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When is the individually rational payoff in a repeated game equal to the minmax payoff?

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  • Olivier Gossner
  • Jöhannes Horner

Abstract

We study the relationship between a player’s (stage game) minmax payoff and the individually rational payoff in repeated games with imperfect monitoring. We characterize the signal structures under which these two payoffs coincide for any payoff matrix. Under a full rank assumption, we further show that, if the monitoring structure of an infinitely repeated game ‘nearly’ satisfies this condition, then these two payoffs are approximately equal, independently of the discount factor. This provides conditions under which existing folk theorems exactly characterize the limiting payoff set.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1440.

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Date of creation: Nov 2006
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Handle: RePEc:nwu:cmsems:1440

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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. Fudenberg, Drew & Levine, David I & Maskin, Eric, 1994. "The Folk Theorem with Imperfect Public Information," Econometrica, Econometric Society, vol. 62(5), pages 997-1039, September.
  2. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
  3. George J. Mailath & Stephen Morris, 2004. "Coordination Failure in Repeated Games with Almost-Public Monitoring," PIER Working Paper Archive 05-014, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 23 Mar 2005.
  4. Bhaskar, V. & Obara, Ichiro, 2002. "Belief-Based Equilibria in the Repeated Prisoners' Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 40-69, January.
  5. Gossner, O. & Vieille, N., 1999. "How to play with a biased coin?," Papers 99-31, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  6. Johannes Horner & Wojciech Olszewski, 2005. "The Folk Theorem for Games with Private, Almost-Perfect Monitoring," NajEcon Working Paper Reviews 172782000000000006, www.najecon.org.
  7. Lehrer, E, 1990. "Nash Equilibria of n-Player Repeated Games with Semi-standard Information," International Journal of Game Theory, Springer, vol. 19(2), pages 191-217.
  8. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.
  9. Michihiro Kandori, 2001. "Introduction to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-114, CIRJE, Faculty of Economics, University of Tokyo.
  10. von Stengel, Bernhard & Koller, Daphne, 1997. "Team-Maxmin Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 309-321, October.
  11. O. Gossner & P. Hernandez, 2001. "On the complexity of coordination," THEMA Working Papers 2001-21, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  12. Neyman, Abraham & Okada, Daijiro, 1999. "Strategic Entropy and Complexity in Repeated Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 191-223, October.
  13. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
  14. Robert J. Aumann & Lloyd S. Shapley, 2013. "Long Term Competition -- A Game-Theoretic Analysis," Annals of Economics and Finance, Society for AEF, vol. 14(2), pages 627-640, November.
  15. Moreno, Diego & Wooders, John, 1998. "An Experimental Study of Communication and Coordination in Noncooperative Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 47-76, July.
  16. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
  17. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
  18. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
  19. Friedman, James W, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Wiley Blackwell, vol. 38(113), pages 1-12, January.
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