Radially Symmetric Mean-Field Games with Congestion

2017/03/22 by Evangelista, David, Gomes, Diogo A., Nurbekyan, Levon
#35A01 #35Q91 #35Q93 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.07594

Abstract

Here, we study radial solutions for first- and second-order stationary Mean-Field Games (MFG) with congestion on ℝ^d. MFGs with congestion model problems where the agents' motion is hampered in high-density regions. The radial case, which is one of the simplest non one-dimensional MFG, is relatively tractable. As we observe in this paper, the Fokker-Planck equation is integrable with respect to one of the unknowns. Consequently, we obtain a single equation substituting this solution into the Hamilton-Jacobi equation. For the first-order case, we derive explicit formulas; for the elliptic case, we study a variational formulation of the resulting equation. In both cases, we use our approach to compute numerical approximations to the solutions of the corresponding MFG systems.

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