Reference no: EM13846595
1. For the following 2-player nonzero-sum game, simplify the game as much as you can by eliminating 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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1, 3
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4, 5
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9, 0
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M
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2, 7
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2, 4
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4, 0
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D
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8, 0
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3, 5
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1, 2
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2. List the Pareto efficient outcomes of the game in Question 1 (e.g., (U,L),. . .).
3. Consider the following general 2 × 2 zero-sum game, with the payoff numbers a, b, c, d all distinct.
a) Show that if (U, L) are the maxmin strategies then b > a > c.
b) Show that if (U, L) are the maxmin strategies then at least one player has a dominated strategy.
4. For each of the following two nonzero-sum games, is the game strategically equivalent to a ZSG? If your answer is "YES," give a strategically equivalent ZSG and show why it is strategically equivalent. If your answer is "NO," explain why not.
a)
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U
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L
4, -2
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R
0, 0
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D -2, 1
(2 points)
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6, -3
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L
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R
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U
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-1, 2
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4, 4
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D
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-2, 0
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3, 2
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b
5. Consider the following sequential ZSG. First, nature chooses heads or tails, each with probability one-half. Player 1 then sees nature's choice, and chooses heads or tails. Player 2 then sees player 1's choice but not nature's choice, and chooses heads or tails, which ends the game. If player 2's choice matches nature's choice, player 2 wins a dollar from player 1. If player 2's choice does not match nature's choice, player 1 wins a dollar from player 2. Draw an extensive form for this game (Hint: look at the game tree on page 393 in the text).