The Leader has an advantage and uses it. The nature of the relationship
between the two players (a leader with more market power than the
follower) is modeled here as a sequential game. It is that extra market power
that give rise to higher profits for the leader. The other side of this
relationship forces the weaker follower to accept lower profits than under
Cournot.
and Profits
22
,
2
2
,
(
4
)
8
a
c
−
⎝
⎜
⎠
−
⎟
Vs.
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View Full DocumentChapter 13 –Oligopoly
Slide 19
The Bertrand competition model
The Bertrand oligopoly model
Bertrand
• Firms maximize profits
•
Bertrand conjecture
: Firms choose (the price or the quantity)
assuming that other firm(s) keep their
price
fixed
• Practical matter: easiest to define strategies as “prices”
Difference Cournot model and Bertrand model:
 conjecture how the game of competition is played
• Solution will be radically different, however
Chapter 13 –Oligopoly
Slide 20
The Bertrand competition model
Solution Bertrand model
• Solution concept: Nash Equilibrium
• THE ONLY solution:
• Equilibrium payoffs are zero!
Notes
• With only two firms the outcome is the perfectly competitive
outcome!
• Solution is welfare maximizing
c
p
p
=
=
2
1
Chapter 13 –Oligopoly
Slide 21
Discussion: Cournot vs Bertrand
Cournot
Æ
Cournot conjecture
• Prediction: if few firms compete, they all make positive profits
Bertrand
Æ
Bertrand conjecture
• Prediction: even with few firms perfectly competitive market.
No firm makes profits, even if there are a few
Conclusion: Bertrand model
Æ
Bertrand conjecture seems
more natural, however result is unrealistic!
Defending Cournot
• Assumption realistic if interpreting quantity as
capacity
• So new interpretation: first capacity choice, then price choice
Defending Bertrand
• Prediction of positive profits if there is
collusion
between firms
• Prediction of positive profits if firms price often over time
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 Fall '12
 Danvo
 Game Theory, Perfect Competition, Bertrand, Cournot Competition, Cournot, –Oligopoly Slide

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