On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games
AbstractThis paper provides a dual characterization of the limit set of perfect public equilibrium payoffs in stochastic games (in particular, repeated games) as the discount factor tends to one. As a first corollary, the folk theorems of Fudenberg, Levine and Maskin (1994), Kandori and Matsushima (1998) and HÃ¶rner, Sugaya, Takahashi and Vieille (2011) obtain. As a second corollary, in the context of repeated games, it follows that this limit set of payoffs is a polytope (a bounded polyhedron) when attention is restricted to equilibria in pure strategies. We provide a two-player game in which this limit set is not a polytope when mixed strategies are considered.
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Bibliographic InfoPaper provided by David K. Levine in its series Levine's Working Paper Archive with number 786969000000000412.
Date of creation: 13 Apr 2012
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Other versions of this item:
- Johannes Horner & Satoru Takahashi & Nicolas Vieille, 2012. "On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games," Cowles Foundation Discussion Papers 1848, Cowles Foundation for Research in Economics, Yale University.
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-04-23 (All new papers)
- NEP-GTH-2012-04-23 (Game Theory)
- NEP-MIC-2012-04-23 (Microeconomics)
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"Perfect public equilibrium when players are patient,"
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- Drew Fudenberg & David K. Levine & Satoru Takahashi, 2004. "Perfect Public Equilibrium When Players Are Patient," Harvard Institute of Economic Research Working Papers 2051, Harvard - Institute of Economic Research.
- Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
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- Johannes Hörner & Takuo Sugaya & Satoru Takahashi & Nicolas Vieille, 2011. "Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem," Econometrica, Econometric Society, vol. 79(4), pages 1277-1318, 07.
- Tomala, Tristan, 2009. "Perfect Communication Equilibria in Repeated Games with Imperfect Monitoring," Economics Papers from University Paris Dauphine 123456789/6102, Paris Dauphine University.
- Du, Chuang, 2012. "Solving payoff sets of perfect public equilibria: an example," MPRA Paper 38622, University Library of Munich, Germany.
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