A simple adaptive procedure leading to correlated equilibrium

We propose a new and simple adaptive procedure for playing a game: "regret-matching." In this procedure, players may depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies in the past. It is shown that our adaptive procedure guarantees that, with probability one, the empirical distributions of play converge to the set of correlated equilibria of the game.