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Axiomatic characterizations of the core without consistency

Author

Listed:
  • Sylvain Béal

    (Université de Franche-Comté, CRESE EA3190)

  • Stéphane Gonzalez

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne)

  • Philippe Solal

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne)

  • Peter Sudhölter

    (University of Southern Denmark)

Abstract

A TU game is totally positive if it is a linear combination of unanimity games with nonnegative coefficients. We show that the core on each cone of convex games that contains the set of totally positive games is characterized by the traditional properties Pareto efficiency, additivity (ADD), individual rationality, and the null-player property together with one new property, called unanimity requiring that the solution, when applied to a unanimity game on an arbitrary coalition, allows to distribute the entire available amount of money to each player of this coalition. We also show that the foregoing characterization can be generalized to the domain of balanced games by replacing ADD by “ADD on the set of totally positive games plus super-additivity (SUPA) in general”. Adding converse SUPA allows to characterize the core on arbitrary domains of TU games that contain the set of all totally positive games. Converse SUPA requires a vector to be a member of the solution to a game whenever, when adding a totally positive game such that the sum becomes totally additive, the sum of the vector and each solution element of the totally positive game belongs to the solution of the aggregate game. Unlike in traditional characterizations of the core, our results do not use consistency properties.

Suggested Citation

  • Sylvain Béal & Stéphane Gonzalez & Philippe Solal & Peter Sudhölter, 2023. "Axiomatic characterizations of the core without consistency," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 687-701, September.
    • Handle: RePEc:spr:jogath:v:52:y:2023:i:3:d:10.1007_s00182-022-00835-y
    DOI: 10.1007/s00182-022-00835-y
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    1. Michel Grabisch & Hervé Moulin & José Manuel Zarzuelo, 2024. "Professor Peter Sudhölter (1957–2024)," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 289-294, June.

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    More about this item

    Keywords

    Core; Totally positive games; Convex games; Super-additivity;
    All these keywords.

    JEL classification:

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

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