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

  • Joseph M. Abdou
  • Nikolaos PnevmatikosEmail author


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 \(\lambda \)-discounted games and that it coincides with the value of the continuous time game.


Stochastic game Frequency-dependent payoffs Continuous time game Discretization Hamilton–Jacobi–Bellman–Isaacs equation 

Mathematics Subject Classification:

91A15 91A23 91A25 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Centre d’Economie de la Sorbonne, Université Paris 1, Panthéon-SorbonneParis Cedex-13France
  2. 2.Université Paris 2, Panthéon-AssasParisFrance

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