TY - JOUR

T1 - On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of Players

AU - Kolokoltsov, Vassili N.

AU - Troeva, Marianna

AU - Yang, Wei

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

KW - Dynamic law of large numbers

KW - Forward-backward system

KW - Kinetic equation

KW - Nonlinear diffusion

KW - Rates of convergence

KW - Tagged particle

KW - ε{lunate}-Nash equilibrium

UR - http://www.scopus.com/inward/record.url?scp=84899416204&partnerID=8YFLogxK

U2 - 10.1007/s13235-013-0095-6

DO - 10.1007/s13235-013-0095-6

M3 - Article

AN - SCOPUS:84899416204

VL - 4

SP - 208

EP - 230

JO - Dynamic Games and Applications

JF - Dynamic Games and Applications

SN - 2153-0785

IS - 2

ER -