Dave Anderson Centre College Game Theory Dave Anderson Centre College

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Who would swerve?

-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

-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

-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

-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

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

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

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 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

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

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

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 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 2,1; 2,2; 1,2 2 2