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

Author

Listed:
  • Hokari, Toru

    (Faculty of Economics)

  • Funaki, Yukihiko

    (School of Political Science and Economics)

  • Sudhölter, Peter

    (Department of Business and Economics)

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 only two solutions that satisfy Peleg's axioms together with anonymity and converse max consistency on the domain of convex games.

Suggested Citation

  • Hokari, Toru & Funaki, Yukihiko & Sudhölter, Peter, