Unformatted text preview: ot model is the Bertrand model of
oligopoly competition.
In the Cournot model, ﬁrms choose quantities. In practice, choosing
prices may be more reasonable.
What happens if two producers of a homogeneous good charge
diﬀerent prices? Reasonable answer: everybody will purchase from
the lower price ﬁrm.
In this light, suppose that the demand function of the industry is
given by Q (p ) (so that at price p , consumers will purchase a total of
Q (p ) units).
Suppose that two ﬁrms compete in this industry and they both have
marginal cost equal to c > 0 (and can produce as many units as they
wish at that marginal costs). 34 Game Theory: Lecture 2 Examples Bertrand Competition (continued)
Then the proﬁt function of ﬁrm i can be written
⎧
⎨ Q (pi ) (pi − c ) if
1
π i (pi , p−i ) =
Q (pi ) (pi − c ) if
⎩2
0
if as
p−i > pi
p−i = pi
p−i < pi Actually, the middle row is arbitrary, given by some ad hoc
“tiebreaking” rule. Imposing such tiebreaking ru...
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This document was uploaded on 03/19/2014 for the course EECS 6.254 at MIT.
 Spring '10
 AsuOzdaglar

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