# Convergence to the Mean Field Game Limit: A Case Study

## When:

Oct 19, 2018 - 1:00pm to 2:00pm

## Where:

Rettaliata Engineering Center, Room 242

## Speaker:

Marcel Nutz
Department of Statistics and Department of Mathematics, Columbia University

## 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 Type:

Department of Applied Mathematics - Mathematical Finance and Stochastic Analysis Seminar