First-order, stationary mean-field games with congestion

David Evangelista, Rita Ferreira, Diogo A. Gomes, Levon Nurbekyan, Vardan K. Voskanyan

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas. Here, we study stationary MFGs with congestion with quadratic or power-like Hamiltonians. First, using explicit examples, we illustrate two main difficulties: the lack of classical solutions and the existence of areas with vanishing densities. Our main contribution is a new variational formulation for MFGs with congestion. With this formulation, we prove the existence and uniqueness of solutions. Finally, we consider applications to numerical methods.
Original languageEnglish (US)
Pages (from-to)37-74
Number of pages38
JournalNonlinear Analysis
Volume173
DOIs
StatePublished - Apr 30 2018

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