Understanding Game Theory and Oligopoly in Economics

 
Game theory
 
Game theory helps us understand oligopoly and
other situations where “players” interact and behave
strategically.
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Game Theory
 
OLIGOPOLY
 
2
 
The police have caught Bonnie and Clyde,
two suspected bank robbers, but only have enough
evidence to imprison each for 1 year.
The police question each in separate rooms,
offer each the following deal:
If you confess and implicate your partner,
you go free.
If you do not confess but your partner implicates you,
you get 20 years in prison.
If you both confess, each gets 8 years in prison.
 
Prisoners’ Dilemma Example
 
OLIGOPOLY
 
3
4
Prisoners’ Dilemma Example
Confess
Remain silent
Confess
Remain
silent
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Bonnie gets
8 years
 
Clyde
gets 8 years
 
Bonnie gets
20 years
 
Bonnie gets
1 year
 
Bonnie goes
free
 
Clyde
goes free
 
Clyde
gets 1 year
 
Clyde
gets 20 years
 
Confessing is the dominant strategy for both players.
 
Nash equilibrium:
both confess
 
Prisoners’ Dilemma Example
 
Outcome:  Bonnie and Clyde both
confess,
each gets 8 years in prison.
Both would have been better off if both
remained silent.
But even if Bonnie and Clyde had agreed
before being caught to remain silent, the
logic of self-interest takes over and leads
them to confess.
 
 
OLIGOPOLY
 
5
OLIGOPOLY
6
EXAMPLE:
  Cell Phone Duopoly in Smalltown
 
EXAMPLE:
  Cell Phone Duopoly in Smalltown
 
One possible duopoly outcome:  collusion
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T-Mobile and Verizon could agree to each
produce half of the monopoly output:
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7
 
When oligopolies form a cartel in hopes
of reaching the monopoly outcome,
they become players in a prisoners’ dilemma.
Our earlier example:
T-Mobile and Verizon are duopolists in Smalltown.
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Oligopolies as a Prisoners’ Dilemma
 
OLIGOPOLY
 
8
9
T-Mobile & Verizon in the Prisoners’ Dilemma
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T-Mobile’s
profit = $900
Verizon’s
profit = $900
T-Mobile’s
profit = $1000
T-Mobile’s
profit = $800
T-Mobile’s
profit = $750
Verizon’s
profit = $750
Verizon’s
profit = $800
Verizon’s profit
= $1000
 
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The Equilibrium for an Oligopoly
 
OLIGOPOLY
 
10
 
In the following, let the market demand curve be 
P 
= 70 - 2
Q
,
and assume all sellers can produce at a constant marginal
cost of 
c 
= 10, with zero fixed costs.
 
a)
If the market is perfectly competitive, what is
the equilibrium price and quantity?
b)
If the market is controlled by a monopolist,
what is the equilibrium price and quantity?
How much profit does the monopolist earn?
c)
Now suppose that Amy and Beau compete
as duopolists. What is the equilibrium price?
What is total market output, and how much
profit does each seller earn?
 
Boeing and Airbus are competing to fill an
 
order of jets for Singapore Airlines.
Each firm can offer a
 
price of $10 million per jet or $5 million per jet. If both
 
firms
offer the same price, the airline will split the order
 
between the two firms, 50–50. If
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price than the other, the lower-price competitor wins the
entire order. Here is the profit that Boeing and Airbus
 
expect they could earn from
this transaction:
 
If both firm formed a cartel agreement, at what
price e
ach firm 
sell the jet?
What is the Nash equilibrium in this game?
If 
Boeing
 could move first and credibly commit to
its
 
capacity expansion strategy, what is its
optimal strategy?
What will 
Airbus
 do?
Other Examples of the Prisoners’ Dilemma
 
Ad Wars
Two firms spend millions on TV ads to steal
business from each other.  Each firm’s ad
cancels out the effects of the other,
and both firms’ profits fall by the cost of the
ads.
Organization of Petroleum Exporting
Countries
 
Member countries try to act like a
cartel, agree to
limit oil production to boost prices & profits.
But agreements sometimes break down
when individual countries renege.
OLIGOPOLY
13
 
Arms race between military superpowers
Each country would be better off if both disarm,
but each has a dominant strategy of arming.
Common resources
All would be better off if everyone conserved common
resources, but each person’s dominant strategy is
overusing the resources.
Other Examples of the Prisoners’ Dilemma
OLIGOPOLY
14
 
The noncooperative oligopoly equilibrium
Bad for oligopoly firms:
prevents them from achieving monopoly profits
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In other prisoners’ dilemmas, the inability to
cooperate may reduce social welfare.
e.g
., arms race, overuse of common resources
 
Prisoners’ Dilemma and Society’s Welfare
 
OLIGOPOLY
 
15
 
Another Example:  Negative Campaign Ads
 
Election with two candidates, “R” and “D.”
If R runs a negative ad attacking D,
3000 fewer people will vote for D:
1000 of these people vote for R, the rest
abstain.
If D runs a negative ad attacking R,
R loses 3000 votes, D gains 1000, 2000
abstain.
R and D agree to refrain from running
attack ads.  Will each one stick to the
agreement?
 
