Separable and low-rank continuous games

Abstract—Separable games are a structured subclass of continuous games whose payoffs take a sum-of-products form; the zero-sum case has been studied in earlier work. Included in this subclass are all finite games and polynomial games. Separable games provide a unified framework for analyzing and generating results about the structural properties of low rank games. This work extends previous results on low-rank finite games by allowing for multiple players and a broader class of payoff functions. We also discuss computation of exact and approximate equilibria in separable games. We tie these results together with alternative characterizations of separability which show that separable games are the largest class of continuous games to which low-rank arguments apply. I