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Suppose you and I play a game of rock-paper-scissors. As usual, rock beats

scissors, which beats paper, which beats rock. The payoffs are as follows: If we both play the same thing, no money is exchanged. If I play rock and you play paper, I owe you one dollar. If I play rock and you play scissors, you owe me two dollars. If I play scissors and you play paper, you owe me three dollars. If our roles are reversed, so are the payments (for example, if I play paper and you play scissors, I owe you three dollars). Write down the payoff matrix for this zero-sum game, and then solve the game by finding the value and the optimal strategies for both players.

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