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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 coincides with the value of the associated continuous time game. We extend the existence of the asymptotic value to discounted payoffs and we show that V? as ? tends 0, converges to the same limit

Suggested Citation

  • Joseph Abdou & Nikolaos Pnevmatikos, 2016. "Asymptotic value in frequency-dependent games: A differential approach," Documents de travail du Centre d'Economie de la Sorbonne 16076r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jan 2018.
    • Handle: RePEc:mse:cesdoc:16076r
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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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