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

Joseph Abdou and Nikolaos Pnevmatikos ()
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Nikolaos Pnevmatikos: Université Paris 2, Panthéon-Assas

Dynamic Games and Applications, 2019, vol. 9, issue 2, No 1, 295-313

Abstract: 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.

Keywords: Stochastic game; Frequency-dependent payoffs; Continuous time game; Discretization; Hamilton–Jacobi–Bellman–Isaacs equation; 91A15; 91A23; 91A25 (search for similar items in EconPapers)
Date: 2019
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Working Paper: Asymptotic value in frequency-dependent games with separable payoffs: a differential approach (2018)
Working Paper: Asymptotic value in frequency-dependent games with separable payoffs: a differential approach (2018)
Working Paper: Asymptotic value in frequency-dependent games with separable payoffs: a differential approach (2018)
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DOI: 10.1007/s13235-018-0278-2

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