Mean field games systems of first order

¹ Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France
² Commands team (ENSTA ParisTech, INRIA Saclay), 828, Boulevard des Maréchaux, 91762 Palaiseau cedex, France
jameson.graber@ensta-paristech.fr

Received: 1 August 2014
Revised: 23 July 2014

Abstract

We consider a first-order 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.