Mean field games systems of first order
  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. 
Pierre Cardaliaguet (CEREMADE), Philip Jameson Graber (UMA/OC, INRIA   Saclay - Ile de France)
math.OC