Chapter 16
Game Theory and Oligopoly
16.1
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Figure 16.1 The monopoly equilibrium
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Duopoly as a Prisoner’s Dilemma
A
Duopoly is an oligopoly in which
there are only two firms in the
industry.
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Table 16.1 Duopoly profit matrix
16.4
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From Table 16.1
L
is the dominant strategy for the
both the First and the Second Firm
 Thus the Nash-equilibrium
combination is (L,L) in which both
firms produce 20 units and have a
profit of $200.
 Yet, if they could agree to restrict
their individual outputs to 15 units
apiece, each could earn $450.
16.5
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The Oligopoly Problem
 Oligopolists
have a clear incentive to
collude or cooperate.
 Oligopolists have a clear incentive to
cheat on any simple collusive or
cooperative agreement.
 If an agreement is not a Nash
equilibrium, it is not self-enforcing.
16.6
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The Cournot Duopoly Model

1.
2.
Central features of the Cournot Model:
Each firm chooses a quantity of output
instead of a price.
In choosing an output, each firm takes
its rival’s output as given.
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Figure 16.2 Finding a Cournot
best-response function
16.8
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From Figure 16.2
 The
First firm’s best response
function is: y1*=30 – y2/2
 The Second firm’s best response
function is y2*=30 – y1/2
 Taken together, these two best
response functions can be used to
find the equilibrium strategy
combination for Cournot’s model.
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Figure 16.3 The Cournot equilibrium
16.10
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The Cournot Model: Key Assumptions
 The
profit of one firm decreases as the
output of the other firm increases (other
things equal).
 The Nash equilibrium output for each firm
is positive.
16.11
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Isoprofit Curves
 All
strategy combinations that give
the first firm the chosen level of
profits is known as an indifference
curve or iosprofit curve.
 Profits are constant along the
isoprofit curve.
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Figure 16.4 Title
16.13
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From Figure 16.4
 y1*
maximizes profits for the first firm
given the second firm’s output of y2*.
 Any strategy combinations below the
indifference curve gives the first firm
more profit than the Nash equilibrium.
 The result above relates to the key
assumption that the first firm’s profit
increases as the second firm’s output
decreases.
16.14
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Figure 16.5 Joint profit not
maximized in Nash equilibrium
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Cournot’s Model: Conclusions
 In
the Nash equilibrium of this
general version of the Cournot
model, firms fail to maximize their
joint profit.
 Relative to joint profit maximization,
firms produce too much output in the
Nash equilibrium.
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The Cournot Model with Many Firms
With only one firm in the market, the
Cournot-Nash equilibrium is the monopoly
equilibrium.
 As the number of firms increases, output
increases. As a result, price and aggregate
oligopoly profits decrease.
 When there are infinitely many firms, the
Cournot model is, in effect, the perfectly
competitive model.

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The Bertrand Model
 The
Bertrand model substitutes
prices for quantities as the variables
to be chosen.
 The goal is to find the Nash (the
Bertrand-Nash) equilibrium strategy
combination when firms choose
prices instead of quantities.
16.18
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The Bertrand Model: Firm’s Best
Response Function
Funding the best response function entails
answering the question: Given p2, what value
of p1 maximizes the first firm’s profit.
 Four possibilities exist:
1. If its rival charges a price greater than the
monopoly price (MP), the first firm’s best
response is to charge a lower price (than MP)
so it can capture the entire market.

16.19
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The Bertrand Model: Firm’s Best
Response Function
2. If its rival charges a price less than the per
unit cost of production (p2), the first firm’s
best response is to choose any price greater
than this because firm one will attract no
business and incur a zero profit. This outcome
is superior to matching or undercutting p2,
and posting losses.
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The Bertrand Model: Firm’s Best
Response Function
3. If the second firm’s price is greater than the
per unit cost of production and less than the
monopoly price. (see Figure 16.6)
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Figure 16.6 Finding a Bertrand
best-response function
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The Bertrand Model: Firm’s Best
Response Function
4. Suppose the second firm sets its price exactly
equal to the per unit costs.
Then if the first firm sets a lower price it will
incur a loss on every unit it sells and profits
will be negative. If the first firm sets a price
above the per unit it will sell no units and
profits are zero. If the first firm sets price
equal to the per unit costs, it breaks even.
16.23
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The Bertrand-Nash Equilibrium


The Bertrand-Nash equilibrium strategy
combination is the second firm and the first
firm charging a price equal to the per unit
cost of production.
At this equilibrium, each firm’s profit is
exactly zero.
16.24
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The Limited-Output Model
 In
the long run, the number of firms
(market structure ) is endogenous.
 The number of firms is an industry is
determined by economic considerations.
 The key process in determining the longrun equilibrium is the possibility of entry.
16.25
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Barriers to Entry
A
natural barrier to entry is setup costs.
 Assume all firms incur setup costs of $S
 In any period, the rate of interest (i)
determines the set up cost (K):K=iS
 Adding fixed costs to variable costs (40y)
gives total cost function:
C(y)=K+40Y
16.26
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Inducement to Entry
 If
the fixed costs (K) is a barrier to
entry, what is an inducement to
entry?
 An inducement to entry is the excess
of revenue over variable costs.
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Figure16.7 The inducement to entry
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Inducement to Entry
 The
entrant’s best response function
is: yE*=30-y/2
 The entrant’s residual demand
function is: Pe=(100-y)-ye
 The price that will prevail if the
entrant produces ye* units is:
Pe*=70-y/2
 Profit per unit is: Pe* - 40=30-y/2
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Inducement to Entry
 The
inducement to entry, ye* times (pe*40) is then (30-y/)2.
 This expression gives the revenue over
variable costs that the entrant would earn
if established firms continued to produce
y units after entry.
 Entry will occur if inducement to enter
exceeds K
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Inducement to Entry
 Call
the smallest value of y such that no
entry occurs the limit output (yL).
 (30-yL/2)2=K
 Solving for YL: YL= 60-2K1/2
 If K=$100, YL=40 units, If K=$225,
YL=30 units, etc. (see Figure 16.8)
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Inducement to Entry
 Entry
will not occur if the output of
established firms is greater than or
equal to the limit output (yL)
 The limit price (pL) is the price
associated with the limit output.
 In this example:
pL=100-yL or pL = 40+2K1/2
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Figure 16.8 Identifying the limit
price and the limit output
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Refinements of Limited Output
 How
large must the fixed cost K be so
that a third firm will not enter?
 The generalized no-entry condition for
the Cournot models is then:
[60/(n=2)2]≤K
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Figure 16.9 Cournot oligopoly
and entry equilibrium
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Barriers to entry
 Development
cost K is a barrier to
entry, as it differentiates established
firms and new potential entrants.
 The manner in which this
differentiation affects the inducement
to enter (profits) depends upon the
nature of the oligopoly behaviour
upon entry.
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Barriers to entry
 The
more aggressive/less
cooperative is oligopoly behaviour
upon entry, the more effective setup
costs are as a barrier.
 Any firm’s decision to incur the setup
cost is a strategic decision because it
affects the incentives of other firms.
16.37
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Positioning and Reacting
 Positioning
is concerned with action
taken by existing firms prior to entry.
 Reacting refers to actions of
established firms subsequent to
entry.
16.38
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