Oligopoly is a market structure with few sellers influencing market price. Firms in an oligopoly are interdependent since the actions of one firm affect others' profits. This interdependence can be modeled as a prisoner's dilemma game where each firm is incentivized to increase output for higher profits, but overall profits decrease if all firms do so. Cartels like OPEC aim to coordinate production quotas to influence price but members often cheat for greater individual profits, requiring enforcement to maintain cooperation.
Solution Manual for Principles of Corporate Finance 14th Edition by Richard B...
Understanding Oligopoly Markets Through Game Theory
1. OLIGOPOLY
Oligopoly is a market with few sellers selling
similar or identical products. “Few” means more
than one, but not so many that each firm doesn’t
have a substantial influence over market price.
2. OLIGOPOLY
Price Quantity
(P) (Q)
10 0
9 1
8 2
7 3
6 4
5 5
4 6
3 7
2 8
1 9
0 10
The market demand for a product is
given on the left. The technology for
producing the product has zero fixed
cost and constant marginal cost of $1.
Then ATC=AVC=MC=1 for any firm
regardless of size. We will consider
three ways of organizing production
(perfect competition, monopoly, and
oligopoly), and examine the economic
4. PERFECT COMPETITION
Price Quantity
(P) (Q)
10 0
9 1
8 2
7 3
6 4
5 5
4 6
3 7
2 8
1 9
0 10
Each perfectly competitive firm will
produce where Ppc=MC=1, so that a
total of Qpc=9 units will be produced.
This is the socially optimal level of
output. Each firm will have zero
economic profit since ATC=MC=P,
and (P-ATC) x Q = 0.
5. MONOPOLY
P Q TR MR
10 0 0 -
9 1 9 9
8 2 16 7
7 3 21 5
6 4 24 3
5 5 25 1
4 6 24 -1
3 7 21 -3
2 8 16 -5
1 9 9 -7
0 10 0 -9
The monopolist will produce
where P>MR=MC=1, which
occurs at Qm=5 units of
output. Monopoly price will
be Pm=5, and monopoly
profits will be
(Pm-ATC) x Qm = (5-1)x5
=20.
6. MONOPOLY
P Q TR MR
10 0 0 -
9 1 9 9
8 2 16 7
7 3 21 5
6 4 24 3
5 5 25 1
4 6 24 -1
3 7 21 -3
2 8 16 -5
1 9 9 -7
0 10 0 -9
$
Q
ATC=MC
D
MR
Ppc=1
Pm=5
Qm=
5
Qpc=9
DEADWEIGHT
LOSS
The perfectly competitive
industry is efficient in
allocating resources, while the
7. MONOPOLY
P Q TR MR
10 0 0 -
9 1 9 9
8 2 16 7
7 3 21 5
6 4 24 3
5 5 25 1
4 6 24 -1
3 7 21 -3
2 8 16 -5
1 9 9 -7
0 10 0 -9
$
Q
ATC=MC
D
MR
Ppc=1
Pm=5
Qm=
5
Qpc=9
DEADWEIGHT
LOSS
monopoly allocates too few
resources producing a
deadweight loss of
9. DUOPOLY
P Q TR MR
10 0 0 -
9 1 9 9
8 2 16 7
7 3 21 5
6 4 24 3
5 5 25 1
4 6 24 -1
3 7 21 -3
2 8 16 -5
1 9 9 -7
0 10 0 -9
The special case of oligopoly,
where there are only two
firms, is called duopoly.
Assume that the two firms
are identical. Then they can
maximize their combined
profits by together producing
the monopoly output of 5 and
charging the monopoly price
10. DUOPOLY
P Q TR MR
10 0 0 -
9 1 9 9
8 2 16 7
7 3 21 5
6 4 24 3
5 5 25 1
4 6 24 -1
3 7 21 -3
2 8 16 -5
1 9 9 -7
0 10 0 -9
of 5. If each of the duopolists
produce 2.5 units of output,
they will each have a profit of
(P-ATC) x Q = (5-1) x 2.5=10.
Then their combined profit
will be 20 -- the same as a
monopolist’s profit. When
firms enter into an agreement
about their production levels
11. DUOPOLY
and price to charge, this is called collusion, and the
group of firms in the agreement is a cartel. Then
a cartel may allocate resources in the same way as
a monopoly. However there are often strong
incentives for duopolists (oligopolists) to jointly
produce a larger output than a monopolist. When
duopoly firm A sees its competitor, firm B,
producing 2.5 units of output, A can increase its
profit by producing more than 2.5 units.
