Abstract
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.
| Original language | English (US) |
|---|---|
| Title of host publication | 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 3158-3163 |
| Number of pages | 6 |
| ISBN (Electronic) | 9781509028733 |
| DOIs | |
| State | Published - Jun 28 2017 |
| Event | 56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia Duration: Dec 12 2017 → Dec 15 2017 |
Publication series
| Name | 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 |
|---|---|
| Volume | 2018-January |
Conference
| Conference | 56th IEEE Annual Conference on Decision and Control, CDC 2017 |
|---|---|
| Country/Territory | Australia |
| City | Melbourne |
| Period | 12/12/17 → 12/15/17 |
Bibliographical note
Publisher Copyright:© 2017 IEEE.
ASJC Scopus subject areas
- Decision Sciences (miscellaneous)
- Industrial and Manufacturing Engineering
- Control and Optimization