Mean field games are generally interpreted as approximations to n-player games with large n. Indeed, n-player Nash equilibria are known to converge to their mean field counterpart when the latter is unique. In this talk we study a specific stochastic game where both the finite and infinite player versions naturally admit multiple equilibria. It turns out that mean field equilibria satisfying a transversality condition are indeed limits of n-player equilibria, but we also find a complementary class of equilibria that are not limits, thus questioning their interpretation as large n equilibria. (Joint work with Jaime San Martin and Xiaowei Tan)