Computing generalized Nash equilibria by polynomial programming

Computing generalized Nash equilibria by polynomial programming

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Article ID: iaor20133820
Volume: 77
Issue: 3
Start Page Number: 459
End Page Number: 472
Publication Date: Jun 2013
Journal: Mathematical Methods of Operations Research
Authors: ,
Keywords: electricity, New Zealand, polynomial programs, Nash equilibrium
Abstract:

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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