Selecting efficient correlated equilibria through distributed learning

A learning rule is completely uncoupled if each player's behavior is conditioned only on his own realized payoffs, and does not need to know the actions or payoffs of anyone else. We demonstrate a simple, completely uncoupled learning rule such that, in any finite normal form game with generic payoffs, the players' realized strategies implements a socially optimal coarse correlated (Hannan) equilibrium a very high proportion of the time. That is, the empirical frequency associated with the players' collective behavior will be consistent with a socially optimal coarse correlated equilibrium. A variant of the rule implements a socially optimal correlated equilibrium a very high proportion of the time.