Abstract : 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.

Keywords : mean field games; McKean-Vlasov control problem