Simon Fraser University
Spring 2016
Econ 302 D200 Midterm Exam
Instructor: Songzi Du
Tuesday March 8, 2016, 8:30 – 10:20 AM
Write your name, SFU ID number, and tutorial section number both on the exam
booklets and on the questionnaire. Hand in both the exam booklets and this
questionnaire. But note that only the exam booklets are graded.
• Name:
• SFU ID number:
• Tutorial section number:
General instructions
1. This is a closed-book exam: no books, notes, computer, cellphone, internet, or other
aids. A scientific, non-graphing calculator is allowed.
2. If you use decimals in calculation, keep two decimal places.
3. Write clearly. Illegible answers will receive no credit.
4. Show your work! Partial credits are given. Answers without proper explanation/calculation
will be penalized.
5. A request for regrade can be accepted only if the exam is written with a pen.
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1. (20 points) Your club has 10 members, and Julie is interested in joining your club.
The procedure for admitting a new member is simple: each existing member (which includes
you) receives a ballot that has two options: (1) admit Julie and (2) do not admit Julie. Each
person can check one of those two options or abstain by not submitting a ballot. For Julie
to be admitted, she must receive at least six votes in favor of admittance (checking option
1). Letting m be the number of ballots submitted with option 1 checked, assume that your
payoff function is

1 if m ≥ 6 (Julie is admitted)
0
if m ≤ 5 (Julie is not admitted)
For this question, it does not matter what is the payoff function for the other members.
(i) Is checking option 1 your strictly dominant strategy? Why or why not.
(ii) Is checking option 1 your weakly dominant strategy? Why or why not. Recall that a
strategy X is weakly dominant if X weakly dominates every other strategy; that is, for
any other strategy Y , X is always (for any strategies chosen by other players) weakly
better than Y and is sometimes strictly better than Y.
(iii) Explain why abstaining is a weakly dominated strategy for you. Recall that a strategy
X is weakly dominated if another strategy weakly dominates X.
(iv) Now suppose you are tired at the end of the day, so that it is costly for you to attend
the evening’s meeting to vote. By not showing up, you abstain from the vote. This is
reflected in your payoff function having the form:



1




1/2


0




−1/2
if m ≥ 6 and you abstained
if m ≥ 6 and you voted
if m ≤ 5 and you abstained
if m ≤ 5 and you voted
Argue that now abstaining is not a weakly dominated strategy for you.
2. (20 points) Three firms are considering entering a new market. The payoff for each
firm that enters is 150
, where n (1 ≤ n ≤ 3) is the number of firms that enter. The cost of
n
2
entering is 62. (So the net payoff for a firm that enters is 150
− 62, and 0 for a firm that does
n
not enter.)
Part i: Find all the pure-strategy NE, and calculate the firms’ payoffs in the equilibrium.
Part ii: Find the symmetric mixed-strategy NE in which all three firms enter with the
same probability, and calculate the firms’ payoffs in the equilibrium.
3. (15 points) Find all pure-strategy subgame perfect equilibria (if any exists) of the
following game. Explain your answer.
1
a
2
c
0
1
e
b
2
d
1
2
c
2
d
1
4
0
3
f
2
1
g
0
1
4. (20 points) There are two players. Player 1 is either strong or weak (those are his
types), and chooses a meal: beer or quiche. Player 2 observes this food choice, and chooses
to fight or retreat.
Player 2 cannot tell if player 1 is strong or weak, and believes that player 1 is strong with
probability 0.1 and weak with probability 0.9. (So Nature chooses player 1 to be strong with
probability 0.1 and weak with probability 0.9.) Player 2 gets 1 if he fights the weak player,
−1 if he fights the strong player, and 0 if he retreats.
The strong player 1 prefers beer; the weak player 1 prefers quiche. Player 1, strong or
weak, gets 2 if Player 2 doesn’t fight him, 0 otherwise; player 1, strong or weak, gets an
additional 1 if he eats his preferred meal.
(i) Draw the game tree.
(ii) Find all pure-strategy subgame perfect equilibria (if any exists), and explain.
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