Mean Field Games Master Equations with Non-separable Hamiltonians and Displacement Monotonicity

Abstract

In this manuscript, we propose a structural condition on non-separable 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.

39 pages, to appear in Annals of Probability

References in corpus (1)

• Stochastic Control on Space of Random Variables

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