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On the limit perfect public equilibrium payoff set in repeated and stochastic games

Author

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  • Hörner, Johannes
  • Takahashi, Satoru
  • Vieille, Nicolas

Abstract

This paper provides a dual characterization of the existing ones for the limit set of perfect public equilibrium payoffs in a class of finite stochastic games (in particular, repeated games) as the discount factor tends to one. As a first corollary, the folk theorems of Fudenberg et al. (1994), Kandori and Matsushima (1998) and Hörner et al. (2011) obtain. As a second corollary, it is shown that this limit set of payoffs is a convex polytope when attention is restricted to perfect public equilibria in pure strategies. This result fails for mixed strategies, even when attention is restricted to two-player repeated games.

Suggested Citation

  • Hörner, Johannes & Takahashi, Satoru & Vieille, Nicolas, 2014. "On the limit perfect public equilibrium payoff set in repeated and stochastic games," Games and Economic Behavior, Elsevier, vol. 85(C), pages 70-83.
  • Handle: RePEc:eee:gamebe:v:85:y:2014:i:c:p:70-83
    DOI: 10.1016/j.geb.2013.12.010
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    References listed on IDEAS

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    1. Johannes Hörner & Stefano Lovo, 2009. "Belief-Free Equilibria in Games With Incomplete Information," Econometrica, Econometric Society, vol. 77(2), pages 453-487, March.
    2. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2011. "Belief-free equilibria in games with incomplete information: Characterization and existence," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1770-1795, September.
    3. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "The folk theorem for irreducible stochastic games with imperfect public monitoring," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1664-1683, July.
    4. Tristan Tomala, 1998. "Pure equilibria of repeated games with public observation," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 93-109.
    5. repec:wsi:wschap:9789812818478_0012 is not listed on IDEAS
    6. Drew Fudenberg & David K. Levine & Satoru Takahashi, 2008. "Perfect public equilibrium when players are patient," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 16, pages 345-367 World Scientific Publishing Co. Pte. Ltd..
    7. Drew Fudenberg & David K. Levine, 2008. "Efficiency and Observability with Long-Run and Short-Run Players," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 13, pages 275-307 World Scientific Publishing Co. Pte. Ltd..
    8. David Rahman & Ichiro Obara, 2010. "Mediated Partnerships," Econometrica, Econometric Society, vol. 78(1), pages 285-308, January.
    9. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273 World Scientific Publishing Co. Pte. Ltd..
    10. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    11. 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, July.
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    14. Tomala, Tristan, 2009. "Perfect communication equilibria in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 67(2), pages 682-694, November.
    15. Abreu, Dilip & Sannikov, Yuliy, 2014. "An algorithm for two-player repeated games with perfect monitoring," Theoretical Economics, Econometric Society, vol. 9(2), May.
    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. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
    18. Drew Fudenberg & Yuichi Yamamoto, 2010. "Repeated Games Where the Payoffs and Monitoring Structure Are Unknown," Econometrica, Econometric Society, vol. 78(5), pages 1673-1710, September.
    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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    Citations

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    Cited by:

    1. Marie Laclau & Tristan Tomala, 2016. "Repeated games with public information revisited," Working Papers hal-01285326, HAL.
    2. Laclau, Marie & Tomala, Tristan, 2017. "Repeated games with public deterministic monitoring," Journal of Economic Theory, Elsevier, vol. 169(C), pages 400-424.
    3. Johannes Hörner & Satoru Takahashi & Nicolas Vieille, 2015. "Truthful Equilibria in Dynamic Bayesian Games," Econometrica, Econometric Society, vol. 83(5), pages 1795-1848, September.
    4. Marie Laclau & Tristan Tomala, 2016. "Repeated games with public information revisited," PSE Working Papers hal-01285326, HAL.

    More about this item

    Keywords

    Stochastic games; Repeated games; Folk theorem;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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