Game Theory Dave Anderson Centre College. Game Theory Hotelling's Beach Payoff Matrices The...
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Transcript of Game Theory Dave Anderson Centre College. Game Theory Hotelling's Beach Payoff Matrices The...
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