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Asymptotic Value in Frequency-Dependent Games with Separable Payoffs: A Differential Approach

Author

Listed:
  • Joseph M. Abdou

    (Centre d’Economie de la Sorbonne, Université Paris 1, Panthéon-Sorbonne)

  • Nikolaos Pnevmatikos

    (Université Paris 2, 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 with 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 $$\lambda $$ λ -discounted games and that it coincides with the value of the continuous time game.

Suggested Citation

  • Joseph M. Abdou & Nikolaos Pnevmatikos, 2019. "Asymptotic Value in Frequency-Dependent Games with Separable Payoffs: A Differential Approach," Dynamic Games and Applications, Springer, vol. 9(2), pages 295-313, June.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:2:d:10.1007_s13235-018-0278-2
    DOI: 10.1007/s13235-018-0278-2
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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.
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    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.
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    More about this item

    Keywords

    Stochastic game; Frequency-dependent payoffs; Continuous time game; Discretization; 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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