报告人：Prof. Yufei Zhang（Imperial College London）
时间：2025年6月13日周五下午16：00-17:00
腾讯会议ID：514-126-405
报告题目: alpha-potential games: A new paradigm for N -player dynamic games
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's change 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 analytical characterization 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, and the intensity of interactions and the level of heterogeneity among players. We further show the alpha -Nash equilibrium of the stochastic game can be constructed through an associated conditional McKean-Vlasov control problem. To illustrate our findings, we examine a linear-quadratic game on a graph, where alpha captures asymmetric interactions and player heterogeneity beyond the mean-field paradigm.
Bio: Yufei Zhang is an Associate Professor in Mathematical Finance and Machine Learning in the Department of Mathematics at Imperial College London. Prior to this, he was an Assistant Professor in the Department of Statistics at the London School of Economics and Political Science. His research lies at the intersection of stochastic control and games, machine learning, and mathematical finance. He has published over 20 papers in leading journals in applied probability and optimal control, including the Annals of Applied Probability and the SIAM Journal on Control and Optimization.