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Computing all solutions of linear generalized Nash equilibrium problems

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Abstract

In this paper we consider linear generalized Nash equilibrium problems, i.e., the cost and the constraint functions of all players in a game are assumed to be linear. Exploiting duality theory, we design an algorithm that is able to compute the entire solution set of these problems and that terminates after finite time. We present numerical results on some academic examples as well as some economic market models to show effectiveness of our algorithm in small dimensions.

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Acknowledgments

I would like to thank two anonymous referees for their helpful comments, and one referee for suggesting to compare the new algorithm with the approach presented in Remark 1.

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Authors and Affiliations

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

    Axel Dreves

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  1. Axel Dreves
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Correspondence to Axel Dreves.

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Dreves, A. Computing all solutions of linear generalized Nash equilibrium problems. Math Meth Oper Res 85, 207–221 (2017). https://doi.org/10.1007/s00186-016-0562-0

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  • DOI: https://doi.org/10.1007/s00186-016-0562-0

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