9 - Quantity precommitment and Bertrand competition yield Cournot outcomes

Summary

Bertrand's model of oligopoly, which gives perfectly competitive outcomes, assumes that: (1) there is competition over prices and (2) production follows the realization of demand. We show that both of these assumptions are required. More precisely, consider a two-stage oligopoly game where, first, there is simultaneous production, and, second, after production levels are made public, there is price competition. Under mild assumptions about demand, the unique equilibrium outcome is the Cournot outcome. This illustrates that solutions to oligopoly games depend on both the strategic variables employed and the context (game form) in which those variables are employed.

Introduction

Since Bertrand's (1883) criticism of Cournot's (1838) work, economists have come to realize that solutions to oligopoly games depend critically on the strategic variables that firms are assumed to use. Consider, for example, the simple case of a duopoly where each firm produces at a constant cost b per unit and where the demand curve is linear, p = a–q. Cournot (quantity) competition yields equilibrium price p = (a + 2b)/3, while Bertrand (price) competition yields p = b.

In this article, we show by example that there is more to Bertrand competition than simply “competition over prices.” It is easiest to explain what we mean by reviewing the stories associated with Cournot and Bertrand.