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# Imposing such tie breaking rules is often not kosher

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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 tie-breaking ru...
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## This document was uploaded on 03/19/2014 for the course EECS 6.254 at MIT.

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