  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.
