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



Author: Michel Benaïm UNINE, Mathieu Faure UNINE

Source: https://arxiv.org/







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