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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
  • Consumer Preferences and Advertising

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.
  • 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.

13-5
6
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
7
Figure 13.1 Nuclear Deterrenceas a Sequential
Game
13-7
8
Figure 13.2 The Decision to Buildthe Tallest
Building
13-8
9
Figure 13.3 Strategic Entry Deterrence
13-9
10
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
12
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
14
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
16
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
17
Figure 13.11 The Monopolistic Competitors Two
Demand Curves
Figure 13.12 Short-Run Equilibrium for the
Chamberlinian Firm
13-17
18
Figure 13.13 Long-Run Equilibriumin the
Chamberlin Model
13-18
19
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
20
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
21
Figure 13.16 The Optimal Number of Outlets
Figure 13.15 Distances with N Outlets
13-21
22
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
23
Figure 13.18 Distributing the Costof Variety
13-23
24
Figure 13.19 The Hot Dog Vendor Location Problem
13-24
25
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.

13-25
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