 Another correlated equilibrium concept formalized by Aumann (1974, 1987) does give a determinate prediction of what agents will do in a game given appropriate common knowledge. To illustrate Aumann’s correlated equilibrium concept, let us consider the Figure 3.1 game once more. If Joanna and Lizzi can tie their strategies to their knowledge of the possible worlds in a certain way, they can follow a system of correlated strategies which will yield a payoff vector they both prefer to that of the mixed Nash equilibrium and which is itself an equilibrium. One way they can achieve this is to have their friend Ron play a variation of the familiar shell game by hiding a pea under one of three walnut shells, numbered 1, 2 and 3. Joanna and Lizzi both think that each of the three relevant possible worlds corresponding to \(\omega_k = \{\)the pea lies under shell \(k\}\) is equally likely. Ron then gives Lizzi and Joanna each a private recommendation, based upon the outcome of the game, which defines a system of strategy combinations f as follows