Simon Fraser University
Spring 2014
Econ 302 D200 Final Exam
Instructor: Songzi Du
Friday April 11, 2014, 8:30 – 11:30 AM
Write your name, SFU ID number, and tutorial section number on both the exam
booklets and the questionnaire. Hand in both the exam booklets and the
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.
Do not turn over this page until instruction to start is given.
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NE = Nash equilibrium, SPE = subgame perfect equilibrium, PBE = perfect
Bayesian equilibrium
Write Question 1 – 4 on booklet #1
1. (10 points) Consider the following simultaneous-move game (Table 1).
W
X
Y
Z
A
1, 7
4, 3
1, 2
6, 2
B
8, 6 4, 6
2, 5
5, 5
C
4, 1
5, 2
3, 3
4, 2
D
5, 5
4, 3
2, 4
9, 3
Table 1
Part i: Find the strategies that survive iterative deletion of strictly dominated strategies
(ISD). For each strategy that you delete, write down the strategy that strictly dominates it.
Part ii: Find all NE (pure and mixed) in this game, and for each NE that you find,
calculate the two players’ expected payoffs in the equilibrium.
2. (10 points) There are two players each with a wealth w = $3. An object that the
two players each value at v = $3 is sold at an auction. In the auction, the two players
alternatively have the opportunity to bid; a bid must be a positive integer greater than the
previous bid and less than or equal to w. On his turn, a player may pass rather than bid,
in which case the game ends and the other player receives the object; both players pay their
last bids (if any). Player 1 moves initially. If player 1 passes initially, for example, player
2 receives the object and makes no payment (net payoff v − 0 = 3) while player 1 receives
nothing and pays nothing (net payoff 0 − 0 = 0); if player 1 bids 1, player 2 bids 3, and then
player 1 passes, player 2 obtains the object and pays 3 (net payoff v − 3 = 0) while player 1
receives nothing and pays 1 (net payoff 0 − 1 = −1).
Part i: draw the game tree.
Part ii: find and completely describe a pure-strategy SPE.
√
3. (10 points) Part i: suppose that you have an utility over money u(m) = m = m0.5
and start with $10000. Consider a risky project with probability 0.25 of gaining $1000,
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probability 0.25 of gaining $2000, probability 0.25 of gaining $10000, and probability 0.25
of losing $10000. Find the expected value of this project (on the total wealth). Find your
expected utility if you take this project, and find your certainty equivalent and risk premium
for this project. Would you take the project, and why?
Part ii: repeat part i with u(m) = m0.9 . Are you more or less risk averse with u(m) = m0.9
√
compared to u(m) = m, and why?
In your calculations keep two decimal places.
4. (10 points) Two firms (firm 1 and 2) compete in quantity of production and face
a market demand function of P = 9 − Q. Each firm has a marginal cost of 3 per unit of
production.
Part i: Find the monopolist quantity, price, and payoff when the two firms merge into
one monopoly firm.
Part ii: Find the NE quantity, price, and payoff when the two firms compete by simultaneously choosing quantities.
Part iii: Suppose that the competition is infinitely repeated, and each firm has a discount
P
t
factor of δ. So firm i’s payoff is ∞
t=0 δ (Pt − 3)qi,t , where qi,t is firm i’s production quantity
in period t, and Pt = 9 − (q1,t + q2,t ) is the market price in period t. In each period, the
two firms set their quantities simultaneously, and observe the quantities from the previous
periods. Describe a grim trigger strategy, and find the range of δ such that both firm playing
the grim-trigger strategy is a SPE of the infinitely repeated game. What is the total payoff
of each firm when both firms follow the grim-trigger strategy?
Write Question 5 – 7 on booklet #2
5. (10 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.
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(i) Draw the game tree.
(ii) Find all separating PBE (if any), and explain.
(iii) Find all pooling PBE (if any), and explain.
For part ii and iii, focus on pure-strategy PBE, and include conditional beliefs (such as
P(strong | beer) = 1 or P(strong | beer) ≤ 1/2.) in your description of PBE.
7. (10 points) Consider a market for used cars with risk-neutral participants, like we
did in Lecture 10. Suppose there are four qualities for cars: A, B, C and D. Let the sellers’
valuations for the four qualities be $10000 (quality A), $9000 (quality B), $5000 (quality C)
and $3000 (quality D), and let the buyers’ valuations be $20000 (quality A), $15000 (quality
B), $7000 (quality C) and $4000 (quality D). Assume that there is an equal number of cars
in each of the four categories.
Suppose only sellers know the quality of each car. Is the sales of quality A cars feasible?
If so what prices for quality A cars could you observe? What about quality B, C, and D
(feasibility of sales and if so the price range)? Explain.
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