Chapter 13
Imperfect Competition:
A Game-Theoretic
Approach
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Chapter Outline
An Introduction to the Theory of Games
Some Specific Oligopoly Models
Competition When There are Increasing
Returns to Scale
Monopolistic Competition
A Spatial Interpretation of Monopolistic
Competition
Historical Note: Hotelling’s Hot Dog Vendors
• Consumer Preferences and Advertising
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Prisoner's Dilemma
 Two prisoners are held in separate cells for a
serious crime that they did in fact commit. The
prosecutor has only enough hard evidence to
convict them of a minor offense, for which the
penalty is a year in jail.
 Each prisoner is told that if one confesses while the
other remains silent, the confessor will go scot-free
while the other spends 20 years in prison.
 If both confess, they will get an intermediate
sentence 5 years.
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Dominant Strategy
 Dominant strategy: the strategy in a game that
produces better results irrespective of the strategy
chosen by one’s opponent.
The Nash Equilibrium Concept
 Nash equilibrium: the combination of strategies in
a game such that neither player has any incentive
to change strategies given the strategy of his
opponent.
– A Nash equilibrium does not require both
players to have a dominant strategy!
The Maximin Strategy
Maximin strategy: choosing the option that makes the lowest
payoff one can receive as large as possible.
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Tit-for-Tat
 Tit-for-tat strategy The first time you interact with someone, you
cooperate. In each subsequent interaction you
simply do what that person did in the previous
interaction.
 Thus, if your partner defected on your first
interaction, you would then defect on your next
interaction with her.
 If she then cooperates, your move next time will be
to cooperate as well.
 Requirement: there not be a known, fixed number of
future interactions.
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Sequential Games
 Sequential game: one player moves first, and the
other is then able to choose his strategy with full
knowledge of the first player’s choice.
– Example - United States and the former Soviet Union
(USSR) during much of the cold war.
 Strategic entry deterrence – they change potential
rivals’ expectations about how the firm will
respond when its market position is threatened.
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Figure 13.1: Nuclear Deterrence
as a Sequential Game
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Figure 13.2: The Decision to Build
the Tallest Building
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Figure 13.3: Strategic Entry Deterrence
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Figure 13.4: The Profit-Maximizing Cournot
Duopolist
The Cournot Model--oligopoly model in which each firm assumes
that rivals will continue producing their current output levels.
Main assumption - each duopolist treats the other’s quantity
as a fixed number, one that will not respond to its own
production decisions.
Reaction function- a curve that tells the profit-maximizing level of
output for one oligopolist for each amount supplied by another.
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Figure 13.5: Reaction Functions
for the Cournot Duopolists
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Figure 13.6: Deriving the Reaction Functions
for Specific Duopolists
The Bertrand Model
Bertrand model - oligopoly model in which each firm assumes
that rivals will continue charging their current prices.
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Stackelberg Model
Figure 13.7: The Stackelberg
Leader’s Demand and
Marginal Revenue Curves
Figure 13.8: The Stackelberg
Equilibrium
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Comparison Of Outcomes--Table & Graph
Figure 13.9: Comparing
Equilibrium Price and
Quantity
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Competition When There Are Increasing
Returns To Scale
 In markets for privately sold goods, buyers are often too
numerous to organize themselves to act collectively
 Where it is impractical for buyers to organize direct
collective action, it may nonetheless be possible for
private agents to accomplish much the same objective
on their behalf.
Figure 13.10: Sharing a Market with Increasing Returns to Scale
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The Chamberlin Model
 Assumption: a clearly defined “industry group,”
which consists of a large number of producers of
products that are close, but imperfect, substitutes
for one another.
 Two implications:
1. Because the products are viewed as close substitutes,
each firm will confront a downward-sloping demand
schedule.
2. Each firm will act as if its own price and quantity
decisions have no effect on the behavior of other firms
in the industry.
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Figure 13.11: The Monopolistic
Competitor’s Two Demand
Curves
Figure 13.12: Short-Run
Equilibrium for the
Chamberlinian Firm
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Figure 13.13: Long-Run Equilibrium
in the Chamberlin Model
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Perfect Competition Versus Chamberlinian
Monopolistic Competition
 Competition meets the test of allocative efficiency,
while monopolistic competition does not.
 Monopolistic competition is less efficient than perfect
competition because in the former case firms do not
produce at the minimum points of their long-run
average cost (LAC) curves.
 In terms of long-run profitability the equilibrium
positions of both the perfect competitor and the
Chamberlinian monopolistic competitor are precisely
the same.
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Figure 13.14: An Industry in Which Location is the
Important Differentiating Feature
The Optimal Number
of Locations
The number of outlets
that emerges from the
independent actions of
profit-seeking firms
will in general be
related to the optimal
number of outlets in
the following simple
way 
Any environmental change that leads to a change in the optimal
number of outlets (here, any change in population density,
transportation cost, or fixed cost) will lead to a change in the
same direction in the equilibrium number of outlets.
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Figure 13.15: Distances with N
Outlets
Figure 13.16: The Optimal
Number of Outlets
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Figure 13.17: A Spatial Interpretation
of Airline Scheduling
Why not have a flight leaving every 5 minutes, so that no
one would be forced to travel at an inconvenient time?
The larger an aircraft is, the lower its average cost per
seat is.
If people want frequent flights, airlines are forced to
use smaller planes and charge higher fares.
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Figure 13.18: Distributing the Cost
of Variety
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Figure 13.19: The Hot Dog Vendor Location
Problem
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Consumer Preferences And Advertising
 Because products are differentiated, producers can
often shift their demand curves outward
significantly by advertising.
 The revised sequence -- the corporation decides
which products are cheapest and most convenient
to produce, and then uses advertising and other
promotional devices to create demand for them.
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