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Asymptotic value in frequency-dependent games: A differential approach

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Abstract

We study the asymptotic value of a frequency-dependent zero-sum game following a differential approach. In such a game the stage payoffs depend on the current action and on the frequency of actions played so far. We associate in a natural way a differential game to the original game and although it presents an irregularity at the origin, we prove existence of the value on the time interval [0,1]. We conclude, using appropriate approximations, that the limit of Vn as n tends to infinity, exists and that it coincides with the value of the associated continuous time game

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  • Joseph Abdou & Nikolaos Pnevmatikos, 2016. "Asymptotic value in frequency-dependent games: A differential approach," Documents de travail du Centre d'Economie de la Sorbonne 16076, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:16076
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    References listed on IDEAS

    as
    1. Reinoud Joosten & Thomas Brenner & Ulrich Witt, 2003. "Games with frequency-dependent stage payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(4), pages 609-620, September.
    2. Rida Laraki, 2002. "Repeated Games with Lack of Information on One Side: The Dual Differential Approach," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 419-440, May.
    3. Pierre Cardaliaguet & Rida Laraki & Sylvain Sorin, 2012. "A Continuous Time Approach for the Asymptotic Value in Two-Person Zero-Sum Repeated Games," Post-Print hal-00609476, HAL.
    4. repec:dau:papers:123456789/6775 is not listed on IDEAS
    5. Brenner, Thomas & Witt, Ulrich, 2003. "Melioration learning in games with constant and frequency-dependent pay-offs," Journal of Economic Behavior & Organization, Elsevier, vol. 50(4), pages 429-448, April.
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    More about this item

    Keywords

    stochastic game; frequency dependent payoffs; continuous-time game; Hamilton-Jacobi-Bellman-Isaacs equation;
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    JEL classification:

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

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