Abstract

Mean field games are interpreted as approximations to n-player games with large n. In this talk we study the convergence of Nash equilibria in a specific setting. If the mean field game has a unique equilibrium, any sequence of n-player equilibria converges to it as n tends to infinity. However, we will see that both the finite and infinite player versions of the game often admit multiple equilibria. We show that mean field equilibria satisfying a transversality condition are indeed limits of n-player equilibria, but we also find mean field equilibria that are not limits, thus questioning their interpretation as "large n" equilibria. (Joint work with Jaime San Martin and Xiaowei Tan)