OLIGOPOLY
 
16
17
Another Example:  Negative Campaign Ads
Do not run attack
ads (cooperate)
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no votes lost
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no votes
no votes
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lost or gained
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R gains 1000
votes
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R loses
R loses
2000 votes
2000 votes
R loses 3000
R loses 3000
votes
votes
D loses
D loses
3000 votes
3000 votes
D loses
D loses
2000 votes
2000 votes
D gains
D gains
1000 votes
1000 votes
 
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Run attack ads
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Do not run
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Run
attack ads
(defect)
 
Nash eq’m:  both candidates run attack ads.
Effects on election outcome:  NONE.
Each side’s ads cancel out the effects of the other
side’s ads.
Effects on society:  NEGATIVE.
Lower voter turnout, higher apathy about politics,
less voter scrutiny of elected officials’ actions.
 
Another Example:  Negative Campaign Ads
 
OLIGOPOLY
 
18
 
When the game is repeated many times, cooperation
may be possible.
These strategies may lead to cooperation:
If your rival reneges in one round,
you renege in all subsequent rounds.
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Why People Sometimes Cooperate
 
OLIGOPOLY
 
19
Public Policy Toward Oligopolies
 
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In oligopolies, production is too low and
prices are too high, relative to the social
optimum.
Role for policymakers:
Promote competition, prevent cooperation
to move the oligopoly outcome closer to
the efficient outcome.
OLIGOPOLY
20
 
Restraint of Trade and Antitrust Laws
 
Sherman Antitrust Act (1890):
Forbids collusion between competitors
Clayton Antitrust Act (1914):
Strengthened rights of individuals
damaged by anticompetitive
arrangements between firms
 
OLIGOPOLY
 
21
 
Most people agree that price-fixing agreements
among competitors should be illegal.
Some economists are concerned that policymakers
go too far when using antitrust laws to stifle business
practices that are not necessarily harmful, and may
have legitimate objectives.
We consider three such practices…
Controversies Over Antitrust Policy
OLIGOPOLY
22
 
1. Resale Price Maintenance (“Fair Trade”)
 
Occurs when a manufacturer imposes
lower limits on the prices retailers can
charge.
Is often opposed because it appears to
reduce competition at the retail level.
Yet, any market power the manufacturer
has
is at the wholesale level; manufacturers
do not gain from restricting competition at
the retail level.
The practice has a legitimate objective:
preventing discount retailers from free-
riding
on the services provided by full-service
retailers.
 
OLIGOPOLY
 
23
 
Occurs when a firm cuts prices to prevent entry
or drive a competitor out of the market,
so that it can charge monopoly prices later.
Illegal under antitrust laws, but hard for the courts to
determine when a price cut is predatory and when it is
competitive & beneficial to consumers.
Many economists doubt that predatory pricing is a
rational strategy:
It involves selling at a loss, which is extremely costly
for the firm.
It can backfire.
 
2. Predatory Pricing
 
OLIGOPOLY
 
24
 
Occurs when a manufacturer bundles two products
together and sells them for one price (
e.g
., Microsoft
including a browser with its operating system)
Critics argue that tying gives firms more market power
by connecting weak products to strong ones.
Others counter that tying cannot change market power:
Buyers are not willing to pay more for two goods
together than for the goods separately.
Firms may use tying for price discrimination,
which is not illegal, and which sometimes
increases economic efficiency.
 
3. Tying
 
OLIGOPOLY
 
25
 
CONCLUSION
 
Oligopolies can end up looking like
monopolies or like competitive markets,
depending on the number of firms and
how cooperative they are.
The prisoners’ dilemma shows how
difficult it is for firms to maintain
cooperation, even when doing so is in
their best interest.
Policymakers use the antitrust laws to
regulate oligopolists’ behavior.  The proper
scope of these laws is the subject of
ongoing controversy.
 
OLIGOPOLY
 
26
 
THANK YOU
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Game theory is a valuable tool for analyzing strategic interactions among players in situations like oligopoly. The concept of dominant strategy and the classic example of the Prisoner's Dilemma shed light on how individual rationality can lead to suboptimal outcomes. The practical example of a cell phone duopoly in a small town further illustrates the implications of different market structures on pricing, output, and profits.


