Abstract
Conference Title: 2017 IEEE 56th Annual Conference on Decision and Control (CDC) Conference Start Date: 2017, Dec. 12 Conference End Date: 2017, Dec. 15 Conference Location: Melbourne, Australia Here, we study radial solutions for first- and second-order stationary Mean-Field Games (MFG) with congestion on Rd. 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.