MEAN FIELD GAMES MASTER EQUATIONS WITH NONSEPARABLE HAMILTONIANS AND DISPLACEMENT MONOTONICITY

By Wilfrid Gangbo, Alpár R. Mészáros, Chenchen Mou, Jianfeng Zhang

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

In this manuscript we propose a structural condition on nonseparable Hamiltonians, which we term displacement monotonicity condition, to study second-order mean field games master equations. A rate of dissipation of a bilinear form is brought to bear a global (in time) well-posedness theory, based on a priori uniform Lipschitz estimates on the solution in the measure variable. Displacement monotonicity being sometimes in dichotomy with the widely used Lasry–Lions monotonicity condition, the novelties of this work persist even when restricted to separable Hamiltonians.
Original languageEnglish (US)
Pages (from-to)2178-2217
Number of pages40
JournalAnnals of Probability
Volume50
Issue number6
DOIs
StatePublished - Nov 1 2022
Externally publishedYes

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