STABILITY ANALYSIS IN A COURNOT – BERTRAND DUOPOLY WITH DIFFERENTIATED PRODUCTS

Abstract

Introduction. For many years, the Cournot and Bertrand models have been important tools for analyzing competitive market dynamics and understanding how firms make pricing and production decisions. In the Cournot model, firms set the volume of production, in the Bertrand model – the price. Despite their idealization and some simplifications, these models still have relevance and importance for the research of competitive processes. On the basis of studies conducted by economists on price and quantity competition in the oligopoly market, it can be argued that there is no such type of competition that would have an absolute advantage. Depending on the characteristics of the markets, one or another type of competition will be optimal. At the same time, in practice there are markets where some firms set the volume of supply, while others set the price. To date, the models of such markets are not as well researched as the Cournot-only or Bertrand-only competition models. The purpose of this paper is to define and analyze the stability of the equilibrium in the spatial duopoly model (Liang, W.J., Hwang, H., & Mai, C.C., (2006). Spatial discrimination: Bertrand vs. Cournot with asymmetric demands. Regional Science and Urban Economics, 36, 790-802) under conditions of product differentiation and asymmetry of market sizes. In order to maximize profits, firms first select a location and then the type of competition – Cournot or Bertrand. Results. The paper defines the state of Nash equilibrium in a spatial duopoly, when one of the firms sets the volume of supply, and the other sets the price. The stability of the Nash equilibrium was investigated. The dependence of the area of equilibrium stability on the asymmetry of market sizes and product differentiation is determined. The nontrivial impact of asymmetry and differentiation on the competitive dynamics of firms and the stability of market equilibrium has been revealed. The results of the analysis are presented on a map of dynamic modes and bifurcation diagrams. Conclusions. The paper proves that the growth of the level of substitutability (complementarity) increases (decreases) the area of the stability region. A high level of substitutability strengthens the level of competition between firms and, at the same time, increases the area of the stability region. A high level of complementarity motivates firms to agglomerate and, at the same time, reduces the stability region of such an equilibrium.