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Best-reply dynamics in large binary-choice anonymous games

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  • Babichenko, Yakov

Abstract

We consider small-influence anonymous games with a large number of players n where every player has two actions. For this class of games we present a best-reply dynamic with the following two properties. First, the dynamic reaches Nash approximate equilibria fast (in at most cnlogn steps for some constant c>0). Second, Nash approximate equilibria are played by the dynamic with a limit frequency of at least 1−e−c′n for some constant c′>0.

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  • Babichenko, Yakov, 2013. "Best-reply dynamics in large binary-choice anonymous games," Games and Economic Behavior, Elsevier, vol. 81(C), pages 130-144.
    • Handle: RePEc:eee:gamebe:v:81:y:2013:i:c:p:130-144
    DOI: 10.1016/j.geb.2013.04.007
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    Cited by:

    1. Arato, Hiroki & Hori, Takeo & Nakamura, Tomoya, 2021. "Endogenous information acquisition and the partial announcement policy," Information Economics and Policy, Elsevier, vol. 55(C).
    2. Torsten Heinrich & Yoojin Jang & Luca Mungo & Marco Pangallo & Alex Scott & Bassel Tarbush & Samuel Wiese, 2023. "Best-response dynamics, playing sequences, and convergence to equilibrium in random games," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 703-735, September.
    3. Pradelski, Bary S.R., 2023. "Social influence: The Usage History heuristic," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 105-113.
    4. Torsten Heinrich & Yoojin Jang & Luca Mungo & Marco Pangallo & Alex Scott & Bassel Tarbush & Samuel Wiese, 2021. "Best-response dynamics, playing sequences, and convergence to equilibrium in random games," Papers 2101.04222, arXiv.org, revised Nov 2022.
    5. Yakov Babichenko, 2018. "Fast Convergence of Best-Reply Dynamics in Aggregative Games," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 333-346, February.
    6. Pangallo, Marco & Heinrich, Torsten & Jang, Yoojin & Scott, Alex & Tarbush, Bassel & Wiese, Samuel & Mungo, Luca, 2021. "Best-Response Dynamics, Playing Sequences, And Convergence To Equilibrium In Random Games," INET Oxford Working Papers 2021-23, Institute for New Economic Thinking at the Oxford Martin School, University of Oxford.
    7. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    8. Bary S.R. Pradelski, 2015. "The Dynamics of Social Influence," Economics Series Working Papers 742, University of Oxford, Department of Economics.

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    More about this item

    Keywords

    Anonymous games; Best-reply dynamic; Rate of convergence;
    All these keywords.

    JEL classification:

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

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