveroommatesinyourcollege?Howmanyofyouhaveroommates?Mostofyouhaveroommatesright?SoI'mguessingnow,Iwon'tmakeyoushowyourhands,becauseit'sprobablyembarrassing,butwhatisthestateofyourdormrooms,yourshareddormrooms,attheendofthesemesterortheendoftheschoolyear?SoI'mjustguessing,havingbeeninafewofthesethingsovertheyears,thatbytheendofthesemester,orcertainlybytheendoftheschoolyear,thestateoftheaverageYaledormroomisquitedisgusting.Whyisitdisgusting?It'sdisgustingbecausepeopledon'ttidyup.Theydon'tcleanupthosebitsofpizzaandbitsofchewedbreadandcheese,butwhydon'ttheytidyup?Welllet'sjustworkitout.Whatwouldyouliketohappenifyou'resharingadormroom?You'dliketohavetheotherguytidyup,right?Thebestthingforyouistohavetheotherguytidyupandtheworstthingforyouistotidyupfortheotherguy.Butnowworkitout:it'saPrisoner'sDilemma.Iftheotherguydoesn'ttidyup,you'rebestoffnottidyingupeither,becausethelastthingyouwantistobetidyingupfortheotherguy.Andiftheotherguydoestidyup,heytheroom'sclean,whocares?Soeitherway,you'renotgoingtotidyupandyouendupwithatypicalYaledormroom.AmIbeingunfair?Areyourdormroomsallperfect?Thismaybeagenderthingbutwe'renotgoingtogothere.SotherearelotsofPrisoner'sDilemmasoutthere,anyonegotanyotherexamples?Otherexamples?Ididn'tquitehearthat,sorry.Let'stryandgetamikeonitsowecanreallyhearit.Student:[inaudible]ProfessorBenPolak:Okay,indivorcestruggles,okay.You'retooyoungtobeworryingaboutsuchthingsbutnevermind.Yeah,okay,that'sagoodexample.Allright,hiringlawyers,bringinginbigguns.WhataboutanEconomicsexample?Whataboutfirmswhoarecompetinginprices?Bothfirmshaveanincentivetoundercuttheotherfirm,drivingdownprofitsforboth.Thelastthingyouwantistohavetheotherfirmundercutyou,inanattempttopushpricesdown.That'sgoodforustheconsumers,butbadforthefirm,badforindustryprofit.Whatremediesdowesee?We'llcomebacktothislateronintheclass,butlet'shaveapreview.SowhatremediesdoweseeinsocietyforPrisoner'sDilemmas?Whatkindofremediesdowesee?Letmetryandgettheguyhererightinfront.Student:Collusion.ProfessorBenPolak:Collusion;sofirmscouldcollude.Sowhatpreventsthemfromcolluding?Onethingtheycoulddo,presumably,istheycouldwriteacontract,thesefirms.TheycouldsayIwon'tlowermypricesifyoudon'tloweryourprices,andtheycouldputthiscontractinwiththepricylawyer,who'stakingadayofffromthedivorcecourt,andthatwouldsecurethattheywouldn'tlowerpricesoneachother.Isthatright?Sowhywouldn'tthatwork?Whywouldn'twritingacontractherework?It'sagainstthelaw.It'sanillegalcontract.Whataboutyouwithyourroommates?Howmanyofyouhaveawrittencontract,stuckwithamagnetonthefridge,tellingyou,whenyou'resupposedtotidyup.Veryfewofyou.Whydoyoumanagetogetsomecooperationbetweenyouandyourroommatesevenwithoutawrittencontract?Student:It'snotlegallyenforceable.ProfessorBenPolak:Wellitprobablyislegallyenforceableactually.Thisguysaysnot,butitprobablyislegallyenforceable.Heprobablycouldhaveawrittencontractabouttidyingup.Thewomaninhere.Student:Repetition;youdoitoverandover.ProfessorBenPolak:Yeah,somaybeevenamongyourroommates,maybeyoudon'tneedacontractbecauseyoucanmanagetoachievethesameends,bythefactthatyou'regoingtobeinteractingwiththesameperson,overandoveragainduringyourtimeatYale.Sowe'llcomebackandrevisittheideathatrepeatinganinteractionmayallowyoutoobtaincooperation,butwe'renotgoingtocomebacktothatuntilafterthemid-term.That'swaydowntheroadbutwe'llgetthere.Nowonepersonearlieronhadmentionedsomethingaboutcommunication.Ithinkitwassomebodyinthefront,right?Solet'sjustthinkaboutthisasecond.Iscommunicationtheproblemhere?Isthereasonpeoplebehavebadly--Idon'tknow"badly"--peoplechooseAlphainthisgamehere,isitthefactthattheycan'tcommunicate?Supposeyou'dbeenabletotalkbeforehand,sosupposethewomanherewhosenamewas…?Student:Mary.ProfessorBenPolak:…Mary,hadbeenabletotalktothepersonnexttoherwhosenameis…?Student:Erica.ProfessorBenPolak:Erica.Andtheysaid,supposeweknowwe'regoingtobepairedtogether,I'llchooseBetaifyouchooseBeta.Wouldthatwork?Whywouldn'tthatwork?Student:There'snoenforcement.ProfessorBenPolak:There'snoenforcement.Soitisn'tafailureofcommunicationperse.Acontractismorethencommunication,acontractiscommunicationwithteeth.Itactuallychangesthepayoffs.SoIcouldcommunicatewithAliceonagreements,butbackhomeI'mgoingtogoaheadandchooseAlphaanyway;allthebetterifhe'schoosingBeta.Sowe'llcomebackandtalkaboutmoreofthesethingsasthecoursegoeson,butlet'sjustcomebacktothetwoweforgotthere:sothecollusioncaseandthecasebackinLaw&Orderwiththeprisonersinthecell.Howdotheyenforcetheircontracts?Theydon'talwaysrateachotheroutandsomefirmsmanagetocollude?Howdotheymanagetoenforcethosecontracts?Thoseagreements,howaretheyenforced?Student:Theytrusteachother.ProfessorBenPolak:Itcouldbetheytrusteachother,althoughifyoutrustacrookthat'snot…Whatelsecoulditbe?Theguyhereagainwiththebeard,yeah.Student:Couldbeazerosumgame.ProfessorBenPolak:Well,butthisisthegame.Sohere'sthegame.Student:No,butthepay,thewaytheyvalue,thewayofvaluingeach--ProfessorBenPolak:Okay,sothepayoffsmaybedifferent.Ihavesomethingsimplerinmind.Supposetheyhaveawrittencontract,orevenanunwrittencontract,whatenforcesthecontractforcolludingfirmsorcrooksinjail?Yeah.Student:GetsoffScottfreeinfiveyearswhentheotherguygetsout,hemightrunintoasituationwhere[inaudible]ProfessorBenPolak:Yeah,soashortversionofthatis,it'sadifferentkindofcontract.Ifyouratsomeoneoutinjail,someoneputsacontractoutonyou.TonySopranoenforcesthosecontracts.That'sthepurposeofTonySoprano.It'sthepurposeofthemafia.Thereasonthemafiathrivesincountrieswhereit'shardtowritelegalcontracts--let'ssaysomenewpartsoftheformerSovietUnionorsomepartsofAfrica--thereasonthemafiathrivesinthoseenvironments,isthatitsubstitutesforthelawandenforcesbothlegalandillegalcontracts.SoIpromisedawhileagonow,thatweweregoingtocomebackandlookatthisgameundersomeotherpossiblepayoffs.SoIwasn'tunderacontractbutlet'scomebackandfulfillthatpromiseanyway.Sowe'regoingtorevisit,ifnottheDivinitySchool,atleastinpeoplewhohavemoremoralitythanmyfriendsupinthebusinessschool.We'regoingtoaskforthesamegradegameweplayedatthebeginning.Whatwouldhappenifplayer'spayoffslookeddifferent?Sotheseare"possiblepayoffs(2)."I'llgivetheseaname..Wecalledtheotherguys"evilgits."We'llcalltheseguys"indignantangels."Icanneverspellindignant..Isthatroughlyright?Doesthatlookright?Ithinkit'sright.In-dig-nantisn'tit:indignant.Indignantangels,andwe'llseewhyinasecond.Soherearetheirpayoffsandonceagainthebasicstructureofthegamehasn'tchanged.It'sstillI'mchoosingAlphaandBeta,mypairischoosingAlphaandBeta,andthegradesarethesameastheywerebefore.They'rehiddenbythatboardbutyousawthembefore.Butthistimethepayoffsareasfollows.Ontheleaddiagonalwestillhave(0,0)and(1,1).Butnowthegradeshereare-1--I'msorry--thepayoffsare-1and-3,andherethey're-3and-1.What'stheideahere?Thesearen'ttheonlyotherpossiblepayoffs.It'sjustanidea.SupposeIgetanAandmypairgetsaC,thensureIgetthatinitialpayoffof3,butunfortunatelyIcan'tsleepatnightbecauseI'mfeelingsoguilty.IhavesomekindofmoralconscienceandafterI'vesubtractedoffmyguiltfeelingsIendupat-1,sothinkofthisasguilt:somenotionofmorality.Conversely,ifIchoseaBetaandmypairchoosesanAlpha,soIendupwithaCandsheendsupwithanA,thenyouknowIhaveabadtimeexplainingtomyparentswhyIgotaCinthisclass,andIhavetosayabouthowI'mgoingtobepresidentanyway.Butthen,inaddition,Ifeelindignationagainstthisperson.Itisn'tjustthatIgotaC;IgotaCbecauseshemademegetaC,sothatmoralindignationtakesusdownto-3.Soagain,I'mnotclaimingthesearetheonlyotherpossiblepayoffs,butjustanotherpossibilitytolookat.Sosupposethesewerethepayoffsinthegame.Again,suspenddisbeliefasecondandimaginethattheseactuallyareyourpayoffs,andletmeaskyouwhatyouwouldhavedoneinthiscase.Sothinkaboutitasecond.Writeitdown.Writedownwhatyou'regoingtodoonthecornerofyournotepad.JustwritedownanAlphaorBeta:whatyou'regoingtodohere.You'renotallwriting.TheguyintheEnglandshirtisn'twriting.You'vegottobewritingifyouareinanEnglandshirt.Showittoyourneighbor.Let'shaveashowofhands,againIwantyoutokeepyourhandsupsothatJudecanseeitnow.SohowmanyofyouchoseAlphainthiscase?Raiseyourhands.Comeon,don'tbeshy.Raiseyourhands.HowmanychoseBetainthiscase?Howmanypeopleabstained?Notallowedtoabstain:let'stryitagain.Alphainthiscase?Noabstentionshere.Betainthiscase?Sowe'reroughlysplittingtheroom.SomeonewhochoseAlpha?Again:raisetheAlpha'sagain.Letmegetthisguyhere.SowhydidyouchooseAlpha?Student:Youwouldminimizeyourlosses;you'dget0or-1insteadof-3or1.ProfessorBenPolak:Allright,sothisgentlemanissaying-Student:There'snodominantstrategyso-ProfessorBenPolak:Right,sothisgentleman'ssaying,agoodreasonforchoosingAlphainthisgameisit'slessrisky.Theworstcasescenarioislessbad,isawayofsayingit.WhataboutsomebodywhochoseBeta?AlotofyouchoseBeta.Let'shaveashowofhandsontheBeta'sagain.LetmeseetheBeta'sagain.So,raiseyourhands.Canwegetthewomanhere?CanweaskherwhyshechoseBeta?Student:BecauseifyouchooseAlpha,thebestcasescenarioisyouget0,sothat's-ProfessorBenPolak:Okaygood,that'sagoodcounterargument.Sothegentlemanherewaslookingattheworstcasescenario,andthewomanherewaslookingatthebestcasescenario.Andthebestcasescenarioherelookslikegettinga1here.Now,let'saskadifferentquestion.Isoneofthestrategiesdominatedinthisgame?No,neitherstrategyisdominated.Let'sjustcheck.IfmypairchoosesAlpha,thenmychoosingAlphayields0,Beta-3:soAlphawouldbebetter.ButifmypairchoosesBetathenAlphayields-1,Betayields1:inthiscaseBetawouldbebetter.SoAlphainthiscaseisbetteragainstAlpha,andBetaisbetteragainstBeta,butneitherdominateseachother.Sohere'sagamewherewejustchangethepayoffs.Wehavethesamebasicstructure,thesameoutcomes,butweimaginepeoplecaredaboutdifferentthingsandweendupwithaverydifferentanswer.Inthefirstgame,itwaskindofclearthatweshouldchooseAlphaandhereit'snotatallclearwhatwecando--whatweshoulddo.Infact,thiskindofgamehasanameandwe'llrevisititlateroninthesemester.Thiskindofgameiscalleda"coordinationproblem."We'lltalkaboutcoordinationproblemslateron.ThemainlessonIwanttogetoutofthisfortoday,isasimplerlesson.It'sthelessonthatpayoffsmatter.Wechangethepayoffs,wechangewhatpeoplecaredabout,andwegetaverydifferentgamewithaverydifferentoutcome.Sothebasiclessonisthatpayoffsmatter,butletmesayitadifferentway.Sowithoutgivingawaymyagetoomuch--Iguessitwillactually