A policy iteration method for Mean Field Games

TL;DR

This paper introduces a policy iteration algorithm tailored for Mean Field Games systems, providing convergence analysis and numerical discretizations for stationary and evolutive cases, with demonstrated effectiveness in low-dimensional examples.

Contribution

It presents a novel policy iteration approach for Mean Field Games, including convergence proofs and practical discretization methods for numerical solutions.

Findings

Convergence of the policy iteration method for discrete MFG problems.

Effective numerical performance demonstrated in 1D and 2D examples.

Applicable to both stationary and evolutive MFG systems.

Abstract

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. We show the convergence of the policy iteration method for the discrete problem and we study the performance of the proposed algorithm on some examples in dimension one and two.