Consider the following one-stage simultaneous move game. Player 2 A B C A 6,6 1,7 0,3 Player 1 B X, 1 4,4 0,1 0 3,0 2,0 1, 1 a) Suppose x = 7.5, and that this game is repeated twice. Further suppose that players discount future period payoffs at a discount rate of 0 ≤ d ≤ 1 (that is, d today is as good for a player as 1 tomorrow). Consider the following statement: "There exists a subgame perfect Nash equilibrium in which (B, B) is played in the first period." In the blank, write the minimum value of d for which the statement is true. If the statement is true for all possible d, write 0. If the statement is not true for any possible d, write 2. b) Suppose x = 7.5, and that this game is repeated twice. Further suppose that players discount future period payoffs at a discount rate of 0 ≤ d < 1 (that is, d today is as good for a player as 1 tomorrow). Consider the following statement: "There exists a subgame perfect Nash equilibrium in which (A, A) is played in the first period." In the blank, write the minimum value of d for which the statement is true. If the statement is true for all possible d, write 0. If the statement is not true for any possible d, write 2. c) Suppose x = 11, and that this game is repeated twice. Further suppose that players discount future period payoffs at a discount rate of 0 ≤ d < 1 (that is, d today is as good for a player as 1 tomorrow). Consider the following statement: "There exists a subgame perfect Nash equilibrium in which (A, A) is played in the first period." In the blank, write the minimum value of d for which the statement is true. If the statement is true for all possible d, write 0. If the statement is not true for any possible d, write 2.
Consider the following one-stage simultaneous move game. Player 2 A B C A 6,6 1,7 0,3 Player 1 B X, 1 4,4 0,1 0 3,0 2,0 1, 1 a) Suppose x = 7.5, and that this game is repeated twice. Further suppose that players discount future period payoffs at a discount rate of 0 ≤ d ≤ 1 (that is, d today is as good for a player as 1 tomorrow). Consider the following statement: "There exists a subgame perfect Nash equilibrium in which (B, B) is played in the first period." In the blank, write the minimum value of d for which the statement is true. If the statement is true for all possible d, write 0. If the statement is not true for any possible d, write 2. b) Suppose x = 7.5, and that this game is repeated twice. Further suppose that players discount future period payoffs at a discount rate of 0 ≤ d < 1 (that is, d today is as good for a player as 1 tomorrow). Consider the following statement: "There exists a subgame perfect Nash equilibrium in which (A, A) is played in the first period." In the blank, write the minimum value of d for which the statement is true. If the statement is true for all possible d, write 0. If the statement is not true for any possible d, write 2. c) Suppose x = 11, and that this game is repeated twice. Further suppose that players discount future period payoffs at a discount rate of 0 ≤ d < 1 (that is, d today is as good for a player as 1 tomorrow). Consider the following statement: "There exists a subgame perfect Nash equilibrium in which (A, A) is played in the first period." In the blank, write the minimum value of d for which the statement is true. If the statement is true for all possible d, write 0. If the statement is not true for any possible d, write 2.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider the following one-stage simultaneous move game.
Player 2
A
B
C
A
6,6
1,7
0,3
Player 1
B
X, 1
4,4
0,1
0
3,0
2,0
1, 1
a) Suppose x = 7.5, and that this game is repeated twice. Further suppose that players discount future period payoffs at a discount rate of 0 ≤ d ≤ 1 (that is, d today is as good for a player as 1 tomorrow). Consider
the following statement:
"There exists a subgame perfect Nash equilibrium in which (B, B) is played in the first period."
In the blank, write the minimum value of d for which the statement is true. If the statement is true for all possible d, write 0. If the statement is not true for any possible d, write 2.
b) Suppose x = 7.5, and that this game is repeated twice. Further suppose that players discount future period payoffs at a discount rate of 0 ≤ d < 1 (that is, d today is as good for a player as 1
tomorrow). Consider the following statement:
"There exists a subgame perfect Nash equilibrium in which (A, A) is played in the first period."
In the blank, write the minimum value of d for which the statement is true. If the statement is true for all possible d, write 0. If the statement is not true for any possible d, write 2.
c) Suppose x = 11, and that this game is repeated twice. Further suppose that players discount future period payoffs at a discount rate of 0 ≤ d < 1 (that is, d today is as good for a player as 1
tomorrow). Consider the following statement:
"There exists a subgame perfect Nash equilibrium in which (A, A) is played in the first period."
In the blank, write the minimum value of d for which the statement is true. If the statement is true for all possible d, write 0. If the statement is not true for any possible d, write 2.
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