#### Speaker: Jiajia Yu (Duke University)

Mean-field games study the Nash Equilibrium in a non-cooperative game with infinitely many agents. Most existing works study solving the Nash Equilibrium with given cost functions. However, it is not always straightforward to obtain these cost functions. On the contrary, it is often possible to observe the Nash Equilibrium in real-world scenarios. In this talk, I will discuss a bilevel optimization approach for solving inverse mean-field game problems, i.e., identifying the cost functions that drive the observed Nash Equilibrium. With the bilevel formulation, we retain the essential characteristics of convex objective and linear constraint in the forward problem. This formulation permits us to solve the problem using a gradient-based optimization algorithm with a nice convergence guarantee. We focus on inverse mean-field games with unknown obstacles and unknown metrics and establish the numerical stability of these two inverse problems. In addition, we prove and numerically verify the unique identifiability for the inverse problem with unknown obstacles. This is a joint work with Quan Xiao (RPI), Rongjie Lai (Purdue) and Tianyi Chen (RPI).

Time: October 6, 2023 3:40pm-4:40pm

Location: LeConte 440

Host: Wuchen Li