Assignment: Games and Economic Behavio
1. Two entrepreneurs trying to decide whether to start a dry cleaning store in a town without any dry cleaners. We call the two firms "Cleaner 1" and "Cleaner 2." They each simultane¬ously chooses its entry decision between enter and stay out. That is, They make choices from {Enter, Stay Out}. If both choose to enter, Cleaner 1 faces an Enter payoff of -100 and Cleaner 2 faces an Enter payoff of -50. If both choose to stay out, they both earn 0. If only Cleaner 1 enters and Cleaner 2 stays out, Cleaner 1 earns 150 and Cleaner 2 earns 0. If only Cleaner 2 enters and Cleaner 1 stays out, Cleaner 2 earns 100 and Cleaner 1 earns 0. Put the strategic situation in Normal form.
2. An Entrepreneur trying to decide whether to start a dry cleaning store in a town already served by one dry cleaning store. In this Dry Cleaners Game, let us specify the players to be "New Cleaner" and "Old Cleaner" and model the possibility of recession as a move by Nature. New Cleaner must also worry about whether Old Cleaner will respond to entry with a price war, or by keeping its initial high prices, and is uncertain about whether the economy will be in a recession or not, which will affect how much consumers pay for dry cleaning. Old Cleaner is a well-established firm, and it would survive any price war, though its profits would fall. With probability 0.3, Nature decides that there will be a recession, and with probability 0.7 there will not. Even if the players always took the same actions, this random move means that the model would yield more than just one prediction. Here is the order of play we have specified for the Dry Cleaners Game:
1) New Cleaner chooses it entry decision from the strategy set;
2) Old Cleaner chooses its price from the strategy set;
3) Nature picks demand to be Recession with probability 0.3 or Normal with probability 0.7.
If New Cleaner chooses to enter and Old Cleaner responds with a price war, the payoffs will be (-160, -110) for New Cleaner and Old Cleaner respectively if Recession and (-100, -50) if Normal. If New Cleaner chooses to enter and Old Cleaner keeps its initial high prices, the payoffs will be (40, 40) if Recession and (100, 100) if Normal. If New Cleaner chooses to stay out and Old Cleaner still chooses to lower its prices, the payoffs will be (0, -10) if Recession and (0, 50) if Normal. If New Cleaner chooses to stay out and Old Cleaner maintains its prices unchanged, the payoffs will be (0, 240) if Recession and (0, 300) if Normal.
(A) Determine the strategy sets for New Cleaner in this game.
(B) Determine the strategy sets for Old Cleaner in this game.
(C) Draw the extensive form of this game.
(D) Draw the normal form of this game.
3. Iteratively eliminate all strictly dominated strategies. Which strategies survive? (Please list the strategies that you delete in the order to delete them, as well as the strategies that you used to dominate them.)
(A) Consider the following abstract game. Player 1 has two strategies and player 2 has three:
S1 = {Up,Down},
S2 = {Left,Center,Right}.
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Player 2
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Left
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Center
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Right
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Player 1
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Up
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(1, 0)
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(1, 2)
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(0, 1)
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Down
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(0, 3)
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(0, 1)
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(2, 0)
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(B) Consider the following abstract game. Player 1 has three strategies and player 2 also has three:
S1 = {Up,Middle,Down},
S2 = {Left,Center,Right}.
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Player 2
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Left
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Center
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Right
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Player 1
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Up
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(2, 12)
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(1, 10)
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(1, 11)
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Middle
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(0, 12)
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(0, 10)
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(0, 11)
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Down
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(0, 12)
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(1, 10)
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(0, 13)
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4. Perform iterative deletion of dominated strategies. (Please list the strategies that you delete in the order to delete them, as well as the (possibly weighted combination of) strategies that you used to dominate them.) Consider the following abstract game. Player 1 has three strategies and player 2 also has three:
S1 = {Up,Middle,Down},
S2 = {Left,Center,Right}.
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Player 2
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Left
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Center
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Right
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Player 1
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Up
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(8, 11)
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(7, 9)
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(21, 18)
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Middle
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(5, 14)
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(18, 18)
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(15, 9)
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Down
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(5, 22)
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(11, 5)
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(17, 6)
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