One-Dimensional Stationary Mean-Field Games with Local Coupling

Diogo A. Gomes (), Levon Nurbekyan () and Mariana Prazeres ()
Additional contact information
Diogo A. Gomes: King Abdullah University of Science and Technology (KAUST)
Levon Nurbekyan: King Abdullah University of Science and Technology (KAUST)
Mariana Prazeres: King Abdullah University of Science and Technology (KAUST)

Dynamic Games and Applications, 2018, vol. 8, issue 2, No 5, 315-351

Abstract: Abstract 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.

Keywords: Mean-field games; Stationary problems; Dynamic games; 91A13; 91A25 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s13235-017-0223-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:dyngam:v:8:y:2018:i:2:d:10.1007_s13235-017-0223-9

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/13235

DOI: 10.1007/s13235-017-0223-9

Access Statistics for this article

Dynamic Games and Applications is currently edited by Georges Zaccour

More articles in Dynamic Games and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().