In this talk we investigate the question of global in time well-posedness of master equations arising in potential deterministic Mean Field Games. The study concerns a class of Lagrangians and initial data functions, which are displacement convex and so, it may be in dichotomy with the class of so-called monotone functions, 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 $\mathbb{R}^d$ and so, it is not compact. The talk is based on a joint work with W. Gangbo.
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