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：我们给出了一个众所周知结果的简单证明：在双人零和博弈中，粗相关均衡的边缘策略构成纳什均衡。这一事实的推论是，收敛到粗相关均衡集的无外部遗憾学习算法在双人零和博弈中也将收敛到纳什均衡。我们展示了一个近似版本：$\epsilon$-粗相关均衡意味着$2\epsilon$-纳什均衡。