--whenIwasakidgrowingupinEngland,therewasthisguy-therewasapopstar--aslightlypost-punkpopstarcalledJoeJackson,whononeofyouwouldhaveheardof,becauseyouwereallabouttenyearsold,myfault.AndJoeJacksonhadthissongwhichhadthelyric,somethinglike,youcan'tgetwhatyouwantunlessyouknowwhatyouwant.Asastatementoflogic,that'sfalse.Itcouldbethatwhatyouwantjustdropsintoyourlapwithoutyouknowingaboutit.Butasastatementofstrategy,it'saprettygoodidea.It'sagoodideatotryandfigureoutwhatyourgoalsare--whatyou'retryingtoachieve--beforeyougoaheadandanalyzethegame.Sopayoffsmatter.Let'sputitinhisversion."Youcan'tgetwhatyouwant,tillyouknowwhatyouwant."Behonest,howmanyofyouhaveheardofJoeJackson?Thatmakesmefeelold,ohman,okay.Goesdowneveryyear.Sofarwe'velookedatthisgameasplayedbypeoplewhoareevilgits,andwe'velookedatthisgameasplayedbypeoplewhoareindignantangels.Butwecandosomethingmoreinteresting.Wecanimagineplayingthisgameonasortofmixandmatch.Forexample,imagine--thisshouldn'tbehardformostofyou--imaginethatyouareanevilgit,butyouknowthatthepersonyou'replayingagainstisanindignantangel.Soagain,imaginethatyouknowyou'reanevilgit,butyouknowthatthepersonyou'replayingagainstorwith,isanindignantangel.Whatshouldyoudointhatcase?Whatshouldwedo?WhothinksyoushouldchooseAlphainthatcase?Let'spantheroomagainifwecan.Keepyourhandsupsothatyoucansee.WhothinksyoushouldchooseBetainthatcase?Who'sabstaininghere?Notallowedtoabstaininthisclass:it'sacompleteno-no.Okay,we'llallowsomeabstentioninthefirstdaybutnotbeyondtoday.Let'shavealook.Let'sanalyzethiscombinedgame.Sowhatdoesthisgamelooklike?It'sanevilgitversusanindignantangelandwecanputthepayoffmatrixtogetherbycombiningthematriceswehadbefore.Sointhiscase,thisismeasalways.Thisismypair,thecolumnplayer.Mypayoffsaregoingtobewhat?Mypayoffsaregoingtobeevil-gitpayoffs,sotheycomefromthematrixupthere.Soifsomeonewilljusthelpmereadingitoffthere.That'sa0,a3,a-1,anda1.Myopponentormypartner'spayoffscomefromtheindignantangelmatrix.Sotheycomefromhere.There'sa0,a-3,a-1,anda1.EveryoneseehowIconstructedthat?Sojusttoremindyouagain,thefirstpayoffistherowplayer'spayoff,inthiscasetheevilgit.Andthesecondpayoffisthecolumnplayer'spayoff,inthiscasetheindignantangel.Nowwe'vesetitupasamatrix,let'stryagainthatquestionIaskedbefore.Supposeyou'retherowplayerhere.You'retheevilgit.Thoseareyourpayoffs.You'replayingagainstanindignantangel,whatwouldyoudo?Soonceagain,noabstentionsthistime:whowouldchooseAlpha?Let'shaveashowofhandsagain,keepyourhandsupasecond.WhowouldchooseBeta?VeryfewBeta's,butmostlyAlpha's.Alpha,Ithink,istherightanswerherebutwhy?WhyisAlphatherightanswerhere?Yeah,canwegetthisguyhere?Student:It'sthedominantstrategy.ProfessorBenPolak:Good.Actuallynothinghaschangedfromthegamewestartedwith.ThefactthatIchangedtheotherguy'spayoffsdidn'tmatterhere.Alphawasdominantbefore--itdominatedBetabefore--anditstilldominatesBeta.Let'sjustcheck.IfmyopponentchoosesAlphaandIchooseAlpha,Iget0;Beta,Iget-1.SoAlphawouldbebetter.IfmyopponentchoosesBetaandIchooseAlpha,Iget3;Beta,Iget1.OnceagainAlphaisbetter.Soasbefore,AlphadoesbetterthanBetaforme,regardlessofwhattheotherpersondoes.AlphadominatesBeta.Whatwasthefirstlessonoftheclass?Shoutitoutplease.Right,soyoushouldallhavebeenchoosinginthisgame,youallshouldhavechosenAlpha.Sotheonepersonwhodidn'twe'lllethimofffortoday.SoAlphadominatesBetahere.Let'sflipthingsaround.Supposenow--hardertoimagine,butlet'stryit