  If the players can contrive to correlate their actions with a common randomizing device, they can achieve a new equilibrium that is fair and that Pareto dominates the old mixed-strategy equilibrium. More specifically, suppose that there is a single coin toss: each player goes to Luigi’s if the toss is heads, Fabio’s if the toss is tails. The resulting strategy combination yields an expected payoff of \(\bfrac{3}{2}\) for each player. Intuitively, this strategy combination is an equilibrium, since no player has reason to deviate unilaterally from it. But the strategy combination does not count as a Nash equilibrium of the original game, since in mixed Nash equilibria players’ actions must be probabilistically independent. Aumann calls this strategy combination a correlated equilibrium, since players’ actions are probabilistically correlated. He develops this intuitive idea in great formal detail, without reliance upon explicit pre-game communication between players.