Mean field games systems of first order

Cardaliaguet, Pierre; Graber, Philip Jameson

Cardaliaguet, Pierre; Graber, Philip Jameson (2015), Mean field games systems of first order, ESAIM. COCV, 21, 3, p. 690-722. 10.1051/cocv/2014044

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1401.1789v1

Date

2015

Journal name

ESAIM. COCV

Volume

Number

Publisher

EDP sciences

Published in

Paris

Pages

690-722

Abstract (EN)

We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this solution as the minimizer of some optimal control of Hamilton-Jacobi and continuity equations. We also prove that this solution converges in the long time average to the solution of the associated ergodic problem.

Subjects / Keywords

nonlinear PDE; optimal control; transport theory; long time average; Hamilton-Jacobi equations; mean field games