A Mathematical Programming Approach to a Nash-Cournot Equilibrium Analysis for a Two-Stage Network of Oligopolies

Abstract

This paper deals with the existence, characterization and computation of equilibrium solutions arising from related mathematical programming problems associated with a particular market structure. The generic structure analyzed herein represents a two-stage production process in which a set of some firms produces a semifinished product that serves as an input to another set of firms which converts this to a final good. In addition, there exists a third set of vertically integrated firms. These firms perform the operations jointly performed by the other two sets of firms in producing the final product. On the demand side, an econometrically derived demand curve is specified for the final product. The aim of this paper is to characterize the nature of the equilibrium solutions for such problems under various market behavioral structures, derive sufficient conditions under which one can claim the existence of these equilibrium solutions, and prescribe methods for computing equilibrium solutions. The analysis provides a machinery for considering the effects of mergers and integrations on a firms' profits and on industry outputs and prices, thereby suggesting incentives, or otherwise, to merge or integrate.