Calculus of Variations and Geometric Measure Theory

S. Cacace - F. Camilli - A. Goffi

A policy iteration method for Mean Field Games

created by goffi on 10 Jul 2020
modified on 29 Aug 2021


Published Paper

Inserted: 10 jul 2020
Last Updated: 29 aug 2021

Volume: 27
Number: 85
Year: 2021
Doi: 10.1051/cocv/2021081

ArXiv: 2007.04818 PDF


The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of the problem. We also introduce suitable discretizations to numerically solve both stationary and evolutive problems, showing the performance of the proposed algorithm on some examples in dimension one and two.

Keywords: Convergence, Mean Field Games, Numerical methods, policy iteration