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EFGNV FIRST-ORDER STATIONARY MEAN-FIELD GAMES WITH CONGESTION.pdf
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ArticleKAUST Department
Applied Mathematics and Computational Science ProgramCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
KAUST Grant Number
OSR-CRG2017-3452Date
2018-04-30Preprint Posting Date
2017-10-04Online Publication Date
2018-04-30Print Publication Date
2018-08Permanent link to this record
http://hdl.handle.net/10754/626821
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Mean-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.Citation
Evangelista 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.Sponsors
The authors were partially supported by King Abdullah University of Science and Technology (KAUST) baseline and start-up funds, and grant OSR-CRG2017-3452.Publisher
Elsevier BVJournal
Nonlinear AnalysisarXiv
1710.01566Additional Links
http://arxiv.org/abs/1710.01566v1http://arxiv.org/pdf/1710.01566v1
http://www.sciencedirect.com/science/article/pii/S0362546X18300695
ae974a485f413a2113503eed53cd6c53
10.1016/j.na.2018.03.011