Prof. Yufei Zhang, Imperial College London

Title: The alpha-Potential Game Paradigm: Theory, Algorithms, and Applications

Abstract: Designing and analyzing non-cooperative multi-agent systems that interact within shared dynamic environments is a central challenge across many established and emerging applications, including autonomous driving, production management, and e-commerce. A key objective in these systems is to identify Nash equilibria, where no agent can benefit by unilaterally deviating from her strategy. However, computing such equilibria is generally intractable unless specific structural properties of the interactions can be leveraged.

In this talk, we provide an overview of a recently developed framework for dynamic N-player games, called alpha-potential games. This approach extends classical potential games to dynamic settings by capturing how individual incentives approximately align with a global alpha-potential function, up to an error level alpha. Within this framework, the problem of computing approximate Nash equilibria reduces to a stochastic control problem for the alpha-potential function, significantly simplifying both analysis and computation. The parameter alpha also reveals important structural properties of the game, such as the population size, the strength of player interactions, and the degree of heterogeneity across agents. We complement these theoretical insights with numerical experiments based on policy gradient methods, illustrating how the alpha-potential framework enables efficient equilibrium computation in large-scale, dynamic multi-agent systems.

Brief bio: Yufei Zhang is an Associate Professor in Mathematical Finance and Machine Learning and also a co-director of the MSc in Mathematics and Finance in the Department of Mathematics, Imperial College London. Previously he was an Assistant Professor at the Department of Statistics, London School of Economics and Political Science. He did his PhD in the Mathematical Institute at University of Oxford. His research interests lie at the intersection of machine learning, stochastic control and games, and mathematical finance. His work combines these two fields, offering a theoretically grounded framework for systematically designing safe and efficient algorithms for high-stakes decision-making in finance and engineering.