On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of Players

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 coefficients. We show that individual optimal strategies based on any solution of the main consistency equation for the backward-forward mean filed game model represent a 1/N-Nash equilibrium for approximating systems of N agents. Copyright Springer Science+Business Media New York 2014