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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 H�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.

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

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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
Handle: RePEc:cla:levarc:786969000000000412
Contact details of provider: Web page: http://www.dklevine.com/

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  1. 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..
  2. Stefano Lovo & Johannes Hörner & Tristan Tomala, 2009. "Belief-Free Equilibria in Games With Incomplete Information," Post-Print hal-00459955, HAL.
  3. repec:dau:papers:123456789/6102 is not listed on IDEAS
  4. Fudenberg, Drew & Yamamoto, Yuichi, 2010. "Repeated Games Where the Payoffs and Monitoring Structure Are Unknown," Scholarly Articles 13411374, Harvard University Department of Economics.
  5. Drew Fudenberg & David K Levine, 1999. "Efficiency and Observability with Long-Run and Short-Run Players," Levine's Working Paper Archive 81, David K. Levine.
  6. Stefano Lovo & Tristan Tomala & Johannes Hörner, 2008. "Belief-free equilibria in games with incomplete information: characterization and existence," Working Papers hal-00489877, HAL.
  7. 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.
  8. Tristan Tomala, 2009. "Perfect communication equilibria in repeated games with imperfect monitoring," Post-Print hal-00464537, HAL.
  9. 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.
  10. A. J. Hoffman & R. M. Karp, 1966. "On Nonterminating Stochastic Games," Management Science, INFORMS, vol. 12(5), pages 359-370, January.
  11. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine.
  12. Johannes Hörner & Stefano Lovo, 2009. "Belief-Free Equilibria in Games With Incomplete Information," Econometrica, Econometric Society, vol. 77(2), pages 453-487, 03.
  13. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  14. repec:dau:papers:123456789/9834 is not listed on IDEAS
  15. 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 Elsevier.
  16. 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.
  17. 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.
  18. 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.
  19. Michihiro Kandori & Hitoshi Matsushima, 1997. "Private observation and Communication and Collusion," Levine's Working Paper Archive 1256, David K. Levine.
  20. David Rahman & Ichiro Obara, 2010. "Mediated Partnerships," Econometrica, Econometric Society, vol. 78(1), pages 285-308, 01.
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