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Correlated Equilibrium as an Expression of Bayesian Rationality

Robert J. Aumann

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.