A numerical method for Mean Field Games on networks

TL;DR

This paper introduces a numerical scheme for stationary Mean Field Games on networks, emphasizing the importance of accurate vertex transition conditions, and demonstrates its effectiveness through theoretical proofs and numerical experiments.

Contribution

It presents a novel numerical method with proven existence, uniqueness, and convergence for Mean Field Games on networks, including a least squares approach for solving the discrete system.

Findings

Proven convergence of the numerical scheme.

Successful numerical experiments validating the method.

Effective handling of transition conditions at network vertices.

Abstract

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence of the scheme and we also propose a least squares method for the solution of the discrete system. Numerical experiments are carried out.