Cournot conjectures under price competition

• Published date: 01 December 2018
• Author: Flavio Delbono,Luca Lambertini
• DOI: http://doi.org/10.1111/ijet.12159
• Date: 01 December 2018

doi: 10.1111/ijet.12159

Cournot conjectures under price competition

Flavio Delbono∗and Luca Lambertini†

In a homogeneous oligopoly, under standard regularity conditions, weprove that the Cournot–

Nash equilibrium emerges under price competition and Cournot conjectures. We illustrate this

result also under exogenous product differentiation.

Key wor ds Cournot equilibrium, price competition

JEL classification D43, L13

Accepted 19 May2017

1 Introduction

One of the cornerstones of oligopoly theory is the debate about price versus quantity competition

stemming from Bertrand’s criticism of the Cournot model. The essence of this critique is the absence

of the auctioneer adjusting price(s) in the quantity-setting model.1

Kreps and Scheinkman (1983) have shown that the two models areone if firms choose capacities

or plant size prior to the market stage. The resulting capacity-constrained price-setting equilibrium

is Cournot. However, to deliver this outcome, Kreps and Scheinkman (1983) must rely on mixed

strategies.2

Here we nest ourselves into this discussion, showing that the Cournot equilibrium may result

from Bertrand competition coupled with Cournot–Nash conjectures. We use the same approach

as in Novshek (1980) and rely on the invertibility of the demand function, which, coupled with

the Cournot–Nash conjecture (whereby the effects on price of a change in individual and aggregate

output coincide), implies the attainment of the Cournot outcome at equilibrium. We prove our

result with homogeneous as well as (exogenously) differentiated products relying on single-stage

games generating pure-strategy equilibria only. Our approach appears simpler than that requiring

an upstream stage modeling the choice of capacity, followed by either price competition as in the

aforementioned literature on this matter.

The paper is organized as follows. In Section 2 we set up a general model of homogeneous

oligopoly and prove the Kreps and Scheinkman resultin a simple sing le-stage price game. InSection

3 we encompass the presence of product differentiation.

∗Department of Economics, University of Bologna, Bologna, Italy.

†Department of Economics, University of Bologna, Bologna, Italy.Email: luca.lambertini@unibo.it

Wethank the editor Makoto Yano, an anonymous referee,and Stephen Martin for helpful comments on an earlier draft.

The usual disclaimer applies.

1An account of the long-lasting debate on this issue is given in Lambertini and Mosca (2014).

2Actually there was an earlier debate, starting with Beckman (1967) and Levitan and Shubik (1972). Later developments

include Dixon (1985, 1986) and Osborne and Pitchik (1986).

International Journal of Economic Theory 14 (2018) 295–301 © IAET 295

International Journal of Economic Theory