Time-Dependent Mean-Field Games in the Subquadratic Case
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In this paper, the authors considered time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure and established existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension.Abstract:
In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.read more
Citations
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Mean Field Games Models—A Brief Survey
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Second order mean field games with degenerate diffusion and local coupling
TL;DR: In this paper, a second order mean field games system of partial differential equations is analyzed and the existence and uniqueness of suitably defined weak solutions are characterized as minimizers of two optimal control problems.
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Weak Solutions to Fokker–Planck Equations and Mean Field Games
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TL;DR: In this paper, the authors studied mean field games in the framework of controlled martingale problems, and general existence theorems were proven in which the equilibrium control is Markovian.
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Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
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