Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games.

This manuscript constructs global in time solutions to master equations for potential mean field games. The study concerns a class of Lagrangians and initial data functions that are displacement convex, and so this property may be in dichotomy with the so‐called Lasry–Lions monotonicity, widely considered in the literature. We construct solutions to both the scalar and vectorial master equations in potential mean field games, when the underlying space is the whole space ℝd, and so it is not compact. © 2022 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]