Calculus of Variations and Geometric Measure Theory

A. R. Mészáros - C. Mou

Mean Field Games systems under displacement monotonicity

created by mészáros on 15 Sep 2021
modified on 22 Aug 2023

[BibTeX]

Accepted Paper

Inserted: 15 sep 2021
Last Updated: 22 aug 2023

Journal: SIAM J. Math. Anal.
Year: 2023

ArXiv: 2109.06687 PDF

Abstract:

In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general non-separable Hamiltonians that satisfy a so-called displacement monotonicity condition. This monotonicity condition that we propose for non-separable Hamiltonians is sharper and more general than the one proposed in our earlier work written jointly with Gangbo and Zhang. The displacement monotonicity assumptions imposed on the data provide actually not only uniqueness, but also the existence and regularity of the solutions. Our analysis uses elementary arguments and does not rely on the well-posedness of the corresponding master equations.