Question 4. Zeynep and Mehmet will eventually play the following game. Mehmet L R U 3,1 0,0 Zeynep D 0,3 1,3 In a preliminary stage, Zeynep has already asked Mehmet to allow her to move first and proposed to pay him 1 unit of her own payoff in exchange. So Mehmet has to options: • If he accepts Zeynep's offer: they will play the sequential move version of the above game in which Zeynep moves first. Mehmet will receive 1 unit of utility more, and Zeynep will receive 1 unit of utility less (in any outcome of the game) compared to the payoffs given in the bimatrix. 2 • If he rejects Zeynep's offer: they will play the simultaneous move game. a. Represent this strategic interaction in a game tree. b. How many information sets does each player have? c. Characterize the set of pure strategies for both players. d. Present this game as a normal-form game, and characterize the set of pure strategy Nash equi- libria.
Question 4. Zeynep and Mehmet will eventually play the following game. Mehmet L R U 3,1 0,0 Zeynep D 0,3 1,3 In a preliminary stage, Zeynep has already asked Mehmet to allow her to move first and proposed to pay him 1 unit of her own payoff in exchange. So Mehmet has to options: • If he accepts Zeynep's offer: they will play the sequential move version of the above game in which Zeynep moves first. Mehmet will receive 1 unit of utility more, and Zeynep will receive 1 unit of utility less (in any outcome of the game) compared to the payoffs given in the bimatrix. 2 • If he rejects Zeynep's offer: they will play the simultaneous move game. a. Represent this strategic interaction in a game tree. b. How many information sets does each player have? c. Characterize the set of pure strategies for both players. d. Present this game as a normal-form game, and characterize the set of pure strategy Nash equi- libria.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.9P
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Transcribed Image Text:Question 4. Zeynep and Mehmet will eventually play the following game.
Mehmet
L
R
U 3,1 0,0
Zeynep D 0,3 1,3
In a preliminary stage, Zeynep has already asked Mehmet to allow her to move first and proposed to
pay him 1 unit of her own payoff in exchange. So Mehmet has to options:
• If he accepts Zeynep's offer: they will play the sequential move version of the above game in which
Zeynep moves first. Mehmet will receive 1 unit of utility more, and Zeynep will receive 1 unit of
utility less (in any outcome of the game) compared to the payoffs given in the bimatrix.
2
• If he rejects Zeynep's offer: they will play the simultaneous move game.
a. Represent this strategic interaction in a game tree.
b. How many information sets does each player have?
c. Characterize the set of pure strategies for both players.
d. Present this game as a normal-form game, and characterize the set of pure strategy Nash equi-
libria.
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