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  1. Game theory

  2. Game Theory Game theory helps us understand oligopoly and other situations where players interact and behave strategically. Dominant strategy: a strategy that is best for a player in a game regardless of the strategies chosen by the other players Prisoners dilemma: a game between two captured criminals that illustrates why cooperation is difficult even when it is mutually beneficial 2 OLIGOPOLY

  3. Prisoners Dilemma Example The police have caught Bonnie and Clyde, two suspected bank robbers, but only have enough evidence to imprison each for 1 year. The police question each in separate rooms, offer each the following deal: If you confess and implicate your partner, you go free. If you do not confess but your partner implicates you, you get 20 years in prison. If you both confess, each gets 8 years in prison. 3 OLIGOPOLY

  4. Prisoners Dilemma Example Confessing is the dominant strategy for both players. Nash equilibrium: both confess Bonnie s decision Confess Remain silent Bonnie gets 8 years Bonnie gets 20 years Confess Clyde gets 8 years Clyde goes free Clyde s decision Bonnie goes Bonnie gets 1 year free Remain silent Clyde gets 1 year Clyde gets 20 years 4

  5. Prisoners Dilemma Example Outcome: Bonnie and Clyde both confess, each gets 8 years in prison. Both would have been better off if both remained silent. But even if Bonnie and Clyde had agreed before being caught to remain silent, the logic of self-interest takes over and leads them to confess. 5 OLIGOPOLY

  6. EXAMPLE: Cell Phone Duopoly in Smalltown Competitive outcome: P = MC = $10 Q = 120 Profit = $0 P Q Revenue Cost Profit $0 140 $0 $1,400 1,400 5 130 650 1,300 650 10 120 1,200 1,200 0 15 110 1,650 1,100 550 20 100 2,000 1,000 1,000 25 90 2,250 900 1,350 Monopoly outcome: P = $40 Q = 60 Profit = $1,800 30 80 2,400 800 1,600 35 70 2,450 700 1,750 40 60 2,400 600 1,800 45 50 2,250 500 1,750 6 OLIGOPOLY

  7. EXAMPLE: Cell Phone Duopoly in Smalltown One possible duopoly outcome: collusion Collusion: an agreement among firms in a market about quantities to produce or prices to charge T-Mobile and Verizon could agree to each produce half of the monopoly output: For each firm: Q = 30, P = $40, profits = $900 Cartel: a group of firms acting in unison, e.g., T-Mobile and Verizon in the outcome with collusion 7

  8. Oligopolies as a Prisoners Dilemma When oligopolies form a cartel in hopes of reaching the monopoly outcome, they become players in a prisoners dilemma. Our earlier example: T-Mobile and Verizon are duopolists in Smalltown. The cartel outcome maximizes profits: Each firm agrees to serve Q = 30 customers. 8 OLIGOPOLY

  9. T-Mobile & Verizon in the Prisoners Dilemma Each firm s dominant strategy: renege on agreement, produce Q = 40. T-Mobile Q = 30 Q = 40 T-Mobile s profit = $900 T-Mobile s profit = $1000 Q = 30 Verizon s profit = $900 Verizon s profit = $750 Verizon T-Mobile s profit = $750 T-Mobile s profit = $800 Q = 40 Verizon s profit = $800 Verizon s profit = $1000 9

  10. The Equilibrium for an Oligopoly Nash equilibrium: a situation in which economic participants interacting with one another each choose their best strategy given the strategies that all the others have chosen Our duopoly example has a Nash equilibrium in which each firm produces Q = 40. Given that Verizon produces Q = 40, T-Mobile s best move is to produce Q = 40. Given that T-Mobile produces Q = 40, Verizon s best move is to produce Q = 40. 10 OLIGOPOLY

  11. In the following, let the market demand curve be P = 70 - 2Q, and assume all sellers can produce at a constant marginal cost of c = 10, with zero fixed costs. a) If the market is perfectly competitive, what is the equilibrium price and quantity? b) If the market is controlled by a monopolist, what is the equilibrium price and quantity? How much profit does the monopolist earn? c) Now suppose that Amy and Beau compete as duopolists. What is the equilibrium price? What is total market output, and how much profit does each seller earn?

  12. Boeing and Airbus are competing to fill an order of jets for Singapore Airlines. Each firm can offer a price of $10 million per jet or $5 million per jet. If both firms offer the same price, the airline will split the order between the two firms, 50 50. If one firm offers a higher price than the other, the lower-price competitor wins the entire order. Here is the profit that Boeing and Airbus expect they could earn from this transaction: If both firm formed a cartel agreement, at what price each firm sell the jet? What is the Nash equilibrium in this game? If Boeing could move first and credibly commit to its capacity expansion strategy, what is its optimal strategy? What will Airbus do?

