Dynamic Games and Applications

, Volume 8, Issue 2, pp 315–351 | Cite as

One-Dimensional Stationary Mean-Field Games with Local Coupling

  • Diogo A. Gomes
  • Levon Nurbekyan
  • Mariana Prazeres
Article

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 

Mathematics Subject Classification

91A13 91A25 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.CEMSE Division and KAUST SRI, Uncertainty Quantification Center in Computational Science and EngineeringKing Abdullah University of Science and Technology (KAUST)ThuwalSaudi Arabia
  2. 2.CEMSE DivisionKing Abdullah University of Science and Technology (KAUST)ThuwalSaudi Arabia

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