割峔狨本立瓜□


2018/11/13(Tue)

16:30--18:00 醒喀項撮 釐本立瓜□撮 (E404)

Marcel Nutz

Columbia University

Convergence to the Mean Field Game Limit: A Case Study

Mean field games are usually interpreted as approximations to n-player games with large n. In this talk we study the convergence of Nash equilibria in a specific stochastic game. 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)