Extensions of Cournot duopoly: An applied mathematical view

Abstract

The aim of the present paper is to analyze, from a dynamical system’s point of view, possible extensions of the classical economic situation of the Cournot duopoly where two firms producing an identical good compete with full information for the market making decisions in each step of the process in terms of what the rival firm did in the previous stage. We generalize this situation to a model with n firms and we discuss different variations of this model in terms of the amount of information available to each firm from the point of view of the dynamical complexity. Finally, we introduce a new model where the firms compete “à la Cournot” in a local way and the information level of each firm depends on the number of firms and on the size of the so-called influence neighboring set.