Relative profit maximization and equivalence of Cournot and Bertrand equilibria in an asymmetric differentiated duopoly

Satoh, Atsuhiro and Tanaka, Yasuhito (2014): Relative profit maximization and equivalence of Cournot and Bertrand equilibria in an asymmetric differentiated duopoly. Published in:

Abstract

We study the relation between a Cournot equilibrium and a Bertrand equilibrium in an \emph{asymmetric} duopoly with differentiated goods in which each firm maximizes its relative profit that is the difference between its profit and the profit of the rival firm. Both demand and cost functions are linear but asymmetric, that is, demand functions for the goods are asymmetric and the firms have different marginal cots. We will show that a Cournot equilibrium and a Bertrand equilibrium coincide even in an asymmetric duopoly.

• Item Type: MPRA Paper
• Language: English
• Keywords: asymmetric duopoly, relative profit maximization, equivalence of Cournot and Bertrand equilibria
• Subjects: D - Microeconomics > D4 - Market Structure, Pricing, and Design > D43 - Oligopoly and Other Forms of Market Imperfection

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