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Axiomatic Foundations of a Unifying Concept of the Core of Games in Effectiveness Form

Author

Listed:
  • Stéphane Gonzalez

    (Univ Lyon, UJM Saint-Etienne, France
    GATE L-SE CNRS UMR 5824)

  • Aymeric Lardon

    (Université Côte d'Azur, France
    GREDEG CNRS)

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, the pairwise stability, and the stable matchings, among others. Our characterization of the core invokes the axioms of non-emptiness, coalitional unanimity, and Maskin monotonicity 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 Concept of the Core of Games in Effectiveness Form," GREDEG Working Papers 2018-15, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), University of Nice Sophia Antipolis.
  • Handle: RePEc:gre:wpaper:2018-15
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Effectiveness function; core; axiomatization; holdover property; consistency principle;

    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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