Mean field games master equations with nonseparable Hamiltonians and displacement monotonicity

In this manuscript we propose a structural condition on nonseparable Hamiltonians, which term displacement monotonicity condition, to study second-order mean field games master equations. A rate of dissipation bilinear form is brought bear global (in time) well-posedness theory, based priori uniform Lipschitz estimates the solution in measure variable. Displacement being sometimes dichotomy with widely used Lasry–Lions novelties work persist even when restricted separable Hamiltonians.