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How fast do equilibrium payoff sets converge in repeated games?

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  • Hörner, Johannes
  • Takahashi, Satoru

Abstract

We provide tight bounds on the rate of convergence of the equilibrium payoff sets for repeated games under both perfect and imperfect public monitoring. The distance between the equilibrium payoff set and its limit vanishes at rate (1−δ)1/2 under perfect monitoring, and at rate (1−δ)1/4 under imperfect monitoring. For strictly individually rational payoff vectors, these rates improve to 0 (i.e., all strictly individually rational payoff vectors are exactly achieved as equilibrium payoffs for δ high enough) and (1−δ)1/2, respectively.

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  • Hörner, Johannes & Takahashi, Satoru, 2016. "How fast do equilibrium payoff sets converge in repeated games?," Journal of Economic Theory, Elsevier, vol. 165(C), pages 332-359.
    • Handle: RePEc:eee:jetheo:v:165:y:2016:i:c:p:332-359
    DOI: 10.1016/j.jet.2016.05.001
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    Cited by:

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      • Matan Harel & Elchanan Mossel & Philipp Strack & Omer Tamuz, 2014. "Rational Groupthink," Papers 1412.7172, arXiv.org, revised Jun 2020.
    2. Ani Dasgupta & Sambuddha Ghosh, 2017. "Repeated Games Without Public Randomization: A Constructive Approach," Boston University - Department of Economics - Working Papers Series WP2017-011, Boston University - Department of Economics, revised Feb 2019.
    3. Joyee Deb & Takuo Sugaya & Alexander Wolitzky, 2020. "The Folk Theorem in Repeated Games With Anonymous Random Matching," Econometrica, Econometric Society, vol. 88(3), pages 917-964, May.
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    5. Mira Frick & Ryota Iijima & Yuhta Ishii, 2023. "Monitoring with Rich Data," Papers 2312.16789, arXiv.org.
    6. Meng, Delong, 2021. "On the value of repetition for communication games," Games and Economic Behavior, Elsevier, vol. 127(C), pages 227-246.

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    More about this item

    Keywords

    Repeated games; Rates of convergence;

    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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