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, http://lemma.u-paris2.fr

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? as ? 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
New Economics Papers: this item is included in nep-gth
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Working Paper: Asymptotic value in frequency-dependent games: A differential approach (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:16076r

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