Long time average of first order mean field games and weak KAM theory

Pierre Cardaliaguet (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Domaines: Optimisation et contrôle [math.OC]

Pierre Cardaliaguet. Long time average of first order mean field games and weak KAM theory. Dynamic Games and Applications, 2013, 3 (4), pp.473-488. ⟨10.1007/s13235-013-0091-x⟩. ⟨hal-00827956⟩