Correlated perfect equilibrium

We propose a refinement of correlated equilibrium based on common perturbations of the mediator’s recommendation distribution, which we call correlated perfect equilibrium (CPE). In finite games, the set of CPEs is nonempty and forms a finite union of convex polyhedra. Like perfect equilibrium, a CPE never assigns positive probability to any weakly dominated strategy. We provide a dual representation of CPE, which yields an iterative procedure for identifying CPEs. These perturbations provide a common source of off-equilibrium beliefs, a feature that distinguishes CPE from two existing refinements of correlated equilibrium—acceptable correlated equilibrium (Myerson, 1986) and perfect direct correlated equilibrium (Dhillon and Mertens, 1996)—as we demonstrate through examples.