Simon Fraser University
Fall 2012
Econ 302 Midterm
Instructor: Songzi Du
Section D200
Tuesday Oct. 30, 2012
Due: end of the class, 10:20 am.
This exam has two parts. Write your name, SFU ID number, and tutorial section number
on each part.
Part I (Questions 1 – 4):
• Name:
• SFU ID number:
• Tutorial section number:
1. This is a closed-book exam.
2. You may use a non-graphing calculator.
3. There is no separate exam booklet. Write your solution in the space following each
question.
4. Show your work! Partial credits are given.
5. We will accept a request for regrade only if the solution is written with a pen.
6. The midterm has 75 points (25% of the class grade).
7. Stay in your seat if less than 20 minutes remain in the class. You may leave early if
you finish more than 20 minutes before the class is over.
1
1.
(10 points) Find all pure-strategy subgame perfect equilibria of the following game.
(Hint: there are two.) Extra credit (5 points): find one (non-pure) mixed-strategy subgame
perfect equilibrium.
1
a
b
(0, 1)
2
c
d
(−1, −1)
1
e
f
(1, −2)
2
g
(0, 0)
2
h
(2, 0)
3
2. (10 points) Find all subgame perfect equilibria (both pure and mixed) of the following
game.
1
a
2
e
c
b
d
2
f
e
(2, −2) (4, −4) (1, 0)
2
e
f
2
f
g
(1, 1) (2, −2) (10, 1)
(3, 1)
4
h
(1, 2)
5
3. (15 points: 5 + 10) There are two players: Alice and Bob. Alice first picks L or R,
which is observed by Bob (and by Alice herself). If L is chosen, then Alice and Bob play a
simultaneous-move Prisoner’s Dilemma game (Table 1). If R is chosen, then Alice and Bob
play a simultaneous-move Battle of the Sexes game (Table 2). (i) Draw the extensive form
of this game. (ii) Find all subgame-perfect equilibria (both pure and mixed).
Table 1: Prisoner’s Dilemma
C
D
C 3, 3 -1, 5
D 5, -1 0, 0
Table 2: Battle of the Sexes
B
H
B
2, 1
-10, -10
H -10, -10
-1, 4
6
7
4. (10 points) Find the strategies that survive iterative deletion of strictly dominated strategies (ISD). Hint: only one strategy of each player survives. What are the Nash equilibria
(pure and mixed) in this game?
D
E
A 1, 0.5
0, 1
B 0, 0.9
1, 1
C 0.4, 1 0.3, 0.3
8
F
1, 0.7
0, 0.6
0.45, 1