Asymptotic value in frequency-dependent games: A differential approach

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

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

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-Lambda as Lambda tends 0, converges to the same limit

Keywords: stochastic game; frequency dependent payoffs; continuous-time game; Hamilton-Jacobi-Bellman-Isaacs equation (search for similar items in EconPapers)
JEL-codes: C73 (search for similar items in EconPapers)
Date: 2016-11, Revised 2018-01
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Working Paper: Asymptotic value in frequency-dependent games: A differential approach (2016)
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