Existence for stationary mean-field games with congestion and quadratic Hamiltonians

Gomes, Diogo A.; Mitake, Hiroyoshi

Existence for stationary mean-field games with congestion and quadratic Hamiltonians

Type

Article

Authors

Gomes, Diogo A.

Mitake, Hiroyoshi

KAUST Department

Applied 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

Online Publication Date

2015-09-03

Print Publication Date

2015-12

Date

2015-09-03

Abstract

Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel

Citation

Gomes DA, Mitake H (2015) Existence for stationary mean-field games with congestion and quadratic Hamiltonians. Nonlinear Differential Equations and Applications NoDEA. Available: http://dx.doi.org/10.1007/s00030-015-0349-7.