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Math Colloquium
Andrew Ledvina
Princeton University
Title: Dynamic Bertrand and Cournot Competition: Effects of Product Differentiation

Abstract: We study continuous time oligopolies in which a small number of firms producing similar goods compete with one another by setting prices or quantities. We study a deterministic version of the problem using an asymptotic expansion of the relevant HJB partial differential equations. We find in this setting that for firms with highly differentiated goods, the type of competition is irrelevant. For less differentiated goods, we find that the Cournot type market produces a greater value to the firms than the Bertrand type market. We then study a stochastic version of the two games using numerical techniques. This allows us to compare firms with a greater degree of product differentiation. The value is still greater to firms in most scenarios in a Cournot market, but in some situations the classical Bertrand/Cournot dichotomy is reversed.

Date: Thursday, February 10, 2011
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Shreve