Appears in collection : Foules : modèles et commande / Crowds: Models and Control

Mean field games (MFG) are dynamic games with infinitely many infinitesimal agents. In this joint work with Catherine Rainer (U. Brest), we study the efficiency of Nash MFG equilibria: Namely, we compare the social cost of a MFG equilibrium with the minimal cost a global planner can achieve. We find a structure condition on the game under which there exists efficient MFG equilibria and, in case this condition is not fulfilled, quantify how inefficient MFG equilibria are.