--supposenowthatyouareanindignantangelandyou'replayingagainst,andyouknowthis,you'replayingagainstanevilgit.You'reanindignantangel,soyouhavethepayoffsthatarestillthereandyou'replayingagainstanevilgit,whichisthepayoffswecoveredupbutwe'llreproducethem.Let'sproducethatmatrix.Bytheway,ifthisisbeginningtosoundlikeawrestlingmatch,Idon'tmeanitto.Let'stryhere:Alpha,Beta,Alpha,Beta,pair,me.Somypayoffsthistime,aretheindignantangelpayoffs.Somineare0,-1,-3,and1.Andmyopponent'spayoffsarewhatwouldhavebeenmypayoffsbefore.Theycomefromtheothermatrix.Let'sjustshowyouit.Theycomefromthismatrix.Sothey'regoingtobe0,-1,3,1.Itookthesecondpayofffromthatmatrixandmadeitthesecondpayoffinthismatrix.EveryoneseehowIdidthat?Onceagain,therowplayeristhefirstpayoffandthecolumnplayeristheotherpayoff.Whatshouldyoudointhiscase?You'retheindignantangel.You'replayingagainstthisevilgit.Whatshouldyoudo?Writedownonyournotepadwhatyoushoulddo.Showittoyourneighborsoyoucan'tcheat,oryoucancheatbutyou'llbeshamedinfrontofyourneighbor.Raiseyourhands.LetJudeseeit.RaiseyourhandsandkeepthemupifyouchoseAlphanow.HowaboutifyouchoseBetanow?SooneortwoBeta's,mostlyAlpha's.Welllet'ssee.Let'sreasonthisthroughasecond.DoesmyAlphadominatemyBeta?No,infact,Alphadoesn'tdominateBetaforme.Itdoesn'tdominateBeta.IfmypairchoosesAlphathenAlphagetsme0;Beta-3.SoAlphadoesbetter.ButifmypairchoosesBeta,thenAlphagetsme-1;Betagetsme1.InthiscaseBetaisbetter.Aswesawbefore,AlphaisbetteragainstAlpha.BetaisbetteragainstBeta.There'snodominancegoingonhere.Nevertheless,atleast90%ofyouchoseAlphahere,andthat'stherightanswer.Why?WhyshouldyouchooseAlphahere?Somebody…canwegettheguywiththebeardhere?Waitforthemike,great.Student:WehadacknowledgedthatAlphaisadominantstrategyformyopponentsowemustchoosebasedupon,orknowingthatmypartnerisgoingtochooseAlpha.ProfessorBenPolak:Good,andyournameis?Student:Henry.ProfessorBenPolak:Henry.SoHenryissayingsureIdon'thaveadominatedstrategy.MyAlphadoesn'tdominatemyBeta.Butlookatmyopponent.Myopponent'sAlphadominatesherBeta.IfIchooseAlphaandshechoosesAlphatoget0;Betashegets-1.Alphaisbetter.IfIchooseBeta,ifshechoosesAlphashegets3;Beta1.AgainAlphaisbetter.Formyopponent,AlphadominatesBeta.Sobythinkingaboutmyopponent,byputtingmyselfinmyopponent'sshoes,Irealizethatshehasadominantstrategy,Alpha.She'sgoingtochooseAlphaandmybestresponseagainstAlphaistochooseAlphamyself.Sohere,thistime,myAlphadoesnotdominateBetabutmypair'schoiceofAlphadominatesherchoice,herpossiblechoiceofBeta.SoshewillchooseAlpha.AndonceIknowthatshe'sgoingtochooseAlpha,it'sclearthatIshouldchooseAlphaandget0ratherthanBetaandget-3.SoIshouldchooseAlphaalso.Okay,sonowwe'veseenfourdifferentcombinations.We'veseenacasewhereanevilgitwasplayinganevilgit;whereanindignantangelwasplayinganindignantangel;andwe'veseenboththeflipsofthose:theevilgitversustheindignantangel;andtheindignantangelagainsttheevilgit.Whyarewedoingthis?Becausethere'sanimportantlessonhere.What'sthelessonhere?Thelessonis--comesfromthisgame--thatagreatwaytoanalyzegames,agreatwaytogetusedtotheideaofstrategicthinking,perhapseventheessenceofstrategicthinking,istheabilitytoputyourselfinsomeoneelse'sshoes,figureoutwhattheirpayoffsare,andtryandfigureoutwhatthey'regoingtodo.Sothebiglessonofthisgameis--Iforgotwhatnumberwe'reuptoo--IguessthisisLesson4Ithink.Lesson4is:putyourselfinothers'shoesandtrytofigureoutwhattheywilldo.Inasense,thisisthefirstdifficultlessonoftheclass.It'seasytospotwhenastrategyisdominant,moreorless.It'sprettyeasytofigureout,youhavetoknowaboutyourownpayoffs.Butthehardthinginlife,isgettingyoutocomeoutofyourownselvesabit,realizingit's"notallaboutyou."You'vegottoputyourselfinotherpeople'sshoestofigureoutwhattheycareaboutandwhatthey'regoingtotryanddo,soyoucanrespondwelltothat.Whilewe'rehere,let'sjustmentionthatthingswillgetmorecomplicatedinaworldwhereIdon'tactuallyknowthepayoffsofmyopponent.It'smucheasiertofigureoutmyownpayoffsthantofigureoutmyopponent'spayoffs.ImightnotknowwhetherI'mplayingsomeonewho'sanevilgitoranindignantangel.SoI'mgoingtohavetofigureoutwhattheoddsareofthatindoingthisexercise.Andwe'regoingtocomebacktothatideatoowayattheendoftheclass,butthat'sgettingabitaheadofourselves,butwe'llgetthere.Now,itturnsoutthatthisgame,thisPrisoner'sDilemma,withtheAlpha'sandBeta's,oressentiallythesamegame,hasbeenplayedmany,many,manytimesinexperiments.Sooutthereintherealworld--Ithinkwecandothishere--outthereintherealworldwhentheydotheseexperiments,theyfindoutthatroughly70%ofpeoplechooseAlphaandroughly30%chooseBeta.Roughly,almostathirdchooseBeta.Whatdowethinkisgoingon?That'sathirdofthepeoplewhoseemtobechoosingadominatedstrategy…orisit?What'sgoingonthere?Whydoyouthink30%ofpeoplearechoosingBeta?Anybody?Canwecatchthisguyhere?Student:TheymightbemotivatedbythefactthateverypersonwhochoosesBetaraisestheaveragescore.ProfessorBenPolak:Theycouldbemoralpeople.Soonepossibilityis:this30%ofpeopleintherealworldwhochooseBetaarejustnicepeople.Whatelsecoulditbe?Yeah?Student:Iknowthismightbechangingthegamealittlebit,butifyoueverexpectedtoplaythesamegamewiththepartneryouhavemore[inaudible]ProfessorBenPolak:Allright,theycouldbethinkingthey'regoingtoplayagain.Student:[inaudible]longrunpayoffsaregreaterifyouchooseBetaeverytime.ProfessorBenPolak:Soitcouldbethattheythinkthatthisisactually--theyhaven'tunderstoodtheexperimentandtheythinkthisisamultishotgame,notaoneshotgame,good.Whatelsecoulditbe?What'sthesimplestexplanation?What'stheotherobviousexplanation?Theycouldjustbestupid,right?Itcouldbe.,Areweallowedtosaythatinclass?Let'sbehonesthere,whenwesayexperimentsintherealworldinGameTheory--ortheonesyoureadaboutinTheNewYorkTimes--therealworldwhenitcomestoexperimentsinEconomicsreallymeansundergraduatesattheUniversityofArizona.Imean,I'mnotmakingitup.Itjustdoes.Theyallare.Idon'tknowanythingabout…areanyofyoufromArizona,Idon'tknow.Idon'tknowwhethertheaverageundergradattheUniversityofArizonajusthasasunnypersonalityorwhetherthey"spenttoolonginthesun."Ijustdon'tknowwhichitis,right?Wecan'treallydistinguishfromthis.HowaboutatYale.What'sournumbershere.Howaboutinthisclass?Doyouwanttomikeyourcolleaguehere?So238atYale--thisisYale--versus36.Soevenatmylevelofarithmeticthat'salotlessthan30%.That'smorelikelessthan15%.It'sabout15%Iguess.So236--I'msorry238--choseAlpha,and36choseBeta.Nowthere'sonemorelessoninthisclassandthisisgoingtobeit.Thisisn'ttheendoftheclassbutonemorelessontotakehome.Youguysaregoingtobeplayinggamesamongeachothertodayanduntil--whateveritis?