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Asymptotic value in frequency-dependent games with separable payoffs: a differential approach

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Abstract

We study the asymptotic value of a frequency-dependent zero-sum game with separable payoff following a differential approach. The stage payoffs in such games depend on the current actions and on a linear function of the frequency of actions played so far. We associate to the repeated game, in a natural way, a differential game and although the latter presents an irregularity at the origin, we prove that it has a value. We conclude, using appropriate approximations, that the asymptotic value of the original game exists in both the n-stage and the ?-discounted games ant that it coincides with the value of the continuous time game

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  • Joseph Abdou & Nikolaos Pnevmatikos, 2016. "Asymptotic value in frequency-dependent games with separable payoffs: a differential approach," Documents de travail du Centre d'Economie de la Sorbonne 16076rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jul 2018.
    • Handle: RePEc:mse:cesdoc:16076rr
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    References listed on IDEAS

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    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.
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    4. 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.
    5. 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.
    6. Reinoud Joosten, 2004. "Strategic Interaction and Externalities: FD-games and pollution," Papers on Economics and Evolution 2004-17, Philipps University Marburg, Department of Geography.
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    More about this item

    Keywords

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