Simon Fraser University
Fall 2014
Econ 302 D100 Midterm Exam
Instructor: Songzi Du
Tuesday October 28, 2014, 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.
1
1. (5 points) Alice and Bob are participants in a televised game show, seated in separate
booths with no possibility of communicating with each other. Each one of them is asked to
submit, in a sealed envelope, one of the following two requests for the show (requests are
guaranteed to be honored):
1. Give me $1000.
2. Give the other participant $4000.
Write the payoff matrix for this game. Find the Nash equilibria. Is there any dominated
strategy, and why? Why is the Nash equilibrium outcome(s) unfortunate in this game?
2. (10 points) Find and describe the pure-strategy subgame perfect equilibria (if any)
in the following game. Explain the steps that you use to find the SPE.
The game has random moves by Nature at the beginning of the tree. You can think of
the two nodes of Player 1 following the moves of Nature as two distinct players, like the
strong and weak types in the Beer-Quiche game.
3.
(10 points) The market (inverse) demand function for a homogeneous good is
P (Q) = 14 − 2Q, where Q is the total quantity of the good on the market. There are two
firms: firm 1 has a constant marginal cost of 4 for producing each unit of the good, and firm
2
2 has a constant marginal cost of 1. Firm 1 is the industry leader, so it sets its quantity
of production first. Firm 2 sets its quantity of production after observing firm 1’s quantity.
Find (i) the subgame perfect equilibrium of this game. And calculate (ii) the market price
and (iii) the firms’ profits in the equilibrium.
4. (15 points) Elizabeth and Mary appear before King Solomon at his palace, along
with an infant. Each woman claims that the infant is her child. The child is “worth” 100
dinars to his true mother, but he is only “worth” 50 dinars to the woman who is not his
mother (the imposter). The king knows that one of the two women is the true mother of
the child, and he knows the “values” that the true mother and the imposter ascribe to the
child, but he does not know which woman is the true mother, and which the imposter.
To determine which of the two women is the true mother, the king explains to Elizabeth
and Mary that he will implement the following steps:
1. He will ask Elizabeth whether the child is hers. If she answers negatively, the child will
be given to Mary. If she answers affirmatively, the king will continue to the next step.
2. He will ask Mary if the child is hers. If she answers negatively, the child will be given to
Elizabeth. If she answers affirmatively, Mary will pay the king 75 dinars, and receive
the child, and Elizabeth will pay the king 10 dinars.
(i) Draw the game tree when (a) Elizabeth is the true mother and when (b) Mary is the
true mother. (Assume that each woman has a payoff of 0 dinar if she does not receive the
child.) (ii) Find and report the subgame perfect equilibrium under (a) and (b), and describe
what happens (who gets the child and how much is paid by each woman) in each equilibrium.
5.
Part (i) [5 points]: find the Nash equilibria (pure and mixed) of the following
simultaneous game, and report the players’ payoffs in each equilibrium:
C
D
A
10, 10
1, 10
B
12, 2
0, 0
Part (ii) [10 points]: now suppose the above game is played twice. In each stage the two
players move simultaneously, and in the second stage the players observe the actions taken
3
in the previous stage. Assume that the final payoff of a player is the sum of his payoffs from
the two stages.
Find and describe a subgame perfect equilibrium (SPE) in which (A, C) is played in the
first stage, and report the players’ payoffs in the equilibrium. Explain why it is a SPE.
4
0
