  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.
