A method to determine oligopolistic market equilibria based on a convex optimization formulation

Abstract

An approach to determine oligopolistic market equilibria using a sequence of mathematical programming problems have recently been presented by Murphy, Sherali and Soyster. Harker has presented an alternative approach based on a variational inequality representation of the problem. In his paper Marker applies a diagonalization/relaxation algorithm to the variational inequality formulation of the oligopolistic market equilibrium problem. In this paper we use another method to solve an oligopolistic equilibrium problem in its variational inequality formulation. The method is based on the convex optimization formulation for variational inequalities used by Nguyen and Dupuis for the solution of asymmetric traffic assignment problems. As is the case for the general traffic equilibrium problem the oligopolistic market equilibrium problem can with the use of this method be solved by postoptimizing a linear sub -problem in each iteration. However due to the simplicity of the constraint set an alternative search me...