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arXiv · 1611.08161

One-dimensional stationary mean-field games with local coupling

Diogo A. Gomes·Levon Nurbekyan·Mariana Prazeres
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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.

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Diogo A. Gomes, Levon Nurbekyan, Mariana Prazeres. 2016-11-24. One-dimensional stationary mean-field games with local coupling. https://arxiv.org/abs/1611.08161

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