Download Homework 7

Game Theory
Homework 7
Consider the following Prisoner’s Dilemma:
P1 \ P2
C
D
C
3, 6
5, 2
D
0, 8
2, 4
Assume that player 2 is playing tit-for-tat, and that player 1 knows this. For what effective rate of return,
R, will player 1 defect once?
For what values of R will player 1 defect forever?
If the payer 1’s discount rate is 90%, δ = 0.90, then for what probabilities of playing the game again, p,
will player 1 defect once?
If the probability of playing the game again is 75%, p = 0.75, then for what discount rate will player 1
defect once?
Assume that player 1 is playing tit-for-tat, and that player 2 knows this. For what effective rate of return,
R, will player 2 defect once?
For what values of R will player 2 defect forever?
If the payer 2’s discount rate is 85%, δ = 0.85, then for what probabilities of playing the game again, p,
will player 2 defect once?
If the probability of playing the game again is 80%, p = 0.80, then for what discount rate will player 2
defect once?
Consider the following Prisoner’s Dilemma:
P1 \ P2
C
D
C
3, 4
H1, 0
D
0, 5
2, D2
The probability of playing the game again is 75% and both players have a discount rate of 80%.
What is the effective rate of return, R?
Assume player 2 is playing tit-for-tat. For what values of H1 will player 1 defect forever?
Assume player 1 is playing tit-for-tat. For what values of D2 will player 2 defect forever?
Consider the following Prisoner’s Dilemma:
P1 \ P2
C
D
C
C1, C2
4, 1
D
0, 5
2, 2
Both players have an effective rate of return of 50%, R = 0.50.
Assume player 2 is playing tit-for-tat. For what values of C1 will player 1 defect forever?
Assume player 1 is playing tit-for-tat. For what values of C2 will player 2 defect forever?