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Game Theory Dave Anderson Centre College. Game Theory Hotelling's Beach Payoff Matrices The Prisoners' Dilemma Dominant Strategies Nash Equilibria The.

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Presentation on theme: "Game Theory Dave Anderson Centre College. Game Theory Hotelling's Beach Payoff Matrices The Prisoners' Dilemma Dominant Strategies Nash Equilibria The."— Presentation transcript:

1 Game Theory Dave Anderson Centre College

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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

21 A Classroom Experiment II XYZ X C, CA, DA, F Y D, AB, BB, C Z F, AC, BB, B Your Strategy Your Classmate’s Strategy

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

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

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

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

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

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

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

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

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

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

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

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

34 Who would swerve?

35 First Mover Advantage OpenDon’t Open -2, -417, 0 Don’t 0, 22 0, 0 Bagels Now Tiny Bagels

36 First Mover Advantage OpenDon’t Open -2, -417, 0 Don’t 0, 22 0, 0 Bagels Now Tiny Bagels

37 First Mover Advantage OpenDon’t Open -2, -417, 0 Don’t 0, 22 0, 0 Bagels Now Tiny Bagels

38 First Mover Advantage OpenDon’t Open -2, -417, 0 Don’t 0, 22 0, 0 Bagels Now Tiny Bagels

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

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

41 Dominant Strategies Nash Equilibria A B GAME 1B ’ s Strategies ChickenN ot Chicken A ’ s StrategiesChicken2, 21, 3 Not Chicken3, 10, 0 GAME 2 B ’ s Strategies ConfessDeny A ’ s StrategiesConfess15, 152, 20 Deny20, 25, 5 GAME 3 B ’ s Strategies HighLow A ’ s StrategiesHigh10, 102, 16 Low16, 24, 4

42 Dominant Strategies Nash Equilibria A B GAME 1B ’ s Strategies ChickenN ot Chicken A ’ s StrategiesChicken2, 21, 3 Not Chicken3, 10, 0 GAME 2 B ’ s Strategies ConfessDeny A ’ s StrategiesConfess15, 152, 20 Deny20, 25, 5 GAME 3 B ’ s Strategies HighLow A ’ s StrategiesHigh10, 102, 16 Low16, 24, 4 NC, CNnone CC C C LL L L

43 Payoff Matrix Practice Sheet Dominant Strategies Nash Equilibria A B GAME 4 B ’ s Strategies ParkZoo A ’ s StrategiesPark9, 75, 2 Zoo3, 86, 12 GAME 5 B ’ s Strategies ConfessDeny A ’ s StrategiesConfess3, 32, 5 Deny5, 21, 1 GAME 6B ’ s Strategies HeadsTails A ’ s StrategiesHeads1, -1-1, 1 Tails-1, 11, A ’ s Strategies15, 16, 3 24, 28, 7 GAME 8B ’ s Strategies 12 A ’ s Strategies13, 25, 4 26, 15, 1 Dominant Strategies Nash Equilibria A B

44 Payoff Matrix Practice Sheet Dominant Strategies Nash Equilibria A B GAME 4 B ’ s Strategies ParkZoo A ’ s StrategiesPark9, 75, 2 Zoo3, 86, 12 GAME 5 B ’ s Strategies ConfessDeny A ’ s StrategiesConfess3, 32, 5 Deny5, 21, 1 GAME 6B ’ s Strategies HeadsTails A ’ s StrategiesHeads1, -1-1, 1 Tails-1, 11, A ’ s Strategies15, 16, 3 24, 28, 7 GAME 8B ’ s Strategies 12 A ’ s Strategies13, 25, 4 26, 15, 1 Dominant Strategies Nash Equilibria A B PP, ZZnone none CC, DDnone

45 Payoff Matrix Practice Sheet Dominant Strategies Nash Equilibria A B GAME 7 B ’ s Strategies 12 A ’ s Strategies15, 16, 3 24, 28, 7 GAME 8 B ’ s Strategies 12 A ’ s Strategies13, 25, 4 26, 15, 1 Dominant Strategies Nash Equilibria A B

46 Payoff Matrix Practice Sheet Dominant Strategies Nash Equilibria A B GAME 7 B ’ s Strategies 12 A ’ s Strategies15, 16, 3 24, 28, 7 GAME 8 B ’ s Strategies 12 A ’ s Strategies13, 25, 4 26, 15, 1 Dominant Strategies Nash Equilibria A B 2,2 none 2 2,1; 2,2; 1,2 2 2


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