In this paper we establish an isomorphism between the set of correlated equilibria of a game on the one hand and the set of ordered pairs of coordination mechanisms and equilibrium decision rules for the same game on the other, in the case of bounded and unbounded rationality. The paper develops a systematic theory establishing an injection from the set of ordered pairs of coordination mechanisms and equilibrium decision rules tot he set of correlated equilibria. The converses follow easily from the methods of the proofs. As an intermediate step, we introduce the concept of a conditionally correlated equilibrium under bounded rationality.