  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.
