1. Dave Anderson Centre College
Game Theory
Dave Anderson
Centre College

3. Game Theory Hotelling's Beach Payoff Matrices The Prisoners' Dilemma
Dominant Strategies
Nash Equilibria
The Battle of the Sexes
Chicken
First-Mover Advantages
The Advertising Game

5. The Payoff Matrix
Pat
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

6. The Payoff Matrix
Pat
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

7. The Payoff Matrix
Pat
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

8. The Payoff Matrix
Pat
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

9. The Payoff Matrix
Pat
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

10. The Circle Trick
Pat
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

11. The Circle Trick
Pat
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

12. The Circle Trick
Pat
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

13. The Circle Trick
Pat
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

14. Chris has a Dominant Strategy: The “Confess” strategy is best regardless of Pat’s move.
Deny
5, 5
1,10
10, 1
2, 2
Chris

15. Checking Pat’s Options
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

16. Checking Pat’s Options
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

17. Checking Pat’s Options
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

18. Checking Pat’s Options
Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

19. Pat has a dominant strategy: Confess
Deny
5, 5
1,10
10, 1
2, 2
Chris

20. Nash Equilibrium: Neither side has a desire to switch strategies given what the other is doing.
Pat
Confess
Deny
5, 5
1,10
10, 1
2, 2
Two Circles in the Same Square
Chris

21. A Classroom Experiment II
Your Classmate’s Strategy X Y Z
C, C
A, D
A, F
D, A
B, B
B, C
F, A
C, B
Your Strategy

22. 20, 30 9, 4 10, 16 40, 27 Battle of the Sexes Sarah John Rally
Town Hall
20, 30
9, 4
10, 16
40, 27
John

23. John Analyzes the Possibilities
Sarah
Rally
Town Hall
20, 30
9, 4
10, 16
40, 27
John

24. John Analyzes the Possibilities
Sarah
Rally
Town Hall
20, 30
9, 4
10, 16
40, 27
John

25. John Analyzes the Possibilities
Sarah
Rally
Town Hall
20, 30
9, 4
10, 16
40, 27
John

26. John Analyzes the Possibilities
Sarah
Rally
Town Hall
20, 30
9, 4
10, 16
40, 27
John

27. Sarah Analyzes the Possibilities
Rally
Town Hall
20, 30
9, 4
10, 16
40, 27
John

28. Sarah Analyzes the Possibilities
Rally
Town Hall
20, 30
9, 4
10, 16
40, 27
John

29. Sarah Analyzes the Possibilities
Rally
Town Hall
20, 30
9, 4
10, 16
40, 27
John

30. Sarah Analyzes the Possibilities
Rally
Town Hall
20, 30
9, 4
10, 16
40, 27
John

31. Two Nash Equilibria, No Dominant Strategies
Sarah
Rally
Town Hall
20, 30
9, 4
10, 16
40, 27
John

32. Chicken
Sarah
Straight
Swerve
-10,-10
+5, -5
-5, +5
0, 0
John

33. Chicken
Sarah
Straight
Swerve
-10,-10
+5, -5
-5, +5
0, 0
John

34. Who would swerve?

35. -2, -4 17, 0 0, 22 0, 0 First Mover Advantage Bagels Now Tiny Bagels
Open
Don’t
-2, -4
17, 0
0, 22
0, 0
Tiny
Bagels

36. -2, -4 17, 0 0, 22 0, 0 First Mover Advantage Bagels Now Tiny Bagels
Open
Don’t
-2, -4
17, 0
0, 22
0, 0
Tiny
Bagels

37. -2, -4 17, 0 0, 22 0, 0 First Mover Advantage Bagels Now Tiny Bagels
Open
Don’t
-2, -4
17, 0
0, 22
0, 0
Tiny
Bagels

38. -2, -4 17, 0 0, 22 0, 0 First Mover Advantage Bagels Now Tiny Bagels
Open
Don’t
-2, -4
17, 0
0, 22
0, 0
Tiny
Bagels

39. Advertising Game
Jmart
Low
High
10, 15
27, 5
3, 25
18, 20
TalMart

40. Advertising Game
Jmart
Low
High
10, 15
27, 5
3, 25
18, 20
TalMart

41. Dominant Strategies Nash Equilibria A B
GAME 1
B’s Strategies
Chicken
Not Chicken
A’s Strategies
2, 2
1, 3
3, 1
0, 0
GAME 2
Confess
Deny
15, 15
2, 20
20, 2
5, 5
GAME 3
High
Low
10, 10
2, 16
16, 2
4, 4
Dominant Strategies Nash Equilibria A B

42. NC, CN none CC C C LL L L Dominant Strategies Nash Equilibria A B
GAME 1
B’s Strategies
Chicken
Not Chicken
A’s Strategies
2, 2
1, 3
3, 1
0, 0
GAME 2
Confess
Deny
15, 15
2, 20
20, 2
5, 5
GAME 3
High
Low
10, 10
2, 16
16, 2
4, 4
Dominant Strategies Nash Equilibria A B
NC, CN none
CC C C
LL L L

43. Dominant Strategies Nash Equilibria A B
GAME 4
B’s Strategies
Park
Zoo
A’s Strategies
9, 7
5, 2
3, 8
6, 12
GAME 5
Confess
Deny
3, 3
2, 5
1, 1
GAME 6
Heads
Tails
1, -1
-1, 1 1 2
5, 1
6, 3
4, 2
8, 7
GAME 8
3, 2
5, 4
6, 1
Payoff Matrix Practice Sheet Dominant Strategies Nash Equilibria A B
Dominant Strategies Nash Equilibria A B

44. PP, ZZ none CC, DD none none none
GAME 4
B’s Strategies
Park
Zoo
A’s Strategies
9, 7
5, 2
3, 8
6, 12
GAME 5
Confess
Deny
3, 3
2, 5
1, 1
GAME 6
Heads
Tails
1, -1
-1, 1 1 2
5, 1
6, 3
4, 2
8, 7
GAME 8
3, 2
5, 4
6, 1
Payoff Matrix Practice Sheet Dominant Strategies Nash Equilibria A B
Dominant Strategies Nash Equilibria A B
PP, ZZ none
CC, DD none
none none

45. Dominant Strategies Nash Equilibria A B
Payoff Matrix Practice Sheet Dominant Strategies Nash Equilibria A B
Dominant Strategies Nash Equilibria A B
GAME 7
B’s Strategies 1 2
A’s Strategies
5, 1
6, 3
4, 2
8, 7
GAME 8
3, 2
5, 4
6, 1

46. 2,2 none 2 2,1; 2,2; 1,2 2 2 Dominant Strategies Nash Equilibria A B
Payoff Matrix Practice Sheet Dominant Strategies Nash Equilibria A B
Dominant Strategies Nash Equilibria A B
GAME 7
B’s Strategies 1 2
A’s Strategies
5, 1
6, 3
4, 2
8, 7
GAME 8
3, 2
5, 4
6, 1
2,2 none
2,1; 2,2; 1,