# Radially symmetric mean-field games with congestion

### 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.

Publication
56th IEEE Conference on Decision and Control
Date