Extremal Pure Strategies and Monotonicity in Repeated Games

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• 作者：Kimmo Berg
• 关键词：Repeated games ; Minimum payoff ; Monotonicity ; Equilibrium path ; Unequal discount factors ; Subgame perfection
• 刊名：Computational Economics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：49
• 期：3
• 页码：387-404
• 全文大小：
• 刊物类别：Business and Economics
• 刊物主题：Economic Theory/Quantitative Economics/Mathematical Methods; Computer Appl. in Social and Behavioral Sciences; Operation Research/Decision Theory; Behavioral/Experimental Economics; Math Applications
• 出版者：Springer US
• ISSN：1572-9974
• 卷排序：49

文摘

The recent development of computational methods in repeated games has made it possible to study the properties of subgame-perfect equilibria in more detail. This paper shows that the lowest equilibrium payoffs may increase in pure strategies when the players become more patient and this may cause the set of equilibrium paths to be non-monotonic. A numerical example is constructed such that a path is no longer equilibrium when the players’ discount factors increase. This property can be more easily seen when the players have different time preferences, since in these games the punishment strategies may rely on the differences between the players’ discount factors. A sufficient condition for the monotonicity of equilibrium paths is that the lowest equilibrium payoffs do not increase, i.e., the punishments should not become milder.