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

Joseph Abdou () and Nikolaos Pnevmatikos ()
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Joseph 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 nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Nikolaos Pnevmatikos: Université Paris-Panthéon-Assas, LEMMA - Laboratoire d'économie mathématique et de microéconomie appliquée - Université Paris-Panthéon-Assas

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

Keywords: Stochastic game; Frequency-dependent payoffs; Continuous time game; Discretization; Hamilton–Jacobi–Bellman–Isaacs equation (search for similar items in EconPapers)
Date: 2019-06-15
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Published in Dynamic Games and Applications, 2019, 9 (2), pp.295-313. ⟨10.1007/s13235-018-0278-2⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03967796

DOI: 10.1007/s13235-018-0278-2

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