A Dynamic Network Oligopoly Model with Transportation Costs, Product Differentiation, and Quality Competition

Abstract

This paper develops a new dynamic model of Cournot-Nash oligopolistic competition that includes production and transportation costs, product differentiation, and quality levels in a network framework. The production costs capture the total quality cost, which, in turn, can also represent the R&D cost. We first present the equilibrium version and derive alternative variational inequality formulations. We then construct the projected dynamical systems model, which provides a continuous-time evolution of the firms’ product shipments and product quality levels, and whose set of stationary points coincides with the set of solutions to the variational inequality problem. We establish stability analysis results using a monotonicity approach and construct a discrete-time version of the continuous-time adjustment process, which yields an algorithm, with closed form expressions at each iteration. The algorithm is then utilized to compute solutions to several numerical examples.

The framework can serve as the foundation for the modeling and analysis of competition among firms in industries ranging from food to pharmaceuticals to durable goods and high tech products, as well as Internet services, where quality and product differentiation are seminal.

Keywords: oligopolies, networks, game theory, product quality, product differentiation, variational inequalities, projected dynamical systems