One-dimensional stationary mean-field games with local coupling
Analysis of PDEs
2016-11-29 v2
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
Cite
@article{arxiv.1611.08161,
title = {One-dimensional stationary mean-field games with local coupling},
author = {Diogo A. Gomes and Levon Nurbekyan and Mariana Prazeres},
journal= {arXiv preprint arXiv:1611.08161},
year = {2016}
}
Comments
30 pages, 19 figures