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On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games

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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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File URL: http://cowles.yale.edu/sites/default/files/files/pub/d18/d1848.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1848.

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Length: 20 pages
Date of creation: Feb 2012
Publication status: Published in Games and Economic Behavior (May 2014), 85: 70-83
Handle: RePEc:cwl:cwldpp:1848
Contact details of provider: Postal:
Yale University, Box 208281, New Haven, CT 06520-8281 USA

Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Stefano Lovo & Johannes Hörner & Tristan Tomala, 2011. "Belief-free equilibria in games with incomplete information: characterization and existence," Post-Print hal-00630299, HAL.
  2. David Rahman & Ichiro Obara, 2010. "Mediated Partnerships," Econometrica, Econometric Society, vol. 78(1), pages 285-308, 01.
  3. D. Fudenberg & D. K. Levine, 1994. "Efficiency and Observability with Long-Run and Short-Run Players," Levine's Working Paper Archive 627, David K. Levine.
  4. LOVO, Stefano & HÖRNER, Johanes, 2006. "Belief-free Equilibria in games with incomplete information," Les Cahiers de Recherche 845, HEC Paris.
  5. Tristan Tomala, 2009. "Perfect communication equilibria in repeated games with imperfect monitoring," Post-Print hal-00464537, HAL.
  6. Drew Fudenberg & Yuichi Yamamoto, 2010. "Repeated Games Where the Payoffs and Monitoring Structure Are Unknown," Econometrica, Econometric Society, vol. 78(5), pages 1673-1710, 09.
  7. Nicolas Vieille & Johannes Hörner & Takuo Sugaya & Satoru Takahashi, 2011. "Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem," Post-Print hal-00609191, HAL.
  8. SORIN, Sylvain, 1988. "Repeated games with complete information," CORE Discussion Papers 1988022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine.
  10. 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.
  11. repec:dau:papers:123456789/6102 is not listed on IDEAS
  12. Yuichi Yamamoto, 2010. "The use of public randomization in discounted repeated games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 431-443, July.
  13. repec:dau:papers:123456789/9834 is not listed on IDEAS
  14. Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
  15. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  16. Tristan Tomala & J. Hörner & S. Lovo, 2009. "Existence of belief-free equilibria in games with incomplete information and known-own payoffs," Post-Print hal-00495690, HAL.
  17. Dilip Abreu & Yuliy Sannikov, 2011. "An Algorithm for Two Player Repeated Games with Perfect Monitoring," Working Papers 1360, Princeton University, Department of Economics, Econometric Research Program..
  18. Renault, Jerome & Tomala, Tristan, 2004. "Communication equilibrium payoffs in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 49(2), pages 313-344, November.
  19. A. J. Hoffman & R. M. Karp, 1966. "On Nonterminating Stochastic Games," Management Science, INFORMS, vol. 12(5), pages 359-370, January.
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