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Department of Economics, University of California, Davis
Ecn 122

Game Theory

Professor Giacomo Bonanno
ANSWERS
TO
PRACTICE
PROBLEMS for
WEEK 9
1.
Since B is strictly dominated, it cannot be assigned positive probability at a Nash
equilibrium. Let
p
be the probability of T and
q
the probability of L. Then
p
must satisfy
the condition:
4
p
+ 0 (1

p
) = 3
p
+ 2(1

p
)
while
q
must satisfy the condition:
1
q
+ 4 (1

q
) = 2
q
+ 1(1

q
).
Thus
p
=
2
3
and
q
=
3
4
. Hence the mixedstrategy equilibrium is given by:
T
C
B
L
R
2
3
1
3
3
4
1
4
0
F
H
G
I
K
J
2.
(a)
The normal form is as follows:
PLAYER
2
AC
AD
BC
BD
LEG
2 , 0
2 , 0
0 , 2
0 , 2
LEH
2 , 0
2 , 0
0 , 2
0 , 2
LFG
0 , 6
0 , 6
4 , 1
4 , 1
LFH
0 , 6
0 , 6
4 , 1
4 , 1
REG
1 , 4
4 , 3
1 , 4
4 , 3
REH
2 , 0
1 , 2
2 , 0
1 , 2
RFG
1 , 4
4 , 3
1 , 4
4 , 3
P
L
A
Y
E
R
1
RFH
2 , 0
1 , 2
2 , 0
1 , 2
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(b)
There are no purestrategy Nash equilibria.
(c)
First let us solve the subgame on the left:
Player
2
A
B
E
2 , 0
0 , 2
Player
1
F
0 , 6
4 , 1
There is no purestrategy equilibrium. Let us find the mixedstrategy equilibrium. Let
p
be
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 Spring '10
 Bonnano
 Game Theory, player, Reh

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