Occasionally, two parties resolve a dispute (pick a "winner") by playing a variant of Rock-Paper-Scissors. In this version, the parties are penalized if there is a delay before a winner is declared; a delay occurs when both players choose the same strategy. The resulting payoff matrix is the following: player II Rock Paper Scissors player I Rock (1, 1) (0, 1) (1, 0) Paper (1, 0) (1, 1) (0, 1) Scissors (0, 1) (1, 0) (1, 1) Show that this game has a unique Nash equilibrium that is fully mixed, and results in expected payoffs of 0 to both players. Then show that the following probability distribution is a correlated equilibrium in which the players obtain expected payoffs of 1/2: player II Rock Paper Scissors player I Rock 0 1/6 1/6 Paper 1/6 0 1/6 Scissors 1/6 1/6 0