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
1
2
3
4
A
5
7
6
4
11
12
8
22
NE occur where Best Responses intersect,
i.e. in cells with two circles
Player 1
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)