Learning in mean field games: The fictitious play

Pierre Cardaliaguet (1) , Saeed Hadikhanloo (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

Mean Field Game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. We introduce a learning procedure (similar to the Fictitious Play) for these games and show its convergence when the Mean Field Game is potential.

Mots clés: Mean field games; learning

Domaines: Mathématiques [math]

Pierre Cardaliaguet, Saeed Hadikhanloo. Learning in mean field games: The fictitious play. ESAIM: Control, Optimisation and Calculus of Variations, 2017, 23 (2), pp.569-591. ⟨10.1051/cocv/2016004⟩. ⟨hal-02922726⟩