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Abstract
We propose a structural condition on 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 which sometimes in dichotomy with the widely used Lasry-Lions monotonicity condition, allows to handle non-separable Hamiltonians. (Joint work with A. Meszaros, C. Mou and J. Zhang).