Correlation Without Mediation: Expanding the Set of Equilibria Outcomes by ‘Cheap’ Pre-Play Procedures

Let P be a correlated equilibrium distribution on the set of outcomes of a game G. Can P be implemented by some "cheap" pre-play procedure that does not involve a mediator? It is shown that if there are two distinct Nash equilibrium payoffs for each player in G and if P is rational (that is, consists of probabilities which are rational numbers) and generates for each player i an expected payoff which is above her worst Nash equilibrium payoff, then P can be virtually implemented in a sequential equilibrium of an extended game which is generated by adding a "cheap" pre-play phase.