Asymptotic value in frequency-dependent games: A differential approach

Joseph Abdou (1) , Nikolaos Pnevmatikos (1)

1 CES - Centre d'économie de la Sorbonne

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 that it coincides with the value of the associated continuous time game.

Mots clés: Hamilton-Jacobi-Bellman-Isaacs equation; stochastic game; frequency dependent payoffs; continuous-time game

Domaines: Economies et finances

Joseph Abdou, Nikolaos Pnevmatikos. Asymptotic value in frequency-dependent games: A differential approach. 2016. ⟨halshs-01400267v1⟩