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On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games

  • Johannes Horner
  • Satoru Takahashi
  • Nicolas Vieille

This 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 Hörner, 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.

(This abstract was borrowed from another version of this item.)

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File URL: http://www.dklevine.com/archive/refs4786969000000000412.pdf
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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 786969000000000412.

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Date of creation: 13 Apr 2012
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Handle: RePEc:cla:levarc:786969000000000412
Contact details of provider: Web page: http://www.dklevine.com/

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  1. Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
  2. Takahashi, Satoru & Levine, David & Fudenberg, Drew, 2007. "Perfect Public Equilibrium When Players Are Patient," Scholarly Articles 3196336, Harvard University Department of Economics.
  3. 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.
  4. SORIN, Sylvain, 1988. "Repeated games with complete information," CORE Discussion Papers 1988022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Tomala, Tristan, 2009. "Perfect Communication Equilibria in Repeated Games with Imperfect Monitoring," Economics Papers from University Paris Dauphine 123456789/6102, Paris Dauphine University.
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