aaboyles
July 04, 2012
56

# More than you ever Wanted to Know about the Prisoner's Dilemma

A basic to mid-level overview of the Prisoner's Dilemma (and game theory) tailored to my Georgia Tech cohort's knowledge base.

July 04, 2012

## Transcript

1. ### More than you ever wanted to know about The Prisoner’s

Dilemma Tony Boyles Georgia Institute of Technology
2. ### What we’re doing here The Three Models of the Prisoner’s

Dilemma • Normal Form Game • Game of Mixed Strategy • Repeated Game …As Applied to Nuclear Strategy, And what’s really goes on.

4. ### The Prisoner’s Dilemma Cooperate Defect Cooperate 3, 3 1, 4

Defect 4, 1 2, 2 Player 1 Player 2
5. ### The Prisoner’s Dilemma Cooperate Defect Cooperate 3, 3 1, 4*

Defect *4, 1 *2, 2* Player 1 Player 2 Nash Equilibrium
6. ### The Prisoner’s Dilemma, Generalized Cooperate Defect Cooperate Good Worst, Best

Defect Best, Worst Bad Player 1 Player 2
7. ### The Prisoner’s Dilemma, Generalized Cooperate Defect Cooperate C, C A,

D Defect D, A B, B Player 1 Player 2 If we know that (Defect, Defect) is the Nash Equilibrium, for what values of A, B, C, and D is this a Prisoner’s Dilemma?
8. ### The Prisoner’s Dilemma, Generalized Cooperate Defect Cooperate C, C A,

D Defect D, A B, B Player 1 Player 2 D > C C > B B > A So, D > C > B > A
9. ### Is This A Prisoner’s Dilemma? Cooperate Defect Cooperate 4, 4

2, 13 Defect 13, 2 1, 1 Player 1 Player 2
10. ### Is This A Prisoner’s Dilemma? Cooperate Defect Cooperate 4, 4

*2, 13* Defect *13, 2* 1, 1 Player 1 Player 2 Nope!
11. ### Is Nuclear War a Prisoner’s Dilemma? Cooperate Defect Cooperate 0,

0 -100, 10 Defect 10, -100 -90, -90
12. ### Is Nuclear War a Prisoner’s Dilemma? Cooperate Defect Cooperate 0,

0 -100, 10 Defect 10, -100 -90, -90
13. ### Is Nuclear War a Prisoner’s Dilemma? Cooperate Defect Cooperate 0,

0 -100, 10 Defect 10, -100 -90, -90 Substantive Assumptions: • Threat is a nontrivial factor • Decision makers view themselves as better off if everyone suffers
14. ### Could a Nuclear War have Happened? p (1-p) Cooperate Defect

q Cooperate 0, 0 -100, 10 (1-q) Defect 10, -100 -90, -90
15. ### Could a Nuclear War have Happened? p (1-p) Cooperate Defect

q Cooperate 0, 0 -100, 10 (1-q) Defect 10, -100 -90, -90 E(Cooperate) = 0(p) + -100(1-p)
16. ### Could a Nuclear War have Happened? p (1-p) Cooperate Defect

q Cooperate 0, 0 -100, 10 (1-q) Defect 10, -100 -90, -90 E(Cooperate) = 0(p) + -100(1-p) E(Defect) = 10(p) + -90(1-p)
17. ### Could a Nuclear War have Happened? E(Cooperate) = 0(p) +

-100(1-p) E(Defect) = 10(p) + -90(1-p)
18. ### Could a Nuclear War have Happened? E(Cooperate) = 0(p) +

-100(1-p) E(Defect) = 10(p) + -90(1-p) 0(p) + -100(1-p) = 10(p) + -90(1-p)
19. ### Could a Nuclear War have Happened? E(Cooperate) = 0(p) +

-100(1-p) E(Defect) = 10(p) + -90(1-p) 0(p) + -100(1-p) = 10(p) + -90(1-p) -100 + 100p = 10p – 90 + 90p
20. ### Could a Nuclear War have Happened? E(Cooperate) = 0(p) +

-100(1-p) E(Defect) = 10(p) + -90(1-p) 0(p) + -100(1-p) = 10(p) + -90(1-p) -100 + 100p = 10p – 90 + 90p -10 = 0
21. ### Could a Nuclear War have Happened? E(Cooperate) = 0(p) +

-100(1-p) E(Defect) = 10(p) + -90(1-p) 0(p) + -100(1-p) = 10(p) + -90(1-p) -100 + 100p = 10p – 90 + 90p -10 = 0 There does not exist any possible probability value which satisfies this relationship!

= p = .999
24. ### What if we could assign a probability? Pr(No Attack today)

= p = .999 Pr(No Attack today AND tomorrow) = .9992
25. ### What if we could assign a probability? Pr(No Attack today)

= p = .999 Pr(No Attack today AND tomorrow) = .9992 Pr(No Attack over n days) = (.999)n
26. ### What if we could assign a probability? Pr(No Attack today)

= p = .999 Pr(No Attack today AND tomorrow) = .9992 Pr(No Attack over n days) = (.999)n Pr(Attack over n days) = 1 – (.999)n
27. ### Probability of a Nuclear Attack 0 0.1 0.2 0.3 0.4

0.5 0.6 0.7 0.8 0.9 1 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 Pr(Attack) Year
28. ### If Probability Theory doesn’t help… What if it’s a repeated

game? Cooperate Defect Cooperate 0, 0 -100, 10 Defect 10, -100 -90, -90
29. ### If Probability Theory doesn’t help… What if it’s a repeated

game? Cooperate Defect Cooperate 0, 0 -100, 10 Defect 10, -100 -90, -90 Cooperate Defect Cooperate 0, 0 -100, 10 Defect 10, -100 -90, -90
30. ### If Probability Theory doesn’t help… What if it’s a repeated

game? Cooperate Defect Cooperate 0, 0 -100, 10 Defect 10, -100 -90, -90 Cooperate Defect Cooperate 0, 0 -100, 10 Defect 10, -100 -90, -90
31. ### If Probability Theory doesn’t help… What if it’s a repeated

game? Grim Trigger?
32. ### If Probability Theory doesn’t help… What if it’s a repeated

game? Grim Trigger? Tit-for-tat!
33. ### If Probability Theory doesn’t help… What if it’s a repeated

game? Grim Trigger? Tit-for-tat! Tit-for-two-tats?
34. ### The Prisoner’s Dilemma, Generalized Cooperate Defect Cooperate Good Worst, Best

Defect Best, Worst Bad Player 1 Player 2
35. ### The Prisoner’s Dilemma, Generalized Cooperate Defect Cooperate Good Worst, Best

Defect Best, Worst Bad Player 1 Player 2 Substantive Assumptions: • Threat is a nontrivial factor • Decision makers view themselves as better off if everyone suffers

Player 2
37. ### The Nuclear Prisoner’s Dilemma? Cooperate Defect Cooperate 0, 0 -100,

0 Defect 0, -100 -100, -100 Player 1 Player 2
38. ### The Nuclear Game Cooperate Defect Cooperate *0, 0* *-100, 0*

Defect *0, -100* *-100, -100* Player 1 Player 2
39. ### The Nuclear Game Cooperate Defect Cooperate *0, 0* *-100, 0*

Defect *0, -100* *-100, -100* Player 1 Player 2
40. ### And Deterrence is Born! Cooperate Defect Cooperate *0, 0* *-100,

0* Defect *0, -100* *-100, -100* Player 1 Player 2