886 research outputs found
Long time average of first order mean field games and weak KAM theory
We show that the long time average of solutions of first order mean field
game systems in finite horizon is governed by an ergodic system of mean field
game type. The well-posedness of this later system and the uniqueness of the
ergodic constant rely on weak KAM theory
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
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