Oligopoly
1
Oligopoly - Competition among
the Few




In an oligopoly there are very few sellers of the good.
The product may be differentiated among the sellers
(e.g. automobiles) or homogeneous (e.g. gasoline).
Entry is often limited either by legal restrictions (e.g.
banking in most of the world) or by a very large
minimum efficient scale (e.g. overnight mail service)
or by strategic behavior.
Sill assuming complete and full information.
2
How Oligopolists Compete
 In
an oligopoly
– firms know that there are only a few large
competitors;
– competitors take account of the effects of
their actions on the overall market.
 To
predict the outcome of such a
market, economists must model the
interaction between firms and so often
use game theory or game theoretic
principles.
3
Three Basic Models
Competition in quantities: Cournot-Nash
equilibrium
 Competition in prices: Bertrand-Nash
equilibrium
 Collusive oligopoly: Chamberlin notion of
conscious parallelism
 It is very useful to know some basic game
theory to understand these models as well as
other oligopoly models.

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Game Theory: Setup
 List
of players: all the players are specified in
advance.
 List of actions: all the actions each player can
take.
 Rules of play: who moves and when.
 Information structure: who knows what and
when.
 Payoffs: the amount each player gets for
every possible combination of the the players’
actions.
5
A Classic Two Player, Two Action
Game - The Prisoners’ Dilemma
Roger

Lie
Confess
Chris
Lie
Confess
-1, -1
-6, 0
0, -6
-5,-5
Roger’s best response function:
– If Chris lies, then Roger should confess (check out left column, 1st
entries)
– If Chris confesses, then Roger should confess (right column, 1st entries)
– Confess is a dominant strategy for Roger

Chris’s best response function:
– If Roger lies, then Chris should confess (see top row, 2nd entries)
– If Roger confesses, then Chris should confess (bottom row, 2nd entries)
– Confess is a dominant strategy for Chris
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A Classic Two Player, Two Action
Game - The Prisoners’ Dilemma
Roger

Lie
Confess
Chris
Lie
Confess
-1,-1
-6, 0
0, -6
-5,-5
There is a single dominant strategy equilibrium:
– Rogers confesses and
– Chris confesses
– They both go to jail for 5 years


Note: the game is played simultaneously and non-cooperatively!
Ways to sustain the cooperative equilibrium (lie, lie)
– different payoff structures
– repeated play and trigger strategies
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Question: Will There Always Be A
Dominant Strategy Equilibrium?
Answer…NO!
Then
what?
Look for Nash Equilibrium.
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Nash Equilibrium
 Named
after John Nash - a Nobel Prize
winner in Economics.
 The Nash Non-cooperative Equilibrium of a
game is a set of actions for all players that,
when played simultaneously, have the
property that no player can improve his
payoff by playing a different action, given the
actions the others are playing.
 Each player maximizes his or her payoff
under the assumption that all other players
will do likewise.
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Another Example - The Price Game
Roger

Low
High
Chris
Low
High
20, 20
60, 0
0, 60
100, 100
Roger’s best response function:
– If Chris goes low, then Roger should go low (check out left column, 1st
entries)
– If Chris goes high, then Roger should high (right column, 1st entries)
– There is no dominant strategy for Roger

Chris’s best response function:
– If Roger goes low, then Chris should go low (see top row, 2nd entries)
– If Roger goes high, then Chris should go high (bottom row, 2nd entries)
– There is no dominant strategy for Chris
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Another Example - The Price Game
Roger

Low
High
Chris
Low
High
20, 20
60, 0
0, 60
100, 100
Roger’s best response function:
– If Chris goes low, then Roger should go low
– If Chris goes high, then Roger should high

Chris’s best response function:
– If Roger goes low, then Chris should go low
– If Roger goes high, then Chris should go high



Two Nash Equilibria: (low, low) and (high, high)
Respective Nash equilibrium payoffs: (20,20) and (100,100)
Which equilibrium will prevail? Good question.
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Another Example - The Simultaneous
Entry Game
Roger - the entrant
enter
not enter
Chris - the incumbent
fight
accommodate
(Roger = 0,Chris = 0) (Roger = 2, Chris = 2)

fight
(Roger =1,Chris = 5)
accommodate
(Roger =1,Chris = 5)
Get two Nash equilibria:
– (enter, accommodate) and (not enter, fight)
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Another Example - The Sequential
Entry Game
Roger - the entrant
enter
not enter
Chris - the incumbent
fight
accommodate
(Roger = 0,Chris = 0) (Roger = 2, Chris = 2)

fight
(Roger =1,Chris = 5)
accommodate
(Roger = 1,Chris = 5)
Still get two Nash equilibria:
– (enter, accommodate) and (not enter, fight)

Only one, however, is credible: (enter, accommodate)
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Another Two Player, Two
Action Example
Player 1





Up
Down
Player
Left
1,0
0,3
2
Right
1,2
0,1
The game has two players 1 & 2.
Player 1 can move “up” or “down” (actions).
Player 2 can move “left” or “right” (actions).
If player 1 moves “up” and player 2 moves “left” then player 1 gets $1
and player 2 gets $0 (payoffs).
The table shows all possible action pairs and their associated payoffs.
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Player 1’s Best Strategies
Player 1
Up
Down
Player 2
Left
Right
1,0
1,2
0,3
0,1
player 2 plays “right,” the best strategy (action)
for player 1 is to play “up.”
 In this case player 1 will get a payoff of $1,
underlined.
 If
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Player 2’s Best Strategies
Player 1
Up
Down
Player
Left
1,0
0,3
2
Right
1,2
0,1
player 1 plays “up” then player 2’s best
strategy (action) is to play “right.”
 In this case, player 2 gets a payoff of $2,
underlined.
 If
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