Global Well-Posedness of Displacement Monotone Degenerate Mean Field Games Master Equations

TL;DR

This paper establishes the global well-posedness of displacement monotone mean field games master equations without idiosyncratic noise, covering deterministic and common noise-driven models, thus generalizing recent results in the field.

Contribution

It constructs global classical solutions for a broad class of displacement monotone master equations, extending existing well-posedness results to more general models.

Findings

Unified and generalized well-posedness results

Applicable to models with only common noise or deterministic dynamics

Extended the class of Hamiltonians and data functions covered

Abstract

In this paper we construct global in time classical solutions to mean field games master equations in the lack of idiosyncratic noise in the individual agents' dynamics. These include both deterministic models and dynamics driven solely by a Brownian common noise. We consider a general class of non-separable Hamiltonians and final data functions that are supposed to be displacement monotone. Our main results unify and generalize in particular some of the well-posedness results on displacement monotone master equations obtained recently by Gangbo--M\'esz\'aros and Gangbo--M\'esz\'aros--Mou--Zhang.