Calibrated Learning and Correlated Equilibrium
Statistics and Probability
Suppose two players repeatedly meet each other to play a game where: 1. each uses a learning rule with the property that it is a calibrated forecast of the other's plays, and 2. each plays a myopic best response to this forecast distribution. Then, the limit points of the sequence of plays are correlated equilibria. In fact, for each correlated equilibrium there is some calibrated learning rule that the players can use which results in their playing this correlated equilibrium in the limit. Thus, the statistical concept of a calibration is strongly related to the game theoretic concept of correlated equilibrium.