Cornell University
Economics 3130
Problem Set 10
Due 4/24/09
1. Using any method, ﬁnd
all
the Nash equilibria (in pure and mixed strategies) of the
game. Brieﬂy explain the steps you take in ﬁnding the equilibria.
Player 2
Player 1
L
C
R
T
3,4
4,2
2,1
M
1,7
3,8
0,0
B
1,0
1,1
4,3
2. Find all equilibria of the following game.
Player 2
Player 1
L
C
R
U
4,2
3,2
0,4
M
1,1
2,0
2,1
D
2,4
3,1
6,0
3. You (player 1) and a friend (player 2) are in an Italian restaurant, and the owner
oﬀers both of you an 8-slice pizza under the following condition: Each one of you must
simultaneously announce how many slices you would like to have; that is, each player
i
∈ {
1
,
2
}
names his or her desired amount of pizza slices 0
≤
s
i
≤
8. If
s
1
+
s
2
≤
8
then the two of you get your demands (and any remainder is eaten by the owner).
If
s
1
+
s
2
>
8, then the players get nothing. Both you and your friend prefer more
pizza to less, but do not care about the amount of pizza eaten by the other. How
many pure-strategy Nash equilibria are there in this game? What are they? Rank the