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Axiomatic Foundations of a Unifying Core

Author

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  • Stéphane Gonzalez

    (Univ Lyon, UJM Saint-Etienne, GATE UMR 5824, F-42023 Saint-Etienne, France)

  • Aymeric Lardon

    (Université Côte d’Azur, CNRS, GREDEG, France)

Abstract

We provide an axiomatic characterization of the core of games in effectiveness form. We point out that the core, whenever it applies to appropriate classes of these games, coincides with a wide variety of prominent stability concepts in social choice and game theory, such as the Condorcet winner, the Nash equilibrium, pairwise stability, and stable matchings, among others. Our characterization of the core invokes the axioms of restricted non-emptiness, coalitional unanimity, and Maskin invariance together with a principle of independence of irrelevant states, and uses in its proof a holdover property echoing the conventional ancestor property. Taking special cases of this general characterization of the core, we derive new characterizations of the previously mentioned stability concepts.

Suggested Citation

  • Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Core," Working Papers 1817, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    • Handle: RePEc:gat:wpaper:1817
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    References listed on IDEAS

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    More about this item

    Keywords

    Effectiveness function; core; axiomatization; holdover property; consistency;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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