MN3212
Time allowed: 3 hours.
STRATEGY
This assessment is a closed-book assessment with a duration of 3 hours. Candidates
are strongly advised to divide their time accordingly.
The examination paper contains FOUR questions. You should answer ALL
QUESTIONS. Each question will be given equal weight (25%).
Candidates should read the questions carefully and provide clear and concise answers.
You should motivate your answers and document your calculations.
A permitted calculator may be used when answering questions on this paper. The make
and type of machine must be clearly stated on the front cover of the answer book.
[Calculator]
Page 1 of 7
QUESTION 1 (Game Theory)
Consider the following game between Player R and Player C represented in normal
form, where Player R can choose between a=1, 2 or 3 and Player C can choose
between b=1, 2 or 3.
Player R
a=1
a=2
a=3
b=1
30, 30
20, 30
40, 10
Player C
b=2
25, 30
20, 25
40, 15
b=3
10, 40
15, 40
20, 20
a. Define the concepts of pure strategy and dominant strategy. Suppose that the
game is played once, and Player R and Player C choose actions simultaneously.
How many pure strategies does Player R have? Does Player R have a dominant
strategy? Does Player C have a dominant strategy? Explain.
Answer
A pure strategy is a complete, contingent plan of action that specifies the action that
a player would choose under any contingency he/she may face in a game. In the
above game there is a single contingency and player R has a choice of 3 actions so
there are 3 pure strategies.
A dominant strategy outperforms (i.e., give a player a strictly higher payoff relative to)
every other strategy, no matter the strategies played by other players. Player R has a
dominant strategy a=3, while player C has a dominant strategy b=3.
b. Suppose that the game is played once, and Player R and Player C choose
actions simultaneously. Describe all Nash equilibria of this game.
Answer
There is a unique Nash equilibrium (a=3,b=3) characterized by each player choosing
his dominant strategy.
c. Define the concept of pure strategy subgame perfect Nash equilibrium.
Suppose that the game is played for ten rounds. That is, at each round 𝒕 ∈
{𝟏, … , 𝟏𝟎} players R and C choose actions simultaneously. After observing the
outcome of their choices, and if it is not the last round (that is, as long as 𝒕 ≠
𝟏𝟎), they move to the next round and again they choose actions simultaneously.
If the players’ strategies constitute a subgame perfect Nash equilibrium (SPNE),
what would be the outcome of play on each round? Explain.
Page 2 of 7
Answer
A pure strategy SPNE is a profile of strategies that constitutes a Nash equilibrium for
every subgame of a game. As players have a dominant strategy for each round, then
backward induction implies that the unique SPNE is for players to play (a=3, b=3) in
each round.
Page 3 of 7
QUESTION 2 (Competitive Strategy and Asymmetric Information)
a. What is competitive advantage and how does it depend on the resources that a
firm owns? Provide an example of a resource that is the basis of a capability
that confers a competitive advantage in one industry but not in a different
industry.
Answer
See Lecture Notes for definition and examples
Consider a market for consulting services where clients differ in the difficulty for
consultants of carrying out the consulting job. In particular, there are three types
of consulting jobs ranked by their difficulty and expected costs (T1, T2, and T3)
according to the table below. For example, a T3 job is an “easy” job that generates
value of 25 to the client and consultants incur a cost of 20 when performing it.
Suppose that clients know the difficulty of the job, but consultants do not know it
at the time at which they agree to accept the job.
Type
Firm Value
Frequency
25
Consultant Expected
Cost
20
T3
T2
32
30
1/3
T1
65
40
1/3
1/3
b. Can there be a competitive market equilibrium allocation where all three types
of clients/jobs (under the assumption of asymmetric information) are active in
the market? In an equilibrium with asymmetric information, which type of clients
will be active in the market?
