We give a simple proof of the well-known result that the marginal strategies of a coarse correlated equilibrium form a Nash equilibrium in two-player zero-sum games. A corollary of this fact is that no-external-regret learning algorithms that converge to the set of coarse correlated equilibria will also converge to Nash equilibria in two-player zero-sum games. We show an approximate version: that $\epsilon$-coarse correlated equilibria imply $2\epsilon$-Nash equilibria.
翻译:我们给出了一个简单的证明结果,即粗略相关均衡的边际策略构成了二人零和游戏中的纳什均衡。该结果的一个推论是无外悔学习算法收敛于粗略相关均衡集后也会收敛于二人零和游戏中的纳什均衡。我们证明了一个近似版本,即 $\epsilon$ -粗略相关均衡意味着 $2\epsilon$ -纳什均衡。