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Problem Set 3 — Game Theory
Instructor: Todd Sarver
Econ 3102, Fall 2011
TA: Esteban Petruzzello
(Any email questions regarding this PS should be sent to this TA.)
Complete all problems and explain your answers carefully. This problem set is due on
Thursday,
October 27 at 4:45pm
in the mailbox labeled
Todd Sarver
in the Economics Department main
oﬃce (302 Andersen Hall). At the top of your assignment, please include the TA whose discussion
session you attend (Guannan, Robert, Esteban) and the day that you attend (Monday, Friday).
1 Mixed Strategies in the Coordination Game
In class, we discussed the following coordination game:
Player 2
P
C
Player 1
P
5
,
5
0
,
0
C
0
,
0
2
,
2
Recall that the purestrategy Nash equilibria of this game are (
P,P
) and (
C,C
). In the language
of mixed strategies, the equilibrium strategy proﬁle (
P,P
) can be written as (
σ
P
1
,σ
P
2
) = (1
,
1), and
the strategy proﬁle (
C,C
) can be written as (
σ
P
1
,σ
P
2
) = (0
,
0) (since
σ
C
i
= 1

σ
P
i
). There is also
another mixedstrategy equilibrium of this game. Find the mixed strategies (
σ
P
1
,σ
P
2
) in this third
Nash equilibrium.
2 Mixed Strategies and Weakly Dominated Strategies
Consider the following game:
Player 2
L
R
Player 1
U
3
,
5
4
,
3
D
0
,
2
4
,
2
(a) Does either player have a
strictly
dominant strategy? Does either player have a
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This note was uploaded on 01/03/2012 for the course ECON 3102 taught by Professor Sarver during the Spring '08 term at Northwestern.
 Spring '08
 SARVER
 Microeconomics, Game Theory

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