On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games
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.
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- Sorin, Sylvain, 1992.
"Repeated games with complete information,"
Handbook of Game Theory with Economic Applications,
in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 4, pages 71-107
- Fudenberg, Drew & Levine, David K. & Takahashi, Satoru, 2007.
"Perfect public equilibrium when players are patient,"
Games and Economic Behavior,
Elsevier, vol. 61(1), pages 27-49, October.
- 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.
- Takahashi, Satoru & Levine, David & Fudenberg, Drew, 2007. "Perfect Public Equilibrium When Players Are Patient," Scholarly Articles 3196336, Harvard University Department of Economics.
- Drew Fudenberg & David K Levine & Satoru Takahashi, 2004. "Perfect Public Equilibrium When Players are Patient," Levine's Working Paper Archive 618897000000000865, David K. Levine.
- 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.
- Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
- 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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