midterm

# midterm - Professor Rod Garratt ECON 171 Midterm This exam...

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Professor Rod Garratt ECON 171 Midterm April 27, 2011 This exam is worth a total of 40 Points. You have 1 hour and 15 minutes to complete this exam. Good Luck! 1. Consider the game of Marienbad which, like the game of Nim, is zero-sum (there is a winner and a loser). As in Nim, there are two piles of match sticks and two players, player 1 and player 2. Let m be the number of sticks in the first pile and let n be the number of sticks in the second pile. Player 1 moves first and thereafter the players take turns. At each turn, a player can pick up any number of available matches from one of the two piles. The player who removes the last match in Marienbad loses the game (this is just the opposite of the rule for winning Nim). Prove/explain the following claims: a) If m=n=1, then player 1 has a winning strategy. (2 points) b) If m=n>1 (e.g. m=5, n=5), then player 2 has a winning strategy. (2 points) c) If m n, then player 1 has a winning strategy. (1 point)

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Use the minimax method to find the Nash equilibrium for the following zero-sum game. (3 points) Column Left Right Row Up 2 5 Down 3 4 3. Use successive elimination of dominated strategies to solve the following game. (2 points)
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midterm - Professor Rod Garratt ECON 171 Midterm This exam...

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