Consider the following variant of the Rock-Paper-Scissors game where two equal strategies tie with payoff 0 for
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Consider the following variant of the Rock-Paper-Scissors game where two equal strategies tie with payoff 0 for both players, but two unequal strategies give payoff 1 to the winner and -2 to the loser.
(a) Find a Nash equilibrium of this game, and its payoff to the two players. Show that when this Nash equilibrium is considered as a correlated equilibrium, all incentive constraints (12.4) and (12.5) are tight (that is, hold as equalities). This fact may suffice to indicate that the Nash and correlated equilibrium is unique; for a different proof see von Stengel and Zamir (2010, Remark 13).
(b) Find a coarse correlated equilibrium of this game that has higher expected payoff to the players than the Nash equilibrium in (a).
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