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A mathematical programming approach for determining oligopolistic market equilibrium

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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.

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Murphy, F.H., Sherali, H.D. & Soyster, A.L. A mathematical programming approach for determining oligopolistic market equilibrium. Mathematical Programming 24, 92–106 (1982).

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