Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222572 | Nonlinear Analysis: Theory, Methods & Applications | 2018 | 38 Pages |
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.
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Authors
David Evangelista, Rita Ferreira, Diogo A. Gomes, Levon Nurbekyan, Vardan Voskanyan,