Events

Columbia-NYU Financial Engineering Colloquium: An alpha-potential game framework for multi-agent system

Speaker: Yufei Zhang, Imperial College London

Location: TBA

Date: Thursday, October 9, 2025

Location: Columbia University
School of Social Work - Room 903 | 1255 Amsterdam Ave, New York, NY 10027

Designing and analyzing non-cooperative multi-agent systems interacting within shared dynamic environments is a central challenge in many existing and emerging applications, including autonomous driving, smart grid management, and e-commerce. A primary objective in these systems is to identify Nash equilibria, where no agent benefits from unilaterally changing its strategy. However, computing such equilibria is generally intractable unless specific structural properties of the multi-agent interactions can be exploited.

In this talk, we will present a new paradigm for dynamic N-player non-cooperative games called alpha-potential games, where the change of a player's value function upon unilateral deviation from her strategy is equal to the change of an alpha-potential function up to an error alpha. This game framework is shown to reduce the challenging task of finding alpha-Nash equilibria in a dynamic game to minimizing the associated alpha-potential function. The latter is then shown to be a conditional McKean--Vlasov control problem. In such games, analysis of alpha reveals critical game characteristics, including choices of admissible strategies, the intensity of interactions, and the level of heterogeneity among players.

We illustrate the theory through game-theoretic models of crowd motion dynamics and support it with numerical experiments using policy gradient algorithms, highlighting the computational advantages of the alpha-potential game framework in computing Nash equilibria for dynamic games.