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Game Theory

Dave AndersonCentre 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

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

The Payoff Matrix

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

The Payoff Matrix

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

The Payoff Matrix

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

The Payoff Matrix

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

The Circle Trick

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

The Circle Trick

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

The Circle Trick

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

The Circle Trick

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

Chris has a Dominant Strategy:The “Confess” strategy is best

regardless of Pat’s move.

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

Checking Pat’s Options

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

Checking Pat’s Options

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

Checking Pat’s Options

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

Checking Pat’s Options

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

Pat has a dominant strategy: Confess

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

Nash Equilibrium: Neither side has a desire to switch

strategies given what the other is doing.

Confess Deny

Confess 5, 5 1,10Deny 10, 1 2, 2

Pat

Chris

A Classroom Experiment II

X Y Z

X C, C A, D A, F

Y D, A B, B B, C

Z F, A C, B B, B

Your Strategy

Your Classmate’s

Strategy

Battle of the Sexes

Rally Town Hall

Rally 20, 30 9, 4

Town Hall

10, 16 40, 27

Sarah

John

John Analyzes the Possibilities

Rally Town Hall

Rally 20, 30 9, 4

Town Hall

10, 16 40, 27

Sarah

John

John Analyzes the Possibilities

Rally Town Hall

Rally 20, 30 9, 4

Town Hall

10, 16 40, 27

Sarah

John

John Analyzes the Possibilities

Rally Town Hall

Rally 20, 30 9, 4

Town Hall

10, 16 40, 27

Sarah

John

John Analyzes the Possibilities

Rally Town Hall

Rally 20, 30 9, 4

Town Hall

10, 16 40, 27

Sarah

John

Sarah Analyzes the Possibilities

Rally Town Hall

Rally 20, 30 9, 4

Town Hall

10, 16 40, 27

Sarah

John

Sarah Analyzes the Possibilities

Rally Town Hall

Rally 20, 30 9, 4

Town Hall

10, 16 40, 27

Sarah

John

Sarah Analyzes the Possibilities

Rally Town Hall

Rally 20, 30 9, 4

Town Hall

10, 16 40, 27

Sarah

John

Sarah Analyzes the Possibilities

Rally Town Hall

Rally 20, 30 9, 4

Town Hall

10, 16 40, 27

Sarah

John

Two Nash Equilibria, No Dominant Strategies

Rally Town Hall

Rally 20, 30 9, 4

Town Hall

10, 16 40, 27

Sarah

John

Chicken

Straight Swerve

Straight -10,-10 +5, -5

Swerve -5, +5 0, 0

Sarah

John

Chicken

Straight Swerve

Straight -10,-10 +5, -5

Swerve -5, +5 0, 0

Sarah

John

Who would swerve?

First Mover Advantage

Open Don’t

Open -2, -4 17, 0

Don’t 0, 22 0, 0

Bagels Now

TinyBagels

First Mover Advantage

Open Don’t

Open -2, -4 17, 0

Don’t 0, 22 0, 0

Bagels Now

TinyBagels

First Mover Advantage

Open Don’t

Open -2, -4 17, 0

Don’t 0, 22 0, 0

Bagels Now

TinyBagels

First Mover Advantage

Open Don’t

Open -2, -4 17, 0

Don’t 0, 22 0, 0

Bagels Now

TinyBagels

Advertising Game

Low High

Low 10, 15 27, 5

High 3, 25 18, 20

Jmart

TalMart

Advertising Game

Low High

Low 10, 15 27, 5

High 3, 25 18, 20

Jmart

TalMart

Dominant Strategies Nash Equilibria A B

GAME 1 B’s Strategies

Chicken Not Chicken

A’s Strategies Chicken 2, 2 1, 3

Not Chicken 3, 1 0, 0

GAME 2

B’s Strategies

Confess Deny

A’s Strategies Confess 15, 15 2, 20

Deny 20, 2 5, 5

GAME 3B’s Strategies

High Low

A’s Strategies High 10, 10 2, 16

Low 16, 2 4, 4

Dominant Strategies Nash Equilibria A B

GAME 1 B’s Strategies

Chicken Not Chicken

A’s Strategies Chicken 2, 2 1, 3

Not Chicken 3, 1 0, 0

GAME 2

B’s Strategies

Confess Deny

A’s Strategies Confess 15, 15 2, 20

Deny 20, 2 5, 5

GAME 3B’s Strategies

High Low

A’s Strategies High 10, 10 2, 16

Low 16, 2 4, 4

NC, CN none

CC C C

LL L L

GAME 4B’s Strategies

Park Zoo

A’s Strategies Park 9, 7 5, 2

Zoo 3, 8 6, 12

GAME 5B’s Strategies

Confess Deny

A’s Strategies Confess 3, 3 2, 5

Deny 5, 2 1, 1

GAME 6 B’s Strategies

Heads Tails

A’s Strategies Heads 1, -1 -1, 1

Tails -1, 1 1, -1

1 2

A’s Strategies 1 5, 1 6, 3

2 4, 2 8, 7

GAME 8 B’s Strategies

1 2

A’s Strategies 1 3, 2 5, 4

2 6, 1 5, 1

Dominant Strategies Nash Equilibria A B

GAME 4B’s Strategies

Park Zoo

A’s Strategies Park 9, 7 5, 2

Zoo 3, 8 6, 12

GAME 5B’s Strategies

Confess Deny

A’s Strategies Confess 3, 3 2, 5

Deny 5, 2 1, 1

GAME 6 B’s Strategies

Heads Tails

A’s Strategies Heads 1, -1 -1, 1

Tails -1, 1 1, -1

1 2

A’s Strategies 1 5, 1 6, 3

2 4, 2 8, 7

GAME 8 B’s Strategies

1 2

A’s Strategies 1 3, 2 5, 4

2 6, 1 5, 1

Dominant Strategies Nash Equilibria A B

PP, ZZ none

none none

CC, DD none

GAME 7B’s Strategies

1 2

A’s Strategies 1 5, 1 6, 3

2 4, 2 8, 7

GAME 8B’s Strategies

1 2

A’s Strategies 1 3, 2 5, 4

2 6, 1 5, 1

Dominant Strategies Nash Equilibria A B

GAME 7B’s Strategies

1 2

A’s Strategies 1 5, 1 6, 3

2 4, 2 8, 7

GAME 8B’s Strategies

1 2

A’s Strategies 1 3, 2 5, 4

2 6, 1 5, 1

Dominant Strategies Nash Equilibria A B

2,2 none 2

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