Correlated Equilibrium as an Expression of Bayesian Rationality

Abstract

Correlated equilibrium is formulated in a manner that does away with the dichotomy usually perceived between the "Bayesian" and the "game-theoretic" view of the world.From the Bayesian viewpoint, probabilities should be assignable to everything, including the prospect of a player choosing a certain strategy in a certain game.The so-called "game-theoretic" viewpoint holds that probabilities can only be assigned to events not governed by rational decision makers; for the latter, one must substitute an equilibrium (or other game-theoretic) notion.The current formulation synthesizes the two viewpoints: Correlated equilibrium is viewed as the result of Bayesian rationality; the equilibrium condition appears as a simple maximization of utility on the part of each player, given his information.A feature of this approach is that it does not require explicit randomization on the part of the players.Each player always chooses a definite pure strategy, with no attempt to randomize; the probabilistic nature of the strategies reflects the uncertainty of other players about his choice.Examples are given.