Homework 6 Answer
(Total 20 points)
Q1
(3pt.): Find all the purestrategy Nash equilibria of the game below.
B
A
l
m
r
T

5,

3 1,

2 4,

1
M

2, 1
4, 0
2, 0
B

4, 5
3, 6
3, 4
Answer
: (
T,r
) and (
M,l
).
Q2
: Consider the game of Battle of Sexes,
B
A
Boxing Opera
Boxing
7, 4
0, 0
Opera
0, 0
7, 4
Find all the Nash equilibria. There are two purestrategy equilibria and one mixed
strategy equilibrium. (2pt. for each purestrategy equilibrium, and 4pt. for the
mixedstrategy equilibrium)
Answer
: Let
p
A
be the probability that A goes to Baxing, let
p
B
be the probability
that B goes to Boxing. A’s expected utility is given (
p
A
,p
B
) is
EU
A
(
p
A
,p
B
) = 7
p
A
p
B
+ 4(1

p
A
)(1

p
B
)
= (11
p
B

4)
p
A
+ 4

4
p
B
Hence, A’s best response is
BR
A
(
p
B
) =
{
0
}
,
when
p
B
<
4
11
entire [0
,
1]
,
when
p
B
=
4
11
{
1
}
,
when
p
B
>
4
11
.
B’s expected utility is given (
p
A
,p
B
) is
EU
B
(
p
A
,p
B
) = 4
p
A
p
B
+ 7(1

p
A
)(1

p
B
)
= (11
p
A

7)
p
B
+ 7

7
p
A
1