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arXiv · 1703.07594

Radially Symmetric Mean-Field Games with Congestion

David Evangelista·Diogo A. Gomes·Levon Nurbekyan
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Abstract

Here, we study radial solutions for first- and second-order stationary Mean-Field Games (MFG) with congestion on $\mathbb{R}^d$. 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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David Evangelista, Diogo A. Gomes, Levon Nurbekyan. 2017-03-22. Radially Symmetric Mean-Field Games with Congestion. https://arxiv.org/abs/1703.07594

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