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تسجيل مستخدم جديدMean Field Games systems under displacement monotonicity
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In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general non-separable Hamiltonians that satisfy a so-called $displacement monotonicity$ condition. Ours are the first global in time uniqueness results, beyond the well-known Lasry-Lions monotonicity condition, for the Mean Field Games systems involving non-separable Hamiltonians. The displacement monotonicity assumptions imposed on the data provide actually not only uniqueness, but also the existence and regularity of the solutions.
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