Speaker: Yufei Zhang, senior lecturer, Department of Mathematics, Imperial College London

Date: May 10, 2024

Time: 16:00-17:00

Location: Tencent Meeting: 290 967 416

Sponsor: School of Mathematics, Shandong University

Abstract:

Static potential games, pioneered by Monderer and Shapley (1996), are non-cooperative games in which there exists an auxiliary function called static potential function, so that any player'schange in utility function upon unilaterally deviating from her policy can be evaluated through the change in the value of this potential function. The introduction of the potential function is powerful as it simplifies the otherwise challenging task of finding Nash equilibria for non-cooperative games: maximizers of potential functions lead to the game's Nash equilibria.

In this talk, we propose an analogous and new framework called $\alpha$-potential game for dynamic $N$-player games, with the potential function in the static setting replaced by an$\alpha$-potential function. We present an analyticalcharacterization of $\alpha$-potential functions for any dynamic game. For stochastic differential games in which the state dynamic is a controlled diffusion, $\alpha$ is explicitly identified in terms of the number of players, the choice of admissible strategies, and the intensity of interactions and the level of heterogeneity among players.

We provide detailed analysis for games with mean-field interactions,distributed games, and crowd aversion games, for which $\alpha$ is shown to decay to zero as the number of players goes to infinity, even with heterogeneity in state dynamics, cost functions, and admissible strategy classes. We also show $\alpha$ is capable of capturing the subtle difference between the open-loop and closed-loop strategies.

The talk is based on joint work with Xin Guo and Xinyu Li:https;//arxiv.org/abs/2403.16962

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/190704.htm