KAUST DepartmentApplied Mathematics and Computational Science Program
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
KAUST Grant NumberOSR-CRG2017-3452
Preprint Posting Date2017-10-04
Online Publication Date2018-04-30
Print Publication Date2018-08
Permanent link to this recordhttp://hdl.handle.net/10754/626821
MetadataShow full item record
AbstractMean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas. Here, we study stationary MFGs with congestion with quadratic or power-like Hamiltonians. First, using explicit examples, we illustrate two main difficulties: the lack of classical solutions and the existence of areas with vanishing densities. Our main contribution is a new variational formulation for MFGs with congestion. With this formulation, we prove the existence and uniqueness of solutions. Finally, we consider applications to numerical methods.
CitationEvangelista D, Ferreira R, Gomes DA, Nurbekyan L, Voskanyan V (2018) First-order, stationary mean-field games with congestion. Nonlinear Analysis 173: 37–74. Available: http://dx.doi.org/10.1016/j.na.2018.03.011.
SponsorsThe authors were partially supported by King Abdullah University of Science and Technology (KAUST) baseline and start-up funds, and grant OSR-CRG2017-3452.