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

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

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Article ID: iaor2014868
Volume: 4
Issue: 2
Start Page Number: 208
End Page Number: 230
Publication Date: Jun 2014
Journal: Dynamic Games and Applications
Authors: , ,
Keywords: differential equations
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 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.

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