Long time average of mean field games

Pierre Cardaliaguet (1, 2) , Jean-Michel Lasry (1, 2) , Pierre Louis Lions (1, 2, 3) , Alessio Porretta (4)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Université Paris Dauphine-PSL
3 Collège de France - Chaire Équations aux dérivées partielles et applications
4 DIPMAT - Dipartimento di Matematica [Roma II]

We consider a model of mean field games system defined on a time interval [0, T] and investigate its asymptotic behavior as the horizon T tends to infinity. We show that the system, rescaled in a suitable way, converges to a stationary ergodic mean field game. The convergence holds with exponential rate and relies on energy estimates and the Hamiltonian structure of the system.

Domaines: Optimisation et contrôle [math.OC]

Pierre Cardaliaguet, Jean-Michel Lasry, Pierre Louis Lions, Alessio Porretta. Long time average of mean field games. Networks and Heterogeneous Media, 2012, 7 (2), pp.279-301. ⟨10.3934/nhm.2012.7.279⟩. ⟨hal-00767403⟩