Correlated Equilibrium as an Expression of Bayesian Rationality

Correlated equilibrium is formulated in a manner that does away with the dichotomy
usually perceived between the "Bsyesian" 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.
KEYWORDS:Correlated equilibrium, Bayesian rationality, information, noncooperative
games, strategic equilibrium, Nash equilibrium, common priors, Harsanyi doctrine.