Radially symmetric mean-field games with congestion

David Evangelista, Diogo Gomes, Levon Nurbekyan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

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 languageEnglish (US)
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3158-3163
Number of pages6
ISBN (Electronic)9781509028733
DOIs
StatePublished - Jan 18 2018
Event56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia
Duration: Dec 12 2017Dec 15 2017

Publication series

Name2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume2018-January

Conference

Conference56th IEEE Annual Conference on Decision and Control, CDC 2017
CountryAustralia
CityMelbourne
Period12/12/1712/15/17

ASJC Scopus subject areas

  • Decision Sciences (miscellaneous)
  • Industrial and Manufacturing Engineering
  • Control and Optimization

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