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Mean Field Game Master Equations with Anti-monotonicity Conditions
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It is well known that the monotonicity condition, either in Lasry-Lions sense or in displacement sense, is crucial for the global well-posedness of mean field game master equations, as well as for the uniqueness of mean field equilibria and solutions to mean field game systems. In the literature, the monotonicity conditions are always taken in a fixed direction. In this paper we propose a new type of monotonicity condition in the opposite direction, which we call the anti-monotonicity condition, and establish the global well-posedness for mean field game master equations with nonseparable Hamiltonians. Our anti-monotonicity condition allows our data to violate both the Lasry-Lions monotonicity and the displacement monotonicity conditions.
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Beyond separability: convergence rate of vanishing viscosity approximations to mean field games via FBSDE stability
The vanishing viscosity approximation to nonlocal, possibly non-separable mean field games converges at rate O(β) in L∞ on compact sets, matching the classical Hamilton-Jacobi rate.
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