On the rate of convergence for the mean-field approximation of controlled diffusions with large number of players

Kolokoltsov, Vassili N. and Troeva, Marianna and Yang, Wei (2014) On the rate of convergence for the mean-field approximation of controlled diffusions with large number of players. Dynamic Games and Applications, 4 (2). pp. 208-230. ISSN 2153-0785

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Abstract

In this paper, we investigate the mean field games of N agents who are weakly coupled via the empirical measures. The underlying dynamics of the representative agent is assumed to be a controlled nonlinear diffusion process with variable coeffcients. We show that individual optimal strategies based on any solution of the main consistency equation for the backward-forward mean led game model represent a 1=N-Nash equilibrium for approximating systems of N agents.