Time-Dependent Mean-Field Games in the Subquadratic Case

By Diogo A. Gomes, Edgard A. Pimentel, H'ector S'anchez-Morgado. 2013

51 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/44481838ecac9635673ca6b0019f1fedca4c7270

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Citations in the corpus

Second order mean field games with degenerate diffusion and local coupling (2014, background): “, [8, 17, 18, 19, 21, 12, 13, 22]) or by stochastic techniques (see, e.”
Time dependent mean-field games in the superquadratic case (2013, background): “The preceding hypotheses are the same as the corresponding ones in [25].”
Existence for stationary mean-field games with congestion and quadratic Hamiltonians (2015, background): “In principle, unbounded potentials can be studied by adapting the techniques in [4,7,9,18], for instance.”
Existence of a solution to an equation arising from the theory of Mean Field Games (2015, methodology): “This manuscript version is made available under the Elsevier user license http://www.elsevier.com/open-access/userlicense/1.0/”