Transcript The Cournot-Nash Model

Oligopoly
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After reading this chapter, you will
have learned:
• How to derive the Cournot-Nash equilibrium using reaction
functions, and how the Cournot-Nash equilibrium compares to the
competitive and monopoly equilibria.
• How to derive the Stackelberg equilibrium, and how the Stackelberg
equilibrium differs from the Cournot-Nash equilibrium.
• How to derive the Bertrand equilibrium using reaction functions for
a homogeneous product and for a heterogeneous product.
• The dominant firm model for the case of an oligopoly market
dominated by one large firm that competes with a group of small
fringe firms.
• Why the Prisoner’s Dilemma typically makes collusion difficult and
how firms try to solve the Prisoner’s Dilemma by developing
methods of coordinated behavior.
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The Cournot-Nash Model
• Residual Demand Curve — A demand curve that’s the
leftover portion of an industry demand, after a group of
firms in the industry have chosen their outputs.
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The Cournot-Nash Model
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The Cournot-Nash Model
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The Cournot-Nash Model
Reaction Functions and
the Cournot-Nash Equilibrium
• Reaction Function — A function identifying one firm’s
optimal output (price) response to every possible
output (price) produced (charged) by competitors.
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The Cournot-Nash Model
Reaction Functions and
the Cournot-Nash Equilibrium
The Cournot Equilibrium as a Nash Equilibrium
• Cournot-Nash Equilibrium — The equilibrium
outcome in a simultaneous-move game in
which all the firms assume the outputs of all
the other firms in the industry will remain
constant.
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The Cournot-Nash Model
Reaction Functions and
the Cournot-Nash Equilibrium
The Cournot Equilibrium as a Nash Equilibrium
Application: Experimental Games
and the Cournot-Nash Model
• Because it’s difficult to empirically test the validity of the
Cournot-Nash model, economists have developed
experimental games to check the model’s predictions.
• Games played by pairs of college students often confirm
that players reach the Cournot-Nash equilibrium.
• As the number of players increases, the Cournot-Nash
equilibrium becomes less likely, in these experimental
games.
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The Stackelberg Model
• Stackelberg Follower — The firm that
moves second in the Stackelberg game.
• Stackelberg Leader — The firm that moves
first in the Stackelberg game.
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The Stackelberg Model
Firms with Identical Costs and Demand
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The Stackelberg Model
Firms with Identical Costs and Demand
Common Error: Failing to Correctly
Substitute the Follower’s Reaction Function
into the Leader’s Demand Curve
When calculating the Stackelberg equilibrium,
students often incorrectly substitute the
follower’s reaction function into the leader’s
reaction function. If you do this, you’ll calculate
the Cournot-Nash equilibrium, not the
Stackelberg equilibrium.
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The Stackelberg Model
Firms with Different Costs
Application: Fuji's Purchase of Wal-Mart's
Photo-Processing Plants
• From 1993 through 1996, Kodak expanded
its photofinishing capacity substantially.
• After observing Kodak’s capacity expansion,
Fuji responded by dramatically increasing its
capacity and gaining control over all of WalMart’s photofinishing services.
• Fuji’s conduct is consistent with a Stackelberg
follower’s predicted behavior.
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The Bertrand Model
• Bertrand Model — A model developed by Joseph
Bertrand that criticized Cournot’s model by arguing that
if firms assume all other firms hold their prices
constant, Cournot’s logic results in an entirely different
outcome, with price equal to marginal cost.
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The Bertrand Model
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The Bertrand Model
Application: Bertrand Pricing
in the Airline Industry
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The Dominant Firm Model
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The Dominant Firm Model
Common Error: Incorrectly Identifying
the Price in the Dominant Firm Model
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The Dominant Firm Model
Application: The Decline of Dominant Firms
There’s considerable empirical evidence that dominant
firms often lose most of their market power to
competitive fringe firms as a result of high-price policies
and passivity. Examples include U.S. Steel in steel,
Xerox in copiers, Reynolds International Pen Company
in ballpoint pens, International Harvester in farm
equipment, Goodyear in tires, RCA in color televisions,
General Electric in appliances, and IBM in computers.
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Collusion: The Great
Prisoner’s Dilemma
Collusion with Identical
Demand and Cost Conditions
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Collusion: The Great
Prisoner’s Dilemma
Collusion with Identical
Demand and Cost Conditions
• Infinite Game — A static game that’s repeated
forever.
• Tit-for-Tat — A strategy in a Prisoner’s Dilemma
game in which a player starts off cooperating in the
first round and, in every subsequent round, adopts
its opponent’s strategy in the previous round.
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Collusion: The Great
Prisoner’s Dilemma
Collusion with Identical
Demand and Cost Conditions
Application: Price Fixing in the Computer
Memory Market
• The DRAM card price-fixing conspiracy illustrates how
direct collusion can be used to solve the Prisoner's
Dilemma.
• The companies in the cartel solved the Prisoner’s
Dilemma, consistent with Robert Axelrod’s conclusion, by
being extremely nice to each other. They colluded, via
phone calls, meetings, and emails, to set high prices.
• Without the Department of Justice's intervention, it might
have been possible for DRAM card collusion to continue
for many more years.
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Collusion: The Great
Prisoner’s Dilemma
Collusion with Differing Costs
or Demand Conditions
The Kinked Demand Curve Model
• Kinked Demand Curve Model — An oligopoly
model in which a firm’s demand curve is based
on the assumptions that, if it independently
raises price, its competitors maintain their
prices, whereas a price decrease will be
matched. As a consequence, the firm’s demand
curve is highly elastic for price increases, but
highly inelastic for price decreases.
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Collusion: The Great
Prisoner’s Dilemma
Collusion with Differing Costs
or Demand Conditions
The Kinked Demand Curve Model
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Collusion: The Great
Prisoner’s Dilemma
Collusion with Differing Costs
or Demand Conditions
The Price Leadership Model
• Price Leadership — A model of oligopoly
behavior in which the firms depend on one firm
to signal price changes to the other firms, who
then decide whether to follow the changes.
• Price Leader — The firm in an oligopoly that’s
first to change price in response to a change in
an industry’s underlying demand or cost
conditions.
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Collusion: The Great
Prisoner’s Dilemma
Collusion with Differing Costs
or Demand Conditions
The Price Leadership Model
Application: Price Leadership in
Cyberspace: The Airlines Case
• In a 1992 antitrust case, the U.S. Department of Justice
charged eight major American airlines and the Airline Tariff
Publishing Company (ATPCO) with fixing the price of airline
tickets over the Internet.
• According to the charges, the airlines were able to signal each
other when one of them wanted another airline to raise fares.
• In May 1994, the eight airlines and ATPCO settled the case by
agreeing to eliminate some of the signaling practices.
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