--December7,whateveristheendofterm.Lookaroundeachother.Youbettergettoknoweachotherabit.Andwhatdidwelearntodayaboutyouguys?Thelessonhere,Lesson5,is"Yalestudentsareevil."Beawareofthatwhenyou'replayinggames.Iwanttoplayonemoregametodayintheremainingminutes.Itdoesn'tmatterifwefinishalittlebitearly,butIwanttotrytogetthisgameatleaststarted.SodoyouallhaveGame#2infrontofyou?Justwhileyou'rereadingthatover,canIalsomakesureyou'veallgotyourlegalformsandyou'regoingtosign.Don'twalkawaywithyourlegalforms,weneedtogetthosecollectedin.Soattheendoftalkingaboutthisgame,I'mgoingtocollectinboththesecondgamefortheclassandalsothelegalform.Ifyoudon'thavealegalform,ifyou'velostitorsomething,it'sonline.Let'shavealookatthatsecondgame.I'llreaditoutforyou.Game2:"pickanumber."Everyonegotthis?Anyonenotgotthis?Everyonegotit?Good."Withoutshowingyourneighborwhatyou'redoing,putintheboxbelowawholenumberbetween1anda100[wholenumberbetween1and100--integer.]Wewillcalculatetheaveragenumberchosenintheclass.Thewinnerinthisgameisthepersonwhosenumberisclosesttotwo-thirdstimestheaverageintheclass."[Again:thewinneristhepersonwhosenumberisclosesttotwo-thirdstimestheaveragenumberintheclass.]Thewinnerwillwin$5minusthedifferenceinpenniesbetweenherchoiceandthattwo-thirdsoftheaverage."Justtomakesureyou'veunderstoodthis,letmedoanexampleontheboard.I'vegotonemoreboard;that'sgood.Soimaginetherewerethreepeopleintheclass,andimaginethattheychose25,5,and60.So25plus5plus60is90.Peopleshouldfeelfreetocorrectmyarithmeticbecauseit'softenwrong;90right?Two-thirdsof90,whoops,whatdoIneed,startagain.Ineedtodivideitbythreetogettheaverage.Sotheaverageis30.Sothetotalis90,theaverageis30,amIrightsofar?Sotwo-thirdsoftheaverageis20.I'mlookingdesperatelyattheT.A.Isthatright?Okay,sotheaverageis30andtwo-thirdsoftheaverageis20.Sowho'sthewinnerhere,whichnumberwouldhavewonhere?25wouldhavewon.25wouldhavebeentheclosest,andwhatwouldtheyhavewon?Theywouldhavewonfivebucksminusfivecentsforatotaloffourninety-five.Nowtomakethisinteresting,let'splaythisforreal.Sothisofcoursereliesonmehavingbroughtsomemoneyandwe'llhavetodothiswithoutdislodgingthemicrophone.SoI'mgoingtoseeifIhave…sorryaboutthat.I'mgoingtoseeifIhaveenoughmoneytodothisinclassforreal.Whenweplayedthisgameintheolddays,duringthedotcomboomwiththeMBAstudents,youhadtoputfiftydollarsonthetabletogettheminterested.Graduatestudents:fivecentswilldoit.Okay,sothisisa--there'ssomeblokewithabeardonthisone.YeahthisisLincolnapparently.Whoknew,Lincoln?Okay,sothisisafive-dollarnoteandI'mgoingtoputit--sorryaboutthatagain--I'mgoingtoputitinanenvelope.I'mnotcheatinganybody?Nomagictrickshere.Andthisisgoingtobetheprizeforthisgameandwebettergivethistosomeonewetrust.It'stheprizefor159.Whodoyouguystrust?Thecameraguy.OkayJude:weknowJude'sgoingtobetherenextweek.I'mgivingittoJude.Youcan'tseethisoncamera.--peopleathome--butI'mgivingittoJudeokay.I'mgoingtoputithere,andJudehastoshowupnextweekwiththeprize.Ithoughtweshouldgiveittotheguyattheback,whoisthemoralguy.Whoisourmoralguyattheback?Wellnevermind,wewillgiveittoJude.WeknowJude'sgoingtobehere.Allright,haseveryoneputanumberdown?Anyquestions?Justshoutthemouttome.Student:Sogiventhatweonlyhaveonefivedollarbilldoestherehavetobeoneuniquewinner,andifso,howisthatdeterminedifwehavemultiplepeoplewhoare-ProfessorBenPolak:That'sagoodquestion.Ifthere'smultiplewinners,we'lldivideitbutwe'llmakesureeveryonehasapositivewinning.Goodquestion.Giventhenumberofpeopleintheroomtheremaybemultiplewinners,Iacceptthatpossibility.Haseveryonewrittendownanumbernow?Allright,sohandyournumberstotheendoftherow,butdon'tgoyet.Handitontotheendoftherow.BeforeyougoIwantfivethingsfromyou.Iwanttoknowthefivelessonsfromthisclass.Tellmewhatyoulearnt?Whatwerethefivelessons?Withoutlookingatyournotes,whatwerethefivelessons?Anybody,shoutoutoneofthelessons,yesmadam.Student:Don'tplayastrictlydominatedstrategy.ProfessorBenPolak:Don'tplayastrictlydominatedstrategy,anythingelse?Yessir.Student:Yalestudentsareevil.ProfessorBenPolak:Yalestudentsareevil.Twolessonsdown,threetogo.Theguyoverhere.Student:Rationalchoicescanleadtobadoutcomes.ProfessorBenPolak:Rationalchoicescanleadtobadoutcomes.Weputitmoregraphicallybeforebutthat'sfine.Twomoreoutcomes.Student:Putyourselfinotherpeople'sshoes.ProfessorBenPolak:Putyourselfinotherpeople'sshoesandI'mmissingone,Ican'trecallwhichoneI'mmissingnow.Student:Youcan'tgetwhatyouwantsoyou-ProfessorBenPolak:Youcan'tgetwhatyouwant.Youcouldbutit'sagoodideatofigureoutwhatyouwantbeforeyoutryandgetwhatyouwant.Fivethingsyoulearnttoday,handinyournumbersandthelegalformsandI'llseeyouonMonday.[endoftranscript]
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[转帖]博弈论是理解生活的工具
2009年05月01日03:2021世纪经济报道梁捷博弈论已被广泛地运用到现代经济学的各个分支，也先后帮助近十名经济学家获得了诺贝尔奖。只要是两方(也可以多方)相互竞争(也可以合作)的情景，不管结果是零和、双赢、双输，都可以化简为博弈论范式，用它来解释、预测和策略建议。回顾博弈论的发端，如它名字一般，也正是出于实用需要而被发明。说得更准确一点，是战争需要。上世纪40年代，著名美籍匈牙利数学家冯·诺依曼开始把精力转向应用数学，研究诸如导弹弹道、气象预测、密码破解、计算机运算等问题，1947年军队的嘉奖令赞扬他是物理学家、工程师、武器设计师和爱国主义者。他在研究这些问题的间歇，也开始琢磨战争中各方实际可能的策略选择。他以数学家的敏感将问题抽象出来。他研究发现，博弈双方中的任何一方，如果对每种可能的博弈策略，都考虑了可能遭到的极大损失，从而选择“极大损失”中最小的一种策略，那就是“最优”策略，从统计角度来看，他能够确保方案是整体最佳的。这一发现被称作“最小最大定理”，成为当代博弈论的基础，也是博弈论发展史上第一个里程碑。没过多少年，博弈论又遭遇到新问题，60年代的古巴导弹危机引起了全世界的关注。1962年夏，美国发现古巴在建设核导弹基地。到了10月份，肯尼迪终于强硬起来，对古巴进行海上封锁，禁止苏联船只进入古巴。而苏联也不甘示弱，赫鲁晓夫声称，如果美国敢于禁止苏联船舶停靠古巴，苏联将不惜一战。局面紧张，一触即发，经济学家后来归纳说，这就是典型的“懦夫博弈”。教科书上常常用另一个故事来描述这种类型的博弈。美国年轻人中曾经流行这样的游戏，两人分别驾驶两辆汽车，在一条宽阔道路上面对面地高速行驶，看谁先忍不住转动方向盘，谁就被讥为“懦夫”。若两个人谁都不肯做“懦夫”，结果必是车毁人亡。好在后来肯尼迪与赫鲁晓夫都没有逞匹夫之勇。肯尼迪向赫鲁晓夫发出一封婉转的“提议信”，赫鲁晓夫也借这个台阶而下，利用莫斯科电台广播了回信，随后撤走了部署在古巴的42枚导弹。危机终于消弭于无形。这一点给予博弈论专家极大的启示，真正的竞争策略不一定非得真刀实枪，那样做的代价太大。有时通过信息沟通、话语谈判、姿态展示，也可以起到同样的结果。信息是博弈的武器，话语亦是博弈的策略。因为博弈双方是活生生的人，就会根据对方不同策略来动态评估局势，随时修正、改变原定的最优策略。自此以后，这种向度的博弈论研究大大活跃起来，也使得我们更深地了解到经济行为、社会组织以及人类思维的复杂性。计算机在国际象棋上的重大突破即是一个很好的例子。它告诉我们，博弈不只是计算，还有感知、判断和理解。众所周知，国际象棋的空间有限、子力有限、最终目标明确，而且随着棋局进展，棋盘上的棋子逐渐减少，局面趋于简化，理论上有可能用计算机演算出所有可能结果，并从中选择最优路径。如果计算机真的做到这一点，那么在全世界流行上千年、耗费无数聪明人士毕生心血的游戏就再无意义。而上世纪九十年代，电脑深蓝几乎做到了这一点。1996年2月，深蓝与世界冠军卡斯帕罗夫展开六局四胜的较量，很快赢下第一局，先声夺人。但是卡斯帕罗夫摸准对手的缺陷之后，连扳五局，赢得了比赛胜利。表面看起来，这是一场电脑与人脑的决战，但背后更深的含义是计算能力与判断能力的较量。卡斯帕罗夫的计算能力虽然远超常人，但每个回合能思考的深度也不大会超过十步，与计算机每秒数亿步的计算能力比起来，完全不在一个数量级。但是人类大脑会对不同局面做出整体上的判断和评估，选择朝对自己更有利的整体局面去发展。这一点判断力却是计算机不可能完全掌握的。卡斯帕罗夫凭借人脑的判断力，战胜了电脑的计算力。十五个月以后，经过改进的深蓝卷土重来，在新一轮的六局四胜制比赛中打败了卡斯帕罗夫。这至少说明一个问题，计算机的发展比人脑的进步深度要快。而我们仔细探究深蓝在这十五个月里发生了什么改变，就会发现它并非在计算速度上有明显提高，而是对卡斯帕罗夫进行了“针对性训练”，很多象棋大师帮助深蓝学会一些局面判断的技巧，从而它开始模仿人类思维。最终，它并非以超群的计算能力获胜，而只是更像人一样判断和认知，辅助计算能力，才打败了卡斯帕罗夫。事实上，人类博弈有多种复杂手段，都不是单纯计算所能解释。比如下棋时，“弃子”是一种看似非理性的策略，计算机不会贸然采用，可在人与人之间对弈时并不罕见。“弃子”策略可能传递多重含义。第一，我要表明自身陷入狂热的、冒险的、非理性状态，不和你在规定的套路上玩；第二，我自绝退路，在子力上弱于你，唯一选择就是在短期内将你置于死地。如果不幸被拖入阵地战，由于子力弱势，我非输不可；第三，我不想和你维持表面上的客套，平缓地推进局面，就是要和你马上分个高低；第四，我在心理上藐视你，以更少的子力就能将你击败。而如果你不敢吃我的“弃子”，那么在心理上更是落了下风。国际象棋高手无一不是心理战的高手，这种能力与基本的计算、判断能力一道构成棋手的基本素质。电脑不会受到心理影响，也就不会用心理战来对付别人。真要解释和预测世界，博弈论不得不直面这些策略所包含的复杂心理。古人虽不懂博弈论，但早已学会运用策略，并且积累下丰富的经验。现代的博弈论一方面要对这些策略思维经验给予科学解析，一方面也应从传统智慧中汲取营养，丰富自身的框架。出生于印度的数理经济学大师迪克西特很清楚这一点，这才能写出这本深入浅出的《策略博弈》，已经成为20世纪90年代以来国际上最为流行的通俗博弈论教科书之一。迪克西特既写过更通俗、适合MBA学生阅读的《策略思维》，也写过仅供专业人士研读的《经济理论中的最优化方法》。这本《策略博弈》介于两者之间，用严格的博弈论框架拆解了大量日常生活中的案例。迪克西特很好地证明了一点，博弈论不仅是一套学问，也是我们理解生活的工具。用萨缪尔森的话说，了解博弈论，将改变你整个一生的思维方式。
