Perfect Correlated Equilibria

The ([ epsilon ] -) perfect correlated equilibria (P.C.E.) are those induced by a ([ epsilon ] -) perfect equilibrium of some correlation device. The "revelation principle" fails for this concept - the direct mechanism may not yield a perfect equilibrium. The approximately perfect correlated equilibria (A.P.C.E.) are the limits of [ epsilon ]-P.C.E., and we obtain a full characterisation for them. Even the A.P.C.E. are "acceptable". We argue on an example that, among those, these are the P.C.E. which seem the "right" concept.