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Unformatted text preview: Economics 611 Game Theoretic Microeconomics
Spring 2009 First Exam All Syracuse University policies and procedures concerning academic
honesty apply to this course:
"Syracuse University students shall exhibit honesty in all academic
endeavors. Cheating in any form is not tolerated, nor is assisting another
person to cheat. The submission of any work by a student is taken as a
guarantee that the thoughts and expressions in it are the student's own
except when properly credited to another. Violations of this principle
include: giving or receiving aid in an exam or where otherwise prohibited,
fraud, plagiarism, the falsification or forgery of any record, or any other
deceptive act in connection with academic work. Plagiarism is the
representation of another's words, ideas, programs, formulae,
opinions, or other products of work as one's own either overtly
or by failing to attribute them to their true source." (Section 1.0,
University Rules and Regulations)
WARNING!!!
While homework problems may have been done cooperatively,
exams are individual work. Do not communicate about this exam
with anyone except the instructor [x32345 or email
jskelly@maxwell.syr.edu]. Violation of this rule will result in a
grade of 0 for the exam. Any notices will be sent to you by email;
check occasionally.
EXPLAIN your answers carefully.
DUE: 9:30 am, Thursday, February 19, in class. Economics 611 Game Theory Spring 2009 First Exam
EXPLAIN your answers carefully. DUE: 9:30 am, Thursday,
February 19, in class. The four problems are each worth 25
points.
1. A. There are five players. For each individual i, the strategy space is
Si = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. If players choose (s1, s2, ..., s5), the
mean of the si values is m. Player i wins if she has the minimum of
si – (2/3)m. Then $100 divided equally among those who win. Are
there any Nash equilibria? If so, what are they?
B. Same question except that, for each individual i, the strategy space
is Si = [0, 10], the closed interval of real numbers. 2.
A law is passed requiring a monopolistic softdrink manufacturer to
separate the production department and the marketing department. The
marketing department chooses the price P 0 to charge for a bottle of the
firm’s soft drink and the production department chooses the level of output
Q 0. The two departments are forbidden to discuss their decisions with
each other and, therefore, move simultaneously. Managers in both
departments own shares in the firm and want to maximize its profits
ð = PS – Q2
where S denotes the firm’s sales. Sales can not exceed the firm’s output,
nor can they exceed the market demand. Unsold output is thrown away.
This means S = min{Q, D(P)} where market demand is
D(P) = 10 – 2P if P 5 and D(P) = 0 if P > 5
Are there any Nash equilibria? If so, what are they? 3. For the following game, are there any subgame perfect Nash equilibria?
If so, what are they? Are there any other Nash equilibria? Separately treat
the cases x 0 and x < 0. 4. Consider this question from last years exam: There are two players.
Player #1 offers a point s1 . Player #2 can then accept s1 or reject it; in the
latter case the outcome is the status quo value s0 . If #2 accepts, the
outcome is s1. Player #2's preferences are represented by –(s – b2)2 where b2
is #2's bliss point, while player #1's preferences are represented by s (i.e.,
she prefers higher values of s).
Now consider the following modification. There are two periods. In
the first period the above game is played. In the second period, the game is
played again, but the default status quo point is now the outcome of the first
period game.
Payoffs are the undiscounted utilities of the outcome at the end of the
second period
Are there any subgame perfect Nash equilibria? If so, what are they?
[Assume s0 < b2.] ...
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This note was uploaded on 01/13/2012 for the course ECN 611 taught by Professor Kelly,j during the Fall '08 term at Syracuse.
 Fall '08
 Kelly,J
 Microeconomics

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