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Berge Equilibria - An Algebraic Approach

Author

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  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

  • Torrente, Maria-Laura

    (Center for Mathematical Economics, Bielefeld University)

Abstract

Berge equilibrium offers an alternative to Nash equilibrium in game theory, emphasizing coop- erative stability rather than individual optimization. Despite recent interest, a systematic study of Berge equilibria in finite normal form games is still lacking, with fundamental questions like existence remaining open. This paper characterizes Berge equilibria through a polynomial system of equa- tions, enabling computational algebra and algebraic geometry methods to analyze them. Algorithms based on Gröbner bases determine the existence and computation of Berge equilibria. Furthermore, we show that the set of games admitting completely mixed Berge equilibria is contained within a determinantal variety, whose dimension we explicitly bound from above.

Suggested Citation

  • Riedel, Frank & Torrente, Maria-Laura, 2025. "Berge Equilibria - An Algebraic Approach," Center for Mathematical Economics Working Papers 750, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:750
    as

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    File URL: https://pub.uni-bielefeld.de/download/3005463/3005464
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    References listed on IDEAS

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    3. Olivier Musy & Antonin Pottier & Tarik Tazdait, 2012. "A New Theorem To Find Berge Equilibria," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-10.
    4. Olivier Musy & Antonin Pottier & Tarik Tazdait, 2012. "A New Theorem To Find Berge Equilibria," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-10.
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