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Dynamic Games and Applications

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25-05-2017

One-Dimensional Stationary Mean-Field Games with Local Coupling

Authors: Diogo A. Gomes, Levon Nurbekyan, Mariana Prazeres

Published in: Dynamic Games and Applications | Issue 2/2018

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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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Title: One-Dimensional Stationary Mean-Field Games with Local Coupling
Authors: Diogo A. Gomes
Levon Nurbekyan
Mariana Prazeres
Publication date: 25-05-2017
Publisher: Springer US
Published in: Dynamic Games and Applications / Issue 2/2018
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-017-0223-9

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