Neural Fictitious Self-Play in Imperfect Information Games with Many Players

Abstract

Computing Nash equilibrium solutions is an important problem in the domain of imperfect information games. Counterfactual Regret Minimization+ (CFR+) can be used to (essentially weakly) solve two-player limit Texas Hold’em, but it cannot be applied to large multi-player games due to the problem of space complexity. In this paper, we use Neural Fictitious Self-Play (NFSP) to calculate approximate Nash equilibrium solutions for imperfect information games with more than two players. Although there are no theoretical guarantees of convergence for NFSP in such games, we empirically demonstrate that NFSP enables us to calculate strategy profiles that are significantly less exploitable than random players in simple poker variants with three or more players.