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Finding all solutions of affine generalized Nash equilibrium problems with one-dimensional strategy sets

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Abstract

We consider a class of generalized Nash equilibrium problems with quadratic cost functions and common linear constraints for all players. Further we focus on the case where every player has a single strategy variable within a bounded set. For this problem class we present an algorithm that is able to compute all solutions and that terminates finitely. Our method is based on a representation of the solution set as a finite union of polyhedral sets using sign conditions for the derivatives of the cost and constraint functions. The effectiveness of the algorithm is shown in various examples from literature.

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Acknowledgments

We would like to thank two anonymous referees for their helpful comments.

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Authors and Affiliations

  1. Department of Aerospace Engineering, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 , Neubiberg/Munich, Germany

    Axel Dreves

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  1. Axel Dreves
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Correspondence to Axel Dreves.

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Dreves, A. Finding all solutions of affine generalized Nash equilibrium problems with one-dimensional strategy sets. Math Meth Oper Res 80, 139–159 (2014). https://doi.org/10.1007/s00186-014-0473-x

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