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1.9 什么是标准式博弈的混合战略?什么是标准式博弈的混合战略纳什均衡?
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1.10 证明在1.1节中所分析的3个标准式博弈——囚徒困境、图1.1.1和图1.1.4中,不存在混合战略纳什均衡。
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1.11 解出习题1.2所给博弈的混合战略纳什均衡。
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1.12 求出下面标准式博弈的混合战略纳什均衡。
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1.13 两个企业各有一个工作空缺,假设企业所给的工资不同(其原因不在此处讨论,但关系到每一个空缺的价值):企业i给的工资为wi,这里(1/2)w1<w2<2w1。设想有两个工人,每人只能申请一份工作,两人同时决定是申请企业1的工作,还是向企业2申请。如果只有一个工人向一个企业申请,他就会得到这份工作;如果两个工人同时向一个企业申请工作,则企业随机选择一个工人,另一人就会失业(这时收益为0)。解出两工人标准式博弈的纳什均衡。(要更进一步了解企业是如何决定工资的,请参阅蒙哥马利(Montgomery),1991)
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1.14 证明附录1.1.C中的命题B不仅对纯战略成立,对混合战略同样成立:在混合战略纳什均衡中,概率大于0的战略一定不会被重复剔除严格劣战略所剔除。
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博弈论基础 1.6 参考文献
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Aumann,R.1974.“Subjectivity and Correlation in Randomized Strategies”.Journal of Mathematical Economics1:67—96.
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——.1976.“Agreeing to Disagree.”Annals of Statistics4:1236—39.
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——.1987.“Correlated Equilibrium as an Expression of Bayesian Rationality.”Econometrica55:1—18.
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Bertrand,J.1883.“Theorie Mathematique de la Richesse Sociale.”Journal des Savants499—508.
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Brandenburger,A.1992.“Knowledge and Equilibrium in Games.”Forthcoming in Journal of Economic Perspectives.
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Cournot,A.1838.Recherches sur Les Principes Mathematiques de la theorie des Richesses.English edition:Researches into the Methematical Principles of the Thoery of Wealth.Edited by N.Bacon.New York:Macmillan,1897.
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Dasgupta,P.,and E.Maskin.1986.“The Existence of Equilibrium in Discontinuous Economic Games,I:Theory.”Review of Economic Studies53:1—26.
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Farber,H.1980.“An Analysis of Final-Offer Arbitration.”Journal of Conflict Resolution35:683—705.
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Friedman,J.1971.“A Noncooperative Equilirium for Supergames.”Review of Economic Studies28:1—12.
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Gibbons,R.1988.“Learning in Equilibrium Models of Arbitration.”American Economic Review78:896—912.
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Hardin,G.1968“The tragedy of the Commons.”Science162:1243—48.
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Harsanyi,J.1973.“Games with Randomly Disturbed Payoffs:A New Rationale for Mixed Strategy Equilibrium Points.”International Journal of Game Theory2:1—23.
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Hotelling,H.1929.“Stability in Competition.”Economic Journal39:41—57.
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