Mean field games: convergence of a finite difference method

TL;DR

This paper discusses the convergence of a finite difference numerical method for mean field game models, which describe the limiting behavior of large stochastic differential games, providing theoretical guarantees for their accuracy.

Contribution

The paper proves convergence theorems for a finite difference method applied to stationary and evolutive mean field game models, extending previous numerical approaches.

Findings

Convergence of the finite difference method is established under certain assumptions.

Theoretical results support the reliability of the numerical scheme.

The method effectively approximates mean field game solutions.

Abstract

Mean field type models describing the limiting behavior, as the number of players tends to $+\infty$, of stochastic differential game problems, have been recently introduced by J-M. Lasry and P-L. Lions. Numerical methods for the approximation of the stationary and evolutive versions of such models have been proposed by the authors in previous works . Convergence theorems for these methods are proved under various assumptions