Ergodic Mean Field Games with H\"ormander diffusions

TL;DR

This paper establishes the existence of solutions for a class of subelliptic PDE systems derived from Mean Field Games with H"ormander diffusions, relevant for large N-player differential games and Nash equilibria.

Contribution

It provides the first existence results for subelliptic PDE systems in the context of Mean Field Games with H"ormander diffusions.

Findings

Existence of solutions for subelliptic PDE systems in Mean Field Games.

Application to feedback synthesis and Nash equilibria.

Extension of classical results to subelliptic, non-elliptic settings.

Abstract

We prove existence of solutions for a class of systems of subelliptic PDEs arising from Mean Field Game systems with H\"ormander diffusion. These results are motivated by the feedback synthesis Mean Field Game solutions and the Nash equilibria of a large class of $N$-player differential games.