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

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  • Joseph M. Abdou

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Nikolaos Pnevmatikos

    (UP2 - Université Panthéon-Assas)

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 λ-discounted games ant that it coincides with the value of the continuous time game.

Suggested Citation

  • Joseph M. Abdou & Nikolaos Pnevmatikos, 2018. "Asymptotic value in frequency-dependent games with separable payoffs: a differential approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01400267, HAL.
    • Handle: RePEc:hal:cesptp:halshs-01400267
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01400267v3
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    References listed on IDEAS

    as
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    More about this item

    Keywords

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