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When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff?

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  • Gossner, Olivier
  • Hörner, Johannes

Abstract

We study the relationship between a player's lowest equilibrium payoff in a repeated game with imperfect monitoring and this player's minmax payoff in the corresponding one-shot game. We characterize the signal structures under which these two payoffs coincide for any payoff matrix. Under an identifiability 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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  • Gossner, Olivier & Hörner, Johannes, 2010. "When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff?," Journal of Economic Theory, Elsevier, vol. 145(1), pages 63-84, January.
    • Handle: RePEc:eee:jetheo:v:145:y:2010:i:1:p:63-84
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    1. Johannes Hörner & Wojciech Olszewski, 2006. "The Folk Theorem for Games with Private Almost-Perfect Monitoring," Econometrica, Econometric Society, vol. 74(6), pages 1499-1544, November.
    2. 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.
    3. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    4. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    5. , J. & ,, 2006. "Coordination failure in repeated games with almost-public monitoring," Theoretical Economics, Econometric Society, vol. 1(3), pages 311-340, September.
    6. 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.
    7. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    8. Sekiguchi, Tadashi, 1997. "Efficiency in Repeated Prisoner's Dilemma with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 76(2), pages 345-361, October.
    9. Olivier Gossner & Tristan Tomala, 2007. "Secret Correlation in Repeated Games with Imperfect Monitoring," PSE-Ecole d'économie de Paris (Postprint) hal-00487954, HAL.
    10. Gossner, Olivier & Vieille, Nicolas, 2002. "How to play with a biased coin?," Games and Economic Behavior, Elsevier, vol. 41(2), pages 206-226, November.
    11. 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.
    12. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
    13. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
    14. Ehud Lehrer & Sylvain Sorin, 1992. "A Uniform Tauberian Theorem in Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 303-307, May.
    15. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    16. Olivier Gossner & Ehud Kalai & Robert Weber, 2009. "Information Independence and Common Knowledge," Econometrica, Econometric Society, vol. 77(4), pages 1317-1328, July.
    17. Olivier Gossner & Tristan Tomala, 2006. "Empirical Distributions of Beliefs Under Imperfect Observation," Post-Print hal-00487960, HAL.
    18. Olivier Gossner & Tristan Tomala, 2006. "Empirical Distributions of Beliefs Under Imperfect Observation," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 13-30, February.
    19. 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.
    20. Lehrer, E, 1990. "Nash Equilibria of n-Player Repeated Games with Semi-standard Information," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 191-217.
    21. von Stengel, Bernhard & Koller, Daphne, 1997. "Team-Maxmin Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 309-321, October.
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    1. Ghislain-Herman Demeze-Jouatsa, 2020. "A complete folk theorem for finitely repeated games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1129-1142, December.
    2. Deb, Joyee & González-Díaz, Julio & Renault, Jérôme, 2016. "Uniform folk theorems in repeated anonymous random matching games," Games and Economic Behavior, Elsevier, vol. 100(C), pages 1-23.
    3. , & ,, 2015. "A folk theorem for stochastic games with infrequent state changes," Theoretical Economics, Econometric Society, vol. 10(1), January.
    4. Ashkenazi-Golan, Galit & Lehrer, Ehud, 2019. "Blackwell's comparison of experiments and discounted repeated games," Games and Economic Behavior, Elsevier, vol. 117(C), pages 163-194.
    5. Kimmo Berg, 2017. "Extremal Pure Strategies and Monotonicity in Repeated Games," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 387-404, March.
    6. Johannes Hörner & Satoru Takahashi & Nicolas Vieille, 2015. "Truthful Equilibria in Dynamic Bayesian Games," Econometrica, Econometric Society, vol. 83(5), pages 1795-1848, September.
    7. Sugaya, Takuo & Wolitzky, Alexander, 2018. "Bounding payoffs in repeated games with private monitoring: n-player games," Journal of Economic Theory, Elsevier, vol. 175(C), pages 58-87.
    8. Kutay Cingiz & János Flesch & P. Jean-Jacques Herings & Arkadi Predtetchinski, 2020. "Perfect information games where each player acts only once," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 965-985, June.

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