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Axiomatic foundations of a unifying concept of the core of games in effectiveness form

Author

Listed:
  • Stéphane Gonzalez

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - Université de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Aymeric Lardon

    (GREDEG - Groupe de Recherche en Droit, Economie et Gestion - UNS - Université Nice Sophia Antipolis (1965 - 2019) - CNRS - Centre National de la Recherche Scientifique - UniCA - Université Côte d'Azur)

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic foundations of a unifying concept of the core of games in effectiveness form," Post-Print halshs-01902122, HAL.
    • Handle: RePEc:hal:journl:halshs-01902122
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    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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