On the dynamic stability of the Cournot duopoly solution under bounded rationality

Abstract

The most of the oligopolistic models described in the existing literature analyze dynamic processes and the stability of the Nash equilibrium by introducing concrete specifications for the demand and the cost functions. This paper analyzes the dynamic stability of the Cournot-Nash equilibrium in the context of a duopoly using general functions to establish both demand and costs. The condition that guarantees the stability of the Nash equilibrium under the adjustment process implicit in the Cournot’s original model is found to be a key requirement underpinning the dynamic stability of the Cournot-Nash equilibrium regardless of the firms’ expectations scheme. Moreover, this condition is more decisive the higher the degree of rationality of firms.