# Chapter 10

```Chapter 10
Strategic Choice in Oligopoly,
Monopolistic Competition, and
Everyday Life
Odd-numbered Qs.
Problem #1, Chapter 10
• In studying for his economics final, Sam is concerned about
only two things: his grade and the amount of time he spends
studying. A good grade will give him a benefit of 20; an
average grade, a benefit of 5; and a poor grade, a benefit of 0.
By studying a lot, Sam will incur a cost of 10; by studying a
little, a cost of 6. Moreover, if Sam studies a lot and all other
students study a little, he will get a good grade and they will
get poor ones. But if they study a lot and he studies a little,
they will get good grades and he will get a poor one. Finally, if
he and all other students study the same amount of time,
everyone will get average grades. Other students share Sam’s
preferences regarding grades and study time.
Solution to Problem #1 (1)
• A) Model this situation as a two-person prisoner’s dilemma in
which the strategies are to study a little and to study lot, and
the players are Sam and all other students. Include the payoffs
in the matrix
• Payoff = benefit - cost
• Think of all possible combinations of outcomes
– Sam studies a lot while all others also study a lot
• Sam’s payoff: 5-10 =-5; all others’ payoff: 5-10=-5
– Sam studies a lot but all others study a little
• Sam’s payoff: 20-10 =10; all others’ payoff: 0 – 6 = -6
Solution to Problem #1 (2)
– Sam studies a little but all others study a lot
• Sam’s payoff: 0-6 = -6; all others’ payoff: 20-10= 10
– Sam studies a little while all others also study a little
• Sam’s payoff: 5-6= -1; all others’ payoff: 5-6= -1
• Put all these possible combinations into a payoff matrix
Solution to Problem #1 (3)
All others
Study a lot
Study little
Study a lot
-5 for Sam;
-5 for others
10 for Sam;
-6 for others
Study a little
-6 for Sam;
10 for others
-1 for Sam;
-1 for others
Sam
Solution to Problem #1 (4)
• B) What is the equilibrium outcome in this game? From the
students’ perspective, is it the best outcome?
• To find the equilibrium outcome, we first need to find out
how will each player behave in the preparation for final
• The dominant strategy refers to the best strategy for an
individual player regardless of what all players do
• The dominated strategy refers to the strategy that is always
inferior to the dominant strategy
• In this question, both Sam and all others have a dominant
strategy of studying a lot
Solution to Problem #1 (5)
• Therefore, each will follow the best strategy by studying a lot
for preparation for final
• Equilibrium outcome: both studying a lot
• As a result, both Sam and all others will end up with an
average grade of 5 or a payoff of -5
• However, this is actually not a best outcome
• From the students’ perspective, for everyone to study a little
would turn out to better than the equilibrium outcome
Problem #3, Chapter 10 (1)
• Blackadder and Baldrick are rational, self-interested criminals
imprisoned in separate cells in a dark medieval dungeon. They
face the prisoners’ dilemma displayed in the matrix
• Assume that Blackadder is willing to pay \$1000 for each year
by which he can reduce his sentence below 20 years. A
corrupt jailer tells Blackadder that before he decides whether
to confess or deny the crime, she can tell him Baldrick’s
decision. How much is this information worth to Blackadder?
Problem #3, Chapter 10 (2)
Confess
Deny
Confess
5 years for each
0 year for
Baldrick;
20 years for
Deny
0 year for
20 years for
Baldrick
1 year for
each
Baldrick
Solution to Problem #3 (1)
• To find out how much does the information worth to
Blackadder, we will need to know whether the information is
useful
• If one knows the other’s dominant strategy, one will know
what will the other do regardless what one does
• Based on the payoffs in the matrix, we know:
– Baldrick has a dominant strategy of confess
– Blackadder has a dominant strategy of confess
– The equilibrium outcome is thus confess
Solution to Problem #3 (2)
• Therefore, Baldrick will confess no matter Blackadder
confesses or denies
• The information from the corrupt jailer is thus useless
• It is worth nothing to Blackadder
Problem #5, Chapter 10
• Imagine yourself sitting in your car in a campus parking lot
that is currently full, waiting for someone to pull out so that
you can park your car. Somebody pulls out, but at the same
moment a driver who has just arrived overtakes you in an
obvious attempt to park in the vacated spot before you can.
Suppose this driver would be willing to pay up to \$10 to park
in that spot and up to \$30 to avoid getting into an argument
with you. (That is, the benefit of parking is \$10 and the cost an
argument is \$30.) At the same time he guesses, accurately,
that you too would be willing to pay up \$30 to avoid a
confrontation and up to \$10 to park in the vacant spot.
Solution to Problem #5 (1)
• A) Model this situation as a two-stage decision tree in which
his bid to take the space is the opening move and your
strategies are (1) to protest and (2) not to protest. If you
protest (initiate an argument), the rules of game specify that
he has to let you that the space. Show the payoffs at the end
of each branch of tree.
• Start from the first node: the other driver either leave you the
parking lot or overtake the parking lot
• If the driver leaves you the parking lot, you and the driver will
not engage in any form of argument or dispute
• You will finally get a benefit of \$10 as having your car parked
Solution to Problem #5 (2)
• However, if the driver overtakes the parking lot, you will end
having either a defer or a protest against the act of the driver
• If you protest, you will get a payoff of -\$20 and the driver will
have a payoff of -\$30
– Why are that?
