Answers for PS1
Q1.
A
B
C
1
a
1, 1
2, 2
3, 3
2
b
2, 2
3, 2
1, 4
c
3, 3
5, 3
2, 2
For player 1,
A is strictly dominated by B
For player 2,
a is weakly dominated by b.
Q2.
(a) No
For player 1,
1 (, ) = 1 = 1 = 1 (, )
1 (, ) = 2 > 1 = 1 (, )
1 (, ) = 3 > 2 =

ECON3160: Game Theory
Instructor: He Wei
The problem of the commons
n farmers in a village, (n 2).
For i = 1, . . . , n, gi is the number of goats owned
by farmer i. Let G = g1 + . . . + gn.
The cost of a goat is c.
The value to a farmer of grazing a

ECON3160: Game Theory
Instructor: He Wei
Sequential Bargaining
Players 1 and 2 are bargaining over one dollar. They
discount payoffs received a period later by a factor
with 0 < < 1.
The three-period bargaining game:
In the first period,
(1a) player 1 p

ECON3160: Game Theory
Instructor: He Wei
Example: Grenade Game
First, player 1 decides whether to give $1000 to
player 2.
Second, after observing the choice of player 1,
player 2 chooses whether to explode a grenade
that will kill both of them.
Player

ECON3160: Game Theory
Instructor: He Wei
Definition.
A strategy for a player is a complete plan of actions. It specifies a feasible action for the player
in every contingency in which the player might be
called on to act.
An equivalent definition of stra

Nash equilibrium
January 27, 2016
1
Nash equilibrium
Denition 1 A strategy (s1 ; :; sN ) is a Nash equilibrium if, for each player i,
her strategy si is a best response to the other players strategy prole s i .
People do not always play a Nash equilibrium

Imperfect Competition
February 1, 2016
1
Introduction
When there are only a few rms competing with each other, the rms are not
price takers, but not monopolists either.
2
2.1
Cournot Duopoly
Setup
Players: rm 1 and 2
Strategies: quantity of identical prod

Best Response
January 18, 2016
1
Introduction to the concept of Best Response
player 2
l
r
U
5; 1
0; 2
player 1 M
1; 3
4; 1
D
4; 2
2; 3
Does any player have a dominated strategy?
Whats best for player 1 if player 2 chooses l? What if player 2 chooses r?
C

1
Strict Dominance Revisited
T
M
B
player 1
2
L
2; 0
3; 4
1; 3
player 2
M
1; 1
1; 2
0; 2
R
4; 2
2; 3
3; 0
Weak dominance
Example:
defender
E
H
attacker
e
1; 1
0; 2
h
1; 1
2; 0
Denition 1 Player is strategy si is weakly dominated by her strategy s0i if
ui

When Do Trend Followers Make Money?
Rasheed Sabar
Portfolio Manager
Ellington Quantitative Strategies
March 2013
1 Introduction
Investors allocate to long-term trend followers in part because they performed admirably in 2008 (and
steadily prior to 2008).

Answers for PS2 Part 2
Q1.
No.
Because a consumer either buys from firm 1 or from firm 2, one of the firms must have
positive market share. Suppose
in equilibrium.
If firm 1 has positive market share, then firm 1 is making a loss. Firm 1 has a strictly
pr

Game Theory Spring 2016
Problem Set 3 Solution
1. (a) Since x > 25, BRX (N ) = L, the best responses are shown in the table.
The pure NE are (L, N ) and (N, L).
(b) Suppose player X chooses L with probability p, and player Y chooses L with
probability q.

Mixed Strategies
February 22, 2016
1
Introduction
player 2
R
S
P
R
0; 0
1; 1
1; 1
player 1 S
1; 1
0; 0 1; 1
P
1; 1
1; 1 0; 0
No NE. Why? If one plays rock, what is the other players best response?
What is best response to paper? What is best response to s

ECON3160: Game Theory
Instructor: He Wei
What is game theory?
Game theory provides a mathematical tool for multiperson decision making.
Why do we need to study game theory?
Nowadays one cannot find a field of economics (or
of disciplines related to econom