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* Corresponding author 1 UNINE - Institut de Mathématiques

Abstract : This paper considers a stochastic approximation algorithm, with decreasing step size and martingale difference noise. Under very mild assumptions, we prove the non convergence of this process toward a certain class of repulsive sets for the associated ordinary differential equation ODE. We then use this result to derive the convergence of the process when the ODE is cooperative in the sense of Hirsch, 1985. In particular, this allows us to extend significantly the main result of Hofbauer and Sandholm, 2002 on the convergence of stochastic fictitious play in supermodular games.

Keywords : Game theory Stochastic approximations Cooperative dynamical systems Game theory.

Autor: Michel Benaïm - Mathieu Faure -



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