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：本文给出了一个简洁的证明，证明了已知结论：在两人零和博弈中，粗相关均衡的边缘策略构成纳什均衡。这一事实的推论是：收敛于粗相关均衡集合的无外部遗憾学习算法，在两人零和博弈中也将收敛于纳什均衡。我们进一步展示了近似版本：$\epsilon$-粗相关均衡蕴含$2\epsilon$-纳什均衡。