Berge Equilibria - An Algebraic Approach

Frank Riedel and Maria-Laura Torrente
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Frank Riedel: Center for Mathematical Economics, Bielefeld University
Maria-Laura Torrente: Center for Mathematical Economics, Bielefeld University

No 750, Center for Mathematical Economics Working Papers from 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.

Keywords: Berge equilibrium; Algebraic Methods in Economics; Gröbner Bases (search for similar items in EconPapers)
Pages: 32
Date: 2025-07-22
New Economics Papers: this item is included in nep-gth
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