  13. Other Examples of the Prisoners Dilemma Ad Wars Two firms spend millions on TV ads to steal business from each other. Each firm s ad cancels out the effects of the other, and both firms profits fall by the cost of the ads. Organization of Petroleum Exporting Countries Member countries try to act like a cartel, agree to limit oil production to boost prices & profits. But agreements sometimes break down when individual countries renege. 13 OLIGOPOLY

  14. Other Examples of the Prisoners Dilemma Arms race between military superpowers Each country would be better off if both disarm, but each has a dominant strategy of arming. Common resources All would be better off if everyone conserved common resources, but each person s dominant strategy is overusing the resources. 14 OLIGOPOLY

  15. Prisoners Dilemma and Societys Welfare The noncooperative oligopoly equilibrium Bad for oligopoly firms: prevents them from achieving monopoly profits Good for society: Q is closer to the socially efficient output P is closer to MC In other prisoners dilemmas, the inability to cooperate may reduce social welfare. e.g., arms race, overuse of common resources 15 OLIGOPOLY

  16. Another Example: Negative Campaign Ads Election with two candidates, R and D. If R runs a negative ad attacking D, 3000 fewer people will vote for D: 1000 of these people vote for R, the rest abstain. If D runs a negative ad attacking R, R loses 3000 votes, D gains 1000, 2000 abstain. R and D agree to refrain from running attack ads. Will each one stick to the agreement? 16 OLIGOPOLY

  17. Another Example: Negative Campaign Ads Each candidate s dominant strategy: run attack ads. R s decision Run attack ads (defect) Do not run attack ads (cooperate) no votes lost R gains 1000 Do not run attack ads (cooperate) or gained votes no votes lost or gained D loses 3000 votes D s decision R loses 3000 R loses 2000 votes votes Run attack ads (defect) D loses 2000 votes D gains 1000 votes 17

  18. Another Example: Negative Campaign Ads Nash eq m: both candidates run attack ads. Effects on election outcome: NONE. Each side s ads cancel out the effects of the other side s ads. Effects on society: NEGATIVE. Lower voter turnout, higher apathy about politics, less voter scrutiny of elected officials actions. 18 OLIGOPOLY

  19. Why People Sometimes Cooperate When the game is repeated many times, cooperation may be possible. These strategies may lead to cooperation: If your rival reneges in one round, you renege in all subsequent rounds. Tit-for-tat Whatever your rival does in one round (whether renege or cooperate), you do in the following round. 19 OLIGOPOLY

  20. Public Policy Toward Oligopolies Recall one of the Ten Principles from Chap.1: Governments can sometimes improve market outcomes. In oligopolies, production is too low and prices are too high, relative to the social optimum. Role for policymakers: Promote competition, prevent cooperation to move the oligopoly outcome closer to the efficient outcome. 20 OLIGOPOLY

  21. Restraint of Trade and Antitrust Laws Sherman Antitrust Act (1890): Forbids collusion between competitors Clayton Antitrust Act (1914): Strengthened rights of individuals damaged by anticompetitive arrangements between firms 21 OLIGOPOLY

  22. Controversies Over Antitrust Policy Most people agree that price-fixing agreements among competitors should be illegal. Some economists are concerned that policymakers go too far when using antitrust laws to stifle business practices that are not necessarily harmful, and may have legitimate objectives. We consider three such practices 22 OLIGOPOLY

  23. 1. Resale Price Maintenance (Fair Trade) Occurs when a manufacturer imposes lower limits on the prices retailers can charge. Is often opposed because it appears to reduce competition at the retail level. Yet, any market power the manufacturer has is at the wholesale level; manufacturers do not gain from restricting competition at the retail level. The practice has a legitimate objective: preventing discount retailers from free- riding on the services provided by full-service retailers. 23 OLIGOPOLY

  24. 2. Predatory Pricing Occurs when a firm cuts prices to prevent entry or drive a competitor out of the market, so that it can charge monopoly prices later. Illegal under antitrust laws, but hard for the courts to determine when a price cut is predatory and when it is competitive & beneficial to consumers. Many economists doubt that predatory pricing is a rational strategy: It involves selling at a loss, which is extremely costly for the firm. It can backfire. 24 OLIGOPOLY

  25. 3. Tying Occurs when a manufacturer bundles two products together and sells them for one price (e.g., Microsoft including a browser with its operating system) Critics argue that tying gives firms more market power by connecting weak products to strong ones. Others counter that tying cannot change market power: Buyers are not willing to pay more for two goods together than for the goods separately. Firms may use tying for price discrimination, which is not illegal, and which sometimes increases economic efficiency. 25 OLIGOPOLY

  26. CONCLUSION Oligopolies can end up looking like monopolies or like competitive markets, depending on the number of firms and how cooperative they are. The prisoners dilemma shows how difficult it is for firms to maintain cooperation, even when doing so is in their best interest. Policymakers use the antitrust laws to regulate oligopolists behavior. The proper scope of these laws is the subject of ongoing controversy. 26 OLIGOPOLY

  27. THANK YOU

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