# We come upon the game when it is at the position

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of the bars and takes a chunk out of it according to the rules defined above. We come upon the gamewhen it is at the position shown below. Are there any winning moves from this position? If so, list themall.(5 points),,,
5Name:(10 points)5. Solve the following zero-sum games(a)5213(4 points)(b)352623575236(6 points)
6Name:(10 points)6. Suppose you and I play a game of rock-paper-scissors. As usual, rock beats scissors, which beats paper, whichbeats rock. The payoffs are as follows: If we both play the same thing, no money is exchanged. If I play rockand you play paper, I owe you one dollar. If I play rock and you play scissors, you owe me two dollars. If Iplay scissors and you play paper, you owe me three dollars. If our roles are reversed, so are the payments (forexample, if I play paper and you play scissors, I owe you three dollars). Write down the payoff matrix for thiszero-sum game, and then solve the game by finding the value and the optimal strategies for both players. (10points)
7Name:(8 points)7.(a) Find the value of the following zero-sum game and optimal strategies for both players.(4 points)
(b) Show that all saddle points in a zero-sum game (assuming there is at least one) result in the same payoffto player I.(4 points)