Consider the game of Rock, Paper, Scissors (RPS), with payoffs given as follows:
Is there a correlated equilibrium in this game?
Consider, for example the signal given to both players not to play the third strategy. In this case, the game (conditional upon one's opponent following the signal) becomes:
Which has a NE of playing the second strategy for both. This seems like a correlated equilibrium? On the other hand, if you know that your opponent follows the signal and plays the second strategy, you should respond by playing the third strategy. Hence, intuitively, as the signal reveals information on your opponent's play (conditional upon her following it) you should be able to exploit that by violating correlated equilibrium.