Talk information

Speaker: Jiacheng Zhang

Affiliation: UC Berkeley

Title: Optimization Frameworks and Sensitivity Analysis of Stackelberg Mean-Field Games

Abstract:  This paper proposes and studies a class of discrete-time finite-time-horizon Stackelberg mean-field games, with one leader and  an infinite number of identical and indistinguishable followers. In this game, the objective of the leader is to maximize her reward considering the worst-case cost over all possible $\epsilon$-Nash equilibria among followers. A new analytical paradigm is established by showing the equivalence between this Stackelberg mean-field game  and a minimax optimization problem. This optimization framework facilitates studying both analytically and numerically the set of Nash equilibria for the game, and leads to the  sensitivity and the robustness analysis of the game value. In particular, when there is model uncertainty, the game value for the leader suffers non-vanishing sub-optimality as the perturbed model converges to the true model. In order to obtain a near-optimal solution, the leader needs to be more pessimistic with anticipation of model errors and adopts a relaxed version of the original Stackelberg game.

Slides: See below