• Payoff = Benefit – Cost
• Your payoff: \$10 - \$30 = -\$20
• The driver’s payoff: -\$30
• If you defer, you will get a payoff of \$0 and the driver will have
a payoff of \$10
Solution to Problem #5 (3)
• If you defer, you will get a payoff of \$0 and the driver will have
a payoff of \$10
– Why are that?
• If the driver gets the parking spot, he or she will enjoy the associated
benefit (\$10)
• Both of you and the driver do not have to enter an argument
The other driver leaves
you the spot
\$10 for you; \$0 for the driver
You protest
-\$20 for you; -\$30 for the driver
The other driver overtakes
the parking spot
You defer
\$0 for you; \$10 for the driver
Solution to Problem #5 (4)
• B) What is the equilibrium outcome?
• The driver will overtake the parking spot and you will have to
wait for another spot
– Why?
• Given in the question that he has made an accurate guess that you
would be willing to pay up to \$30 to avoid a confrontation and pay up
to \$10 for a parking spot
• The driver understands that if he or she overtakes the parking spot,
you will probably not protest but defer to another spot as your payoff
is -\$20 if protest but \$0 if defer
• You will minimize your loss but deferring to another spot
Solution to Problem #5 (5)
• C) What would be the advantage of being able to
communicate credibly to other driver that your failure to
protest would be a significant psychological cost to you?
• Suppose the other driver perceived that you would
experience a psychological cost of \$30 not only if you entered
into a dispute, but also if you failed to protest his unjust
behaviour
• The driver would then think your net cost of becoming
involved in an argument would be \$0
• This perception would change your protest payoff to \$10
• As a result, the driver would no longer gain from taking the
parking spot
Problem #7, Chapter 10
• Consider the following game, called matching pennies, which
you are playing with a friend. Each of you has a penny hidden
in your hand, facing either heads up or tails up (you know
which way the one in your hand is facing). On the count of
“three,” you simultaneously show your pennies to each other.
If the face-up side of your coin matches the face-up side of
your friend’s coin, you get to keep the two pennies. If the
faces do not match, your friend gets to keep the pennies.
• A) Who are the players in the game? What are each player’s
strategies? Construct a payoff matrix for the game.
Solution to Problem #7 (1)
• Elements of the game
– Players: you and your friend
– 4 possible outcomes:
• 2 heads- you get the other penny from your friend who will end up
have nothing
• 2 tails- you get the other penny from your friend who will end up have
nothing
will be taken by your friend
will be taken by your friend
Solution to Problem #7 (2)
You
Tail
1 for you;
-1 for you;
1 for your
friend
Tail
-1 for you;
1 for you;
-1 for your
friend
Solution to Problem #7 (3)
• B) Is there a dominant strategy? If so, what?
– No. There are no dominant strategy
– No single strategy that is best regardless of what your friend’s coin
outcome
– Head and tails offer same payoff to both you and your friends
• C) Is there an equilibrium outcome? If so, what?
– No. There is no equilibrium outcome
– Every time when your friend plays one side, you will want to match
that side
Problem #9, Chapter 10 (1)
• Two airplanes manufacturers are considering the production
of a new product, a 150-passenger jet. Both are deciding
whether to enter the market and produce the new planes. The
payoff matrix is as follows (payoff values are in millions of
dollars):
Problem #9, Chapter 10 (2)
Airbus
Produce
Don’t produce
Produce
-5 for each
100 for Boeing;
0 for Airbus
Don’t produce
0 for Boeing;
100 for Airbus
0 for
each
Boeing
Problem #9, Chapter 10 (3)
• The implication of these payoffs is that the market demand is
large enough to support only one manufacturer. If both firms
enter, both will sustain a loss.
• A) Identify two possible equilibrium outcomes in this game
• Based on the payoff matrix above, we know that
– Given that one company produces (does not produce), the other
company will get a higher payoff by not producing (producing)
• 1-equilibrium outcome: Airbus produces while Boeing does
not produce
• 2-equilibrium outcome: Boeing produces while Airbus does
not produce
Problem #9, Chapter 10 (4)
• B) Consider the effect of a subsidy. Suppose the European
Union decides to subsidize the European producer, Airbus,
with a check for \$25 million if it enters the market. Revise the
payoff matrix to account for this subsidy. What are the new
equilibrium outcome?
• Due to the subsidy from EU, producing becomes a dominant
strategy for Airbus
• Given Airbus is producing, Boeing will start away from the
market
• For the revised payoff matrix, all Airbus’ payoffs are added by
25
Problem #9, Chapter 10 (5)
New equilibrium is shown in
blue
Produce
Airbus
Produce
Don’t produce
20 for Airbus;
-5 for Boeing
100 for Boeing;
0 for Airbus
Boeing
Don’t produce
125 for Airbus;
0 for Boeing
0 for
each
Problem #9, Chapter 10 (6)
• C) Compare the two outcomes (pre- and post-subsidy). What
qualitative effect does the subsidy have?
• Without the subsidy, both airplane manufacturers kind of
compete on the same ground
• Either one will enter the market but which will enter remains
uncertain
• However, with the subsidy from EU, Airbus is “granted” a
dominant strategy ensuring its production and eliminating
production by Boeing
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