A Note on Bayesian Rationality and Correlated Equilibrium

Abstract: Bayesian rationality in strategic games presumes that it is possible to translate strategic uncertainty into imperfect information. Correlated equilibrium is guided by the idea that players are Bayes rational, have a common prior, and choose their strategies independently. I show that an essential condition for Bayesian rationality is violated in every game with imperfect information. Moreover, without strategic uncertainty, players cannot choose their strategies independently. This means strategic independence requires strategic uncertainty. If we distinguish between strategic certainty and uncertainty, we are able to explain both the existence of the cooperative and the noncooperative solution of the prisoner's dilemma.