Simon Fraser University
Spring 2013
Econ 302 Final Exam
Instructor: Songzi Du
Section D200
Wednesday April 24, 2013, 8:30 – 11:30 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. If you use decimals in calculation, keep two decimal places.
4. There is no separate exam booklet. Write your solution in the space following each
question.
5. Show your work! Partial credits are given. Answers without proper explanation/calculation
will be penalized.
6. We will accept a request for regrade only if the solution is written with a pen.
7. The final exam has 135 points (45% of the class grade).
8. Stay in your seat if less than 20 minutes remain in the exam. You may leave early if
you finish 20 minutes before the exam is over.
1
1. (15 points) Consider the following simultaneous-move game with two players. Each
player simultaneously chooses a bid from the set {1 dollar , 50 dollars, 100 dollars }. The
player with the higher bid wins a prize of 100 dollars; the other player (the loser) does not
receive any prize. If the two bids are the same, neither player receives the prize. Each
player must pay his own bid, whether or not he wins the prize. (The loser pays too.) The
payoff/utility of each player is simply his net winnings. For example, if player 1 bids 100
and player 2 bids 50, then player 1 gets 100 − 100 = 0 and player 2 gets 0 − 50 = −50; if
player 1 bids 50 and player 2 bids 50, then each gets 0 − 50 = −50.
(i) Write the normal form (matrix) of this game.
(ii) Calculate a symmetric mixed strategy Nash equilibrium. Keep two decimal places or
use fraction.
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3
4
2. (15 points) In Burnaby Mountain there is nothing to do at night but look at the
stars or go to the local bar. Let us define the utility of looking at stars as 0, and let the cost
of walking to the bar be 1. Suppose that the utility from being at the bar is 2 (so the net
utility is 2 − 1 = 1) if there are fewer than 3 people (including oneself) at the bar, and 1/2
(the net utility is 1/2 − 1 = −1/2) if there are 3 or more people (including oneself) at the
bar. Suppose that there are only 3 people in Burnaby Mountain at night, and they make
decisions (looking at stars or going to the bar) simultaneously.
(i) Calculate the three pure-strategy Nash equilibria.
(ii) Calculate the symmetric mixed-strategy Nash equilibrium. And calculate the utility
of each player in this equilibrium. Keep two decimal places or use fraction/square root.
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6
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3. (15 points) Find all pure-strategy subgame perfect equilibria of the following game.
Use game matrices to justify your answers.
1
a
2
c
0
1
e
b
2
d
1
2
c
2
d
1
4
0
3
8
f
2
1
g
0
1
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4. (15 points) Suppose that crude oil is a homogenous good, and the market (inverse)
demand function for crude oil is P (Q) = 20 − Q, where Q is the total quantity of crude oil on
the market. Country 1 is the traditional producer of crude oil and has a constant marginal
cost of 1 for producing each unit of oil. Country 1 faces competition from new entrants who
are Country 2 and 3 with superior production technology: Country 2 and 3 both have zero
marginal cost for producing crude oil. The game is as follows: Country 1 first sets/commits
to its quantity of production q1 ; Country 2 and 3 observe the commitment of Country 1 (q1 )
and then simultaneously choose their quantities q2 and q3 . Each country then sells its oil at
the market price P (q1 + q2 + q3 ).
Construct a subgame perfect equilibrium in this game. And calculate the equilibrium
price and quantities.
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12
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