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First-order, stationary mean-field games with congestion.
- Source :
-
Nonlinear Analysis . Aug2018, Vol. 173, p37-74. 38p. - Publication Year :
- 2018
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0362546X
- Volume :
- 173
- Database :
- Academic Search Index
- Journal :
- Nonlinear Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 129647921
- Full Text :
- https://doi.org/10.1016/j.na.2018.03.011