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A correlated equilibrium is a solution concept in game theory where players coordinate their strategies based on signals from an external source, which assigns probabilities to each outcome, resulting in no player benefiting from changing their strategy after the signal.

Unlike a Nash Equilibrium, where players' strategies are independent, in a Correlated Equilibrium players may base their strategies on common signals allowing for the possibility of coordination between their actions.

Consider a traffic light serving as the external signal in a two-driver game at an intersection. If the light is green for one driver and red for the other, each has a recommended strategy (go or stop), leading to a correlated equilibrium.

A probability distribution $P$ over the set of strategy profiles $S$ is a correlated equilibrium if no player has an incentive to unilaterally deviate from their strategy, given the signal they receive.