Mei 509 Advanced Microeconomics Question Paper
Mei 509 Advanced Microeconomics
Course:Master Of Business Administration In Corporate Management
Institution: Kca University question papers
Exam Year:2014
UNIVERSITY EXAMINATIONS: 2013/2014
EXAMINATION FOR THE MASTERS OF BUSINESS ADMINISTRATION
(MBA) CORPORATE MANAGEMENT
MEI 509 ADVANCED MICROECONOMICS
KITENGELA CAMPUS
DATE: AUGUST, 2014
TIME: 3 HOURS
INSTRUCTIONS: Answer Question One and Any Other Three Questions
QUESTION ONE (31 MARKS)
1.
Answer whether each of the following statements is true or false. You do NOT need to explain
the reason.
a)
[5 Marks]
If a game has finite number of players and strategies, there ALWAYS exists a pure
strategy Nash Equilibrium.
b)
If two different pure strategies are used (with positive probabilities) in a mixed strategy
Nash equilibrium, then these strategies MUST yield the same expected payoff given the
equilibrium strategies for other players
c) Every sub-game perfect Nash equilibrium is a Nash equilibrium
d) In the Stackelberg game, the follower becomes better off than in the Cournot game, since she
can move after observing the leader''s strategy
e)
If a static game is played repeatedly, then some outcome other than static Nash equilibria can
possibly be achieved as a subgame perfect Nash equilibrium
2.
Consider the following static game
P1/P2 X Y Z
A (3,3) (0,5) (0,4)
B (0,0) (3,1) (1,2)
1
a) Find the pure-strategy Nash equilibrium in this game
[1 Mark]
b) Solve this game by the iterated elimination of strictly dominated strategies. Does the resulting
combination of strategies coincide with your answer in (a)?
3.
[2 Marks]
Consider the following 2x2 game
P1/P2 Y
A (2,4) (0,0)
B
a)
X (1,6) (3,7)
Find all the pure-strategy equilibria in this game. Can these Nash Equilibria be Pareto ranked? If
so, explain why and give a Nash equilibrium arrived at if there is coordination failure in the
game
b)
[6 Marks]
Now, suppose player 1 takes A with probability q and B with probability (1-q).
Likewise player 2 takes X with probability p and Y with probability (1-p). Find a
combination of p and q which constitutes a mixed strategy Nash equilibrium.
[4 Marks]
4.
See the following game tree
(4, 1)
C
2
A
1
(2, 3)
E
(3, 2)
B
2
a)
(1, 0)
D
F
Translate this game into normal-form and draw the corresponding payoff matrix
(Hint: Remember that a strategy in dynamic games is a complete action plan) [6 Marks]
b) Find all pure-strategy Nash equilibria. How many are there? [3 Marks]
c) Solve this game by backward induction [4 Marks]
QUESTION TWO (23 MARKS)
Suppose two firms produce an identical good. The (inverse) demand function for the good is given as P
= 130 - Q, where Q is the total quantity produced by the two firms. Each firm had a constant marginal
cost 10 of producing the good.
2
a)
Suppose firms compete as quantity setting duopolists. Find the Cournot Nash equilibrium of
this game. What quantities will they produce, what is the market price and how much profit
does each firm earn?
b)
[7 Marks]
Now, suppose firm 1 decides how much to produce first; firm 2 chooses only after observing
firm 1''s choice. Find the sub-game perfect Nash equilibrium (Stackelberg equilibrium) of this
game. What quantities will they produce, what is the market price and how much profit does
each firm earn?
c)
[8 Marks]
Suppose the firms form a cartel: each firm produced the same output and maximizes their joint
profit. What quantity would each firm produce? What would be the market price? What would
be the profit of each firm
[8 Marks]
QUESTION THREE (23 MARKS)
a)
Cooperation in prisoner''s dilemma might be possible if the game will be played repeatedly.
However, there are several cases in which cooperation cannot be achieved in any sub-game
perfect equilibrium. Mention one of those cases and explain why cooperation is impossible in
such a situation.
b)
[10 Marks]
Consider the following two persons 3x3 game.
P1/P2 X Y Z
A (5,5) (8,4) (0,0)
B (4,8) (7,7) (1,9)
C (0,0) (9,1) (0,0)
Consider a two-period in which the above game will be played twice. Suppose the payoffs are
simply the sum of payoffs in each stage game. Then, is there a sub-game perfect Nash
equilibrium that can achieve (B,Y) in the first period? If so, describe the equilibrium. If not,
explain why.
[13 Marks]
QUESTION FOUR (23 MARKS)
See the following game tree.
3
D
(2, 0)
K
A
(3, 4)
1
2
E
F
B
1
(1, 3)
(0, 2)
L
C
1
2
M
G
(1,4 )
H
N
a)
I (4, 0)
H
I
1
(3, 3)
(1, 1)
(0, 4)
How many information sets (containing two or more decision nodes) does this game have?
[5 Marks]
b) How many sub-games (including the entire game) does this game have? [5 Marks]
c) Find all (pure-strategy) sub-game perfect Nash equilibria [13 Marks]
QUESTION FIVE (23 MARKS)
Consider the following game depicting the process of standard setting in high-definition television
(HDTV). The United States and Japan must simultaneously decide whether to invest in high or a low
value into HDTV research. Each country''s payoffs are summarized in the following figure.
US/JAPAN High
Low (4,3) (2,4)
High
a)
Low (3,2) (1,1)
Are there any dominant strategies in this game? What is the Nash equilibrium of the game?
[3 Marks]
b)
Suppose now that the United States has the option of committing to a strategy before Japan''s
decision is reached. Model this situation by a game tree and solve it by backward induction.
[15 Marks]
4
c)
Comparing the answers in (a) and (b), what can you say about the value of commitment for the
United States?
[5 Marks]
QUESTION SIX (23 MARKS)
Suppose a government auctions one block of radio spectrum to two risk neutral mobile phone
companies,
The companies submit bids simultaneously, and the company with higher bids
receives a spectrum block. The loser pays nothing while the winner pays a weighted average of two
bids:
where
satisfying
is the winner''s bid,
is the loser''s bid, and
is some constant
. (In case of ties, each company wins with equal probability). Assume the
valuation of the spectrum block for each company is independently and uniformly distributed between
0 and 1.
a)
Solve a Bayesian Nash equilibrium.
[10 Marks]
(Hint: You can assume the equilibrium strategy is symmetric and linear, i.e.,
)
b)
Show that
is always (weakly) better than
[13 Marks]
5
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