Existence of solutions to contact mean field games of first order

TL;DR

This paper establishes the existence of solutions for contact mean field games systems of first order by linking weak KAM theory for contact Hamiltonian systems with these game systems, using properties of the Mather set.

Contribution

It extends the connection between weak KAM theory and mean field games to contact Hamiltonian systems, providing new existence results.

Findings

Proved existence of solutions for contact mean field games.

Linked weak KAM theory for contact Hamiltonian systems to game solutions.

Analyzed properties of the Mather set for contact systems.

Abstract

This paper deals with the existence of solutions of a class of contact mean field games systems of first order. Cardaliaguet \cite{CAR} found a link between the weak KAM theory for Hamiltonian systems and mean field games systems. We prove that there is still a connection between the weak KAM theory for contact Hamiltonian systems and contact mean field games systems. By the analysis of properties of the Mather set for contact Hamiltonian systems, we prove the main existence result.