One-Dimensional Stationary Mean-Field Games with Local Coupling

Diogo A. Gomes, Levon Nurbekyan, Mariana Prazeres

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton–Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption implies the existence and uniqueness of solutions. Here, we drop that assumption and construct explicit solutions for one-dimensional MFGs. These solutions exhibit phenomena not present in monotonically increasing MFGs: low-regularity, non-uniqueness, and the formation of regions with no agents.
Original languageEnglish (US)
Pages (from-to)315-351
Number of pages37
JournalDynamic Games and Applications
Issue number2
StatePublished - May 25 2017


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