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, smart grid management, and e-commerce. A key objective in these systems is to identify Nash equilibria, where no agent can benefit by unilaterally deviating from its strategy. However, computing such equilibria is generally intractable unless specific structural properties of the interactions can be leveraged.

Recently, we have developed a new paradigm known as the alpha-potential game framework for studying dynamic games. This talk illustrates the framework through a class of dynamic games motivated by game-theoretic models of crowd motion. We show that analyzing alpha-Nash equilibria reduces to solving a finite-dimensional control problem. Beyond providing viscosity and verification characterizations for general games, we examine in detail how spatial population distributions and interaction rules shape the structure of alpha-Nash equilibria, in particular for crowd motion games.

Theoretical insights are complemented by numerical experiments based on policy gradient algorithms, which highlight the computational advantages of the alpha-potential game framework for efficiently computing Nash equilibria in dynamic multi-agent environments.