A Total Variation Flow Scheme for Ergodic Mean Field Games

TL;DR

This paper introduces a variational method based on total variation flow to compute solutions for ergodic mean-field games, especially when such games lack an inherent variational structure, supported by algorithmic implementation and comparisons.

Contribution

It develops a novel variational approach using total variation flow for ergodic mean-field games without a predefined variational framework.

Findings

Successful implementation of the algorithms.

Effective comparison of different algorithms.

Applicability to various mean-field game cases.

Abstract

Motivated by recent developments in mean-field games in ecology, in this paper we introduce a connection between the best response dynamics in evolutionary game theory, the minimization of the highest income of a game, and minimizing movement schemes. The aim of this work is to develop a variational approach to compute solutions of first order ergodic mean-field games that may not possess a priori a variational structure. The study is complemented by a discussion and successful implementation of the algorithms, and comparisons between them in a variety of cases