Jianfeng Zhang, University of Southern California

Set values of non-zero sum games and mean field games
Date
Mar 16, 2022, 4:30 pm5:30 pm
Event Description

A non-zero sum game may typically have multiple Nash equilibria and different equilibria could lead to different values. We propose to study the set of values over all equilibria, which we call the set value of the game. The set value will play the role of the standard value function in the optimal control problem. In particular, we shall establish two major properties of the set value: (i) the dynamic programming principle; and (ii) the stability. The results are extended to mean field games without monotonicity conditions, for which we shall also establish the convergence of the set values of the corresponding N-player games. Some subtle issues on the choices of controls will also be discussed. The talk is based on two works, one with Feinstein and Rudloff, and the other with Iseri.