One-Dimensional Stationary Mean-Field Games with Local Coupling

Gomes, Diogo A.; Nurbekyan, Levon; Prazeres, Mariana

One-Dimensional Stationary Mean-Field Games with Local Coupling

Files

explctsols1d-V5.pdf (1022.48 KB)

Type

Article

Authors

Gomes, Diogo A.

Nurbekyan, Levon

Prazeres, Mariana

KAUST Department

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)

Online Publication Date

2017-05-25

Print Publication Date

2018-06

Date

2017-05-25

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.

Citation

Gomes DA, Nurbekyan L, Prazeres M (2017) One-Dimensional Stationary Mean-Field Games with Local Coupling. Dynamic Games and Applications. Available: http://dx.doi.org/10.1007/s13235-017-0223-9.