7 - Reconsidering Cournot: the Cournot equilibrium is consistent

Summary

This article uses an infinite-regress model of firm-level decisions to find a rational expectations equilibrium for a duopoly and to relate concepts of conjectural variations and consistency to the Cournot equilibrium. The model derives a conjectural variation instead of assuming it. In particular, the Cournot equilibrium is shown to be consistent in the usual sense of the literature. The conflict between notions of consistent conjectures and the Cournot equilibrium results from a compounding problem inherent in the earlier models. We extend these results to the n-firm problem. Alternatively, the article can be viewed as providing a purely static model that generates the Cournot equilibrium without reference to conjectures or quasi dynamics.

Introduction

Recently, the use of the Cournot model as a valid equilibrium solution in noncooperative oligopoly settings has been questioned in a variety of articles using the concept of a consistent conjectural variation (see, e.g., Laitner (1980), Bresnahan (1981), Kamien and Schwartz (1983), Perry (1982), and Kalai and Stanford (1982). A conjectural variation is a conjecture by one firm about how the other firm will adjust its decision variable with respect to potential adjustments in the first firm's action. A consistent conjectural variation is a conjectural variation that is correct: predicted change (locally) in the relevant decision variable (output or price) on the part of one's competitor is what actually occurs. A consistent conjectures equilibrium is a consistent conjectural variation equilibrium, in the sense that no individual change in a decision variable is profitable.