Kathy Sapas
1. Suppose that three students play a game. Each student guesses an integer between 1 and 100. After all the guesses have been collected, we compute the median guess, which we will call M. The player whose guess is closest to 0.6*M is declared the winner and given $300. (If there is a tie, the money is split evenly among the tied players.) Each player has a utility function over the amount of money won, u(x) = x.
a. What are four possible actions that player 1 might choose?
b. What are the four possible outcomes of the game for player 1? Answer without any reference to money or utility.
c. What utility does player 1 get from each of the possible outcomes listed in part b?
d. If the following are the guesses, what is player 1's action, outcome, and payoff?
Player 1 guesses 30; Player 2 guesses 50; Player 3 guesses 50
Player 4 guesses 80; Player 5 guesses 40
e. Explain to player 4 why his guess was strictly dominated by another guess.
2. Consider the strategy profile s = (stag, hare). Locate a strategy profile s' that Pareto dominates profile s. Explicitly check every condition that you need to check to show that s' Pareto dominates s.
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STAG
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HARE
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STAG
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3, 3
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0, 1
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HARE
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1, 0
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1, 1
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3. In the following normal-form game, which strategy profiles survive iterated elimination of strictly dominated strategies?
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L
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C
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R
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U
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6,8
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2,6
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8,2
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M
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8,2
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4,4
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9,5
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D
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8,10
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4,6
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6,7
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