1/22/2009
1
Homework Due Friday 4:15PM
±
Hand homework in to your GSI during
discussion section
OR
±
Turn in homework to the specially marked
box outside Lorch Hall 109 by 4:15PM
±
Today: Chapter 4, Next Week: Chapter 5
Homework Due Friday 4:15PM
±
Dixit & Skeath, Chapter 3, Question 9, Part c)
±
Should read: “Explain intuitively why the
difference between the outcomes in Part a)
and Part b) arises.”
Finding Nash Equilibria
±
We’d like a method for finding NE
Player 2
1234
±
NE occur where Best Responses intersect,
i.e. in cells with two circles
Player 1
A
5 , 7
6 , 4
11 , 12
8 , 22
B
2 , 6
15 , 3
1 , 0
7 , 2
C
3 , 9
2 , 6
19 , 9
6 , 5
D
0 , 0
0 , 1
9 , 17
17 , 12
Nash Equilibrium Philosophy
±
Equilibrium as a point where there are No
Incentives for Change
±
How to talk of “change” and “best response”
in a game that is only played once?
±
Think of Nash Equilibrium as
±
system of beliefs about what others will do
±
beliefs are subjective
±
beliefs are correct in equilibrium
±
action that is optimal given beliefs
Example – Attributed to A.W. Tucker
±
Two Prisoner’s brought in for interrogation
±
They are put in separate rooms
Clyde Barrow
Mum
Fink
±
Known as “The Prisoner’s Dilemma”
Bonnie
Parker
Mum
2 , 2
0 , 3
Fink
3 , 0
1, 1
Bonnie & Clyde (ca 1933)
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Example – The Prisoner’s Dilemma
±
It’s so famous, the payoffs have names!
±
T>R>P>S
Clyde Barrow
Cooperate
Defect
±
T – temptation
R – reward
±
P – punishment
S – sucker
Bonnie
Parker
Cooperate
R , R
S , T
Defect
T , S
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 Spring '07
 Emre
 Game Theory, Nash equilibria, Knight Rook Queen, White Knight Rook, Pawn White Knight

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