Dual two-state mean-field games

TL;DR

This paper explores two-state mean-field games and their dual formulations, focusing on numerical methods and experiments that reveal complex behaviors like shocks and monotonicity issues.

Contribution

It introduces the dual formulation of two-state mean-field games and discusses numerical approaches, highlighting behaviors such as shock formation and invertibility challenges.

Findings

Numerical experiments show shock formation in solutions.

Lack of invertibility observed in certain regimes.

Monotonicity loss affects solution stability.

Abstract

In this paper, we consider two-state mean-field games and its dual formulation. We then discuss numerical methods for these problems. Finally, we present various numerical experiments, exhibiting different behaviours, including shock formation, lack of invertibility, and monotonicity loss.