Convergence to the Mean Field Game Limit: A Case Study
Host
Department of Applied Mathematics
Speaker
Marcel Nutz
Department of Statistics and Department of Mathematics, Columbia University
http://www.math.columbia.edu/~mnutz/
Description
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)
Event Topic
Mathematical Finance, Stochastic Analysis, and Machine Learning