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Consistency, anonymity, and the core on the domain of convex games

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Listed:
  • Toru Hokari

    (Keio University)

  • Yukihiko Funaki

    (Waseda University)

  • Peter Sudhölter

    (University of Southern Denmark)

Abstract

We show that neither Peleg’s nor Tadenuma’s well-known axiomatizations of the core by non-emptiness, individual rationality, super-additivity, and max consistency or complement consistency, respectively, hold when only convex rather than balanced TU games are considered, even if anonymity is required in addition. Moreover, we show that the core and its relative interior are the only two solutions that satisfy Peleg’s axioms together with anonymity and converse max consistency on the domain of convex games.

Suggested Citation

  • Toru Hokari & Yukihiko Funaki & Peter Sudhölter, 2020. "Consistency, anonymity, and the core on the domain of convex games," Review of Economic Design, Springer;Society for Economic Design, vol. 24(3), pages 187-197, December.
    • Handle: RePEc:spr:reecde:v:24:y:2020:i:3:d:10.1007_s10058-020-00231-6
    DOI: 10.1007/s10058-020-00231-6
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    Cited by:

    1. 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.
    2. Bas Dietzenbacher & Peter Sudhölter, 2022. "Hart–Mas-Colell consistency and the core in convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 413-429, June.

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    JEL classification:

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

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