(1) Department of Energy, 20461 Washington, DC, USA;(2) Virginia Polytechnic Institute and State University, 24061 Blacksburg, VA, USA;(3) The Pennsylvania State University, 16802 University Park, PA, USA
Abstract:
During the past several years it has become increasingly common to use mathematical programming methods for deriving economic equilibria of supply and demand. Well-defined approaches exist for the case of a single firm (monopoly) and for the case of many firms (perfect competition). In this paper a certain family of convex programs is formulated to determine equilibria for the case of a few firms (oligopoly). Solutions to this family of convex programs are shown to be Nash equilibria in the formal sense ofN person games. This equivalence leads to a mathematical programming-based algorithm for determining an oligopolistic market equilibrium.