Dynamic Bertrand and Cournot Competition: Asymptotic and Computational Analysis of Product Differentiation

22 Pages Posted: 15 Feb 2011

See all articles by Andrew Fabian Ledvina

Andrew Fabian Ledvina

Princeton University - Department of Operations Research & Financial Engineering (ORFE)

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Date Written: February 14, 2011

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 matters little. 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.

Keywords: Bertrand, Cournot, Oligopoly, Differential Games, Asymptotic Expansion, Product Differentiation

JEL Classification: C72, C73, L11, L13

Suggested Citation

Ledvina, Andrew Fabian and Sircar, Ronnie, Dynamic Bertrand and Cournot Competition: Asymptotic and Computational Analysis of Product Differentiation (February 14, 2011). Available at SSRN: https://ssrn.com/abstract=1761723 or http://dx.doi.org/10.2139/ssrn.1761723

Andrew Fabian Ledvina (Contact Author)

Princeton University - Department of Operations Research & Financial Engineering (ORFE) ( email )

Sherrerd Hall, Charlton Street
Princeton, NJ 08544
United States

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

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