CS 364 A : Algorithmic Game Theory Lecture # 18 : From External Regret to Swap Regret and the Minimax Theorem ∗

Last lecture we proved that coarse correlated equilibria (CCE) are tractable, in a satisfying sense: there are simple and computationally efficient learning procedures that converge quickly to the set of CCE. Of course, if anything in our equilibrium hierarchy (Figure 1) was going to be tractable, it was going to be CCE, the biggest set. The good researcher is never satisfied and always seeks stronger results. What can we say if we zoom in to the next-biggest set, the correlated equilibria? The first part of this lecture shows that correlated equilibria are also tractable. We’ll give computationally efficient — if not quite as simple — learning procedures that converge fairly quickly to this set.