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<p>Berge equilibrium offers an alternative to Nash equilibrium in game theory, emphasizing cooperative 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 equations, 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.</p>

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Berge equilibria – an algebraic approach

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年6月2日

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  • Frank Riedel,
  • Maria-Laura Torrente

摘要

Berge equilibrium offers an alternative to Nash equilibrium in game theory, emphasizing cooperative 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 equations, 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.