12. DUOPOLY
QB QA Q P TRA MRA TCA PROFIT
2.5 0.5 3 7 3.5 - 0.5 3
2.5 1.5 4 6 9 5.5 1.5 7.5
2.5 2.5 5 5 12.5 3.5 2.5 10
2.5 3.5 6 4 14 1.5 3.5 10.5
2.5 4.5 7 3 13.5 -0.5 4.5 9
2.5 5.5 8 2 11 -1.5 5.5 5.5
2.5 6.5 9 1 6.5 -4.5 6.5 0
2.5 7.5 10 0 0 -6.5 7.5 -7.5
If B continues to
produce and sell
2.5 units, A can
increase profits
to 10.5 by selling
3.5 units of output. Price will fall to 4 so that B’s
profit will now be (P-ATC)xQ=(4-1)x2.5=7.5, a
decrease of 2.5. Therefore, when A increases its
sales, B’s profit is affected. Similarly, if B changes
13. DUOPOLY
the quantity that it sells, A’s profit will change.
Therefore the two firms are interdependent.
When each firm believes that the other will
produce and sell 2.5 units, each has the incentive
to produce and sell 3.5 units to increase their
profit. However, when each firm produces 3.5
units, total output is 7 and market price is 3. Then
each firm’s profit is (P-ATC)xQ=(3-1)X3.5=7. Each
firm does worse than when they each produce 2.5.
14. DUOPOLY
Firm A
2.5 3.5
2.5
Firm
B 3.5
10 10.5
10 7.5
7.5 7
10.5 7
The table at the left
summarizes the results of
the two duopolists’ actions.
A’s profits for each output
pair is given in the upper
right of each cell; B’s profit
for each output pair is in the lower left of each cell.
When B sells 2.5 and A sells 3.5, A’s profit is 10.5
and B’s profit is 7.5.
15. GAME THEORY
Since the duopolists’ actions affect each other, they
must develop strategies for deciding how much
output to produce. Strategic decision making can
be conveniently analyzed using game theory. An
elementary game is known as the prisoners’
dilemma.
16. PRISONERS’ DILEMMA
Butch
Remain
Silent Confess
Remain
Sundance Silent
Confess
5 years 0 years
5 years 20 years
20 years 10 years
0 years 10 years
Each prisoner
will get a 5
year sentence
if they both
remain silent.
However, each
has an
incentive to confess and have their sentence
reduced to 0 years. But if both confess, they will
17. PRISONERS’ DILEMMA
Butch
Remain
Silent Confess
Remain
Sundance Silent
Confess
5 years 0 years
5 years 20 years
20 years 10 years
0 years 10 years
both be worse
off than if they
both remain
silent. The
actions of each
will have not
only an effect
on themselves, but also on the other. The results
of their actions are interdependent. If Butch
19. DUOPOLY
Firm A
2.5 3.5
2.5
Firm
B 3.5
10 10.5
10 7.5
7.5 7
10.5 7
The duopolists’ game is
similar to the prisoners’
dilemma. Each has an
incentive to choose an
action that is not jointly
optimal. The actions of
each duopolist has an effect on the profits of the
other.
20. OPEC
Founded in 1960, the Organization of Petroleum
Exporting Countries (OPEC) is a cartel of 11
countries that collectively produce about 75% of
the world’s oil. Periodically, the cartel assigns
production quotas to each of its members to limit
production in order to increase price and profits
of its members. The cartel has no legal means of
enforcing the production quotas. They are simply
accepted by mutual consent. When price is high,
21. OPEC
each country has an incentive to increase its
production to increase its own profits. But when
a number of countries increase production, price
will fall and so will the OPEC members’ profits.
In fact the history of OPEC has seen output quotas
raise petroleum (and gasoline) prices, only to have
some members eventually cheat on the agreement.
Saudi Arabia (which is an OPEC member) has
attempted to penalize the cheaters by flooding the
22. OPEC
world market with oil, and driving down world
price and the profits of oil producers. The idea
that Saudi Arabia is attempting to convey is that
countries who cheat will be “punished” with low
prices and profits when they do not follow their
production quotas. Repeatedly playing this game
OPEC members should eventually learn that the
best strategy to play is to adhere to their production
quotas.