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## Imperfect Competition: A Game-Theoretic Approach

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### A Nash equilibrium does not require both players to have a dominant strategy! The Maximin Strategy Maximin strategy: ... – PowerPoint PPT presentation

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Title: Imperfect Competition: A Game-Theoretic Approach

1
Chapter 13
• Imperfect CompetitionA Game-Theoretic Approach

13-1
2
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 Hotellings Hot Dog Vendors

13-2
3
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.

13-3
4
Dominant Strategy
• Dominant strategy the strategy in a game that
produces better results irrespective of the
strategy chosen by ones 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.

13-4
5
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.
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.

13-5
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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 players 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.

13-6
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Figure 13.1 Nuclear Deterrenceas a Sequential
Game
13-7
8
Figure 13.2 The Decision to Buildthe Tallest
Building
13-8
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Figure 13.3 Strategic Entry Deterrence
13-9
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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
others 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.

13-10
11
Figure 13.5 Reaction Functionsfor the Cournot
Duopolists
13-11
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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.
13-12
13
Stackelberg Model
Figure 13.7 The Stackelberg Leaders Demand and
Marginal Revenue Curves
Figure 13.8 The Stackelberg Equilibrium
13-13
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Comparison Of Outcomes--Table Graph
Figure 13.9 Comparing Equilibrium Price and
Quantity
13-14
15
Competition When There Are IncreasingReturns 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
13-15
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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
• Because the products are viewed as close
substitutes, each firm will confront a
downward-sloping demand schedule.
• Each firm will act as if its own price and
quantity decisions have no effect on the behavior
of other firms in the industry.

13-16
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Figure 13.11 The Monopolistic Competitors Two
Demand Curves
Figure 13.12 Short-Run Equilibrium for the
Chamberlinian Firm
13-17
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Figure 13.13 Long-Run Equilibriumin the
Chamberlin Model
13-18
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Perfect Competition Versus ChamberlinianMonopolis
tic 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.

13-19
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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.
13-20
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Figure 13.16 The Optimal Number of Outlets
Figure 13.15 Distances with N Outlets
13-21
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Figure 13.17 A Spatial Interpretationof 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.

13-22
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Figure 13.18 Distributing the Costof Variety
13-23
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Figure 13.19 The Hot Dog Vendor Location Problem
13-24
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