KAUST DepartmentComputer, 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)
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AbstractA 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.
CitationGomes 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.
JournalDynamic Games and Applications