Xin Guo, University of California, Berkeley

An alpha-potential game framework for dynamic N-player games

Game theory has a long history, and the min-max game has been well studied from Von Neumann and Nash. The leap from min-max (zero-sum) games to general-sum games is a fundamental escalation in computational and conceptual complexity. Over the past decade, mean field game theory has emerged as a pivotal framework, offering profound theoretical insights and computational advances for the analysis of large-scale, non-zero-sum stochastic games. However, mean field games require homogeneity among players and focus on the limiting behavior when N goes to infinity.

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 for a dynamic game to minimize 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 will discuss through simple examples some recent theoretical developments, along with a few open problems for this new game framework.