Computing generalized Nash equilibria by polynomial programming

Couzoudis, Eleftherios and Renner, Philipp (2013) Computing generalized Nash equilibria by polynomial programming. Mathematical Methods of Operational Research, 77 (3). pp. 459-472. ISSN 1432-2994

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We present a new way to solve generalized Nash equilibrium problems. We assume the feasible set to be compact. Furthermore all functions are assumed to be polynomials. However we do not impose convexity on either the utility functions or the action sets. The key idea is to use Putinar’s Positivstellensatz, a representation result for positive polynomials, to replace each agent’s problem by a convex optimization problem. The Nash equilibria are then feasible solutions to a system of polynomial equations and inequalities. Our application is a model of the New Zealand electricity spot market with transmission losses based on a real dataset.

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Journal Article
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Mathematical Methods of Operational Research
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Deposited On:
31 Aug 2017 08:30
Last Modified:
22 Nov 2022 04:55