Answer
No. Consultants that are equally likely to get a type T1, T2 or T3 job expect to incur a
cost 20*(1/3)+30*(1/3)+40*(1/3)=30. The minimum price in the market that would lead
a consultant to accept a job is therefore 30. However, clients with T3 jobs will not seek
a consultant if the price exceeds 25. Therefore, there cannot be an equilibrium in which
all clients seek consultants. If T3 clients do not enter the market, then if consultants
expect only T1 and T2, then they expect a cost of 30*(1/2)+40*(1/2)=35. The minimum
price in the market that would lead consultant to accept jobs is therefore 35. However,
clients with T2 jobs will not seek a consultant if the price exceeds 32, therefore there
cannot be an equilibrium in which T2 and T1 seek consultants. Therefore, the only
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possible equilibrium is for T1 clients to hire consultants are a price between 40 and
65.
c. Suppose that Type T3 customers value consulting services more. In particular,
they value consulting services at 31. Can there be a competitive market
equilibrium allocation where all three types of clients/jobs (under the
assumption of asymmetric information) are active in the market?
Answer
Yes. Consultants are willing to serve a market in which all clients participate if the price
exceeds 30. All clients are willing to participate if the price is below 31.
Page 5 of 7
QUESTION 3 (Motivation and Coordination)
a. Describe four reasons why the use of pay-for-performance schemes might be
beneficial to a firm.
Answer
See Lecture Notes for definition and examples
A hospital employs two ambulances to pick up patients. Whenever a patient is
picked up it generates a revenue of v>1 (and failure to pick up the patient generates
revenue of 0). The costs of sending each ambulance are initially unknown and
independent between ambulances, and can take one of three values: 0, ½ or ¾ .
The probability that one ambulance has cost 0 is p/2, cost ½ is p/2 while the
probability that it has cost ¾ is 1-p. Profits of the hospital equal the revenue from
picking up the patient minus the costs incurred from the ambulances sent.
Managers and ambulance drivers seek to maximize the hospital’s profits when
making decisions.
b. Suppose that the hospital centralizes decision-making and decides which
ambulance to send before they know the costs of each ambulance. Find the
maximum profits of the hospital and describe the optimal decision rule it will
follow.
Answer
Since the value of picking up the patient is always larger than the cost of an ambulance
and both ambulances are identical, the hospital will always send one and only one
ambulance (say ambulance 1) and generate a profit of v-(1/2*p+3/4*(1-p))=v-(3/41/2p)
c. Suppose that the hospital decentralizes decision-making and lets each
ambulance decide whether to pick up the patient. Ambulance drivers make their
decision once they know their costs but without knowledge of the cost of the
other ambulance. Suppose that each ambulance follows the same rule as a
function of its costs. Find the optimal rule and the maximum profits of the firm
under decentralization.
Answer
We consider two possible rules: (i) Ambulances go whatever their cost, and (ii)
ambulances go only if their cost is 0 or ½. In the first case, the revenue is v but the
total cost is 2*(3/4-p/2). In the second case, the probability that the patient is picked
up is (1-(1-p)2) and the expected cost is (1/2*p), so profits are v(1-(1-p)2)-p/2.
Comparing both profits we see that letting ambulances go only if their cost is 0 or ½
yields higher profits if v<(3/2-3p/2)/(1-p)2.
Page 6 of 7
QUESTION 4 (Horizontal and Vertical Scope)
a. You are a winemaker thinking of launching a new boutique red wine (you have
in mind a monovarietal Merlot or Cabernet). There is a close-by vineyard which
grows Merlot grapes that are well suited for your new wine. However, you could
decide to buy the vineyard (including the grapes) from the local farmer, or
directly buy the grapes once harvested. Briefly explain why you would prefer to
buy the grapes rather than become owner of the vineyard.
Answer
See Lecture Notes
b. Discuss three reasons for value-enhancing unrelated diversification in
conglomerates.
Answer
See Lecture Notes
c. “Our external supplier is more efficient than we are at producing the input that
we use. Therefore, we should purchase the input from them”. Do you see this
as the only alternative? If not, provide an alternative arrangement and an
economic reason for why this alternative arrangement may be preferred by the
firm.
Answer
The quote explains that your supplier has a comparative advantage in producing the
input. However, comparative advantage is not the only dimension dictating the
benefits and costs of procuring the input from them. There are also transaction costs
associated with governing the transaction (from investments in the input, to adapting
the input to your particular needs, to costs of ex-post haggling) that may make it very
costly to purchase the input from your supplier. Given that the supplier is more
efficient, the firm should evaluate whether vertical integration, and thus making your
supplier your employee, ameliorates transaction costs. If this is true, the firm will prefer
to “make the input” in-house.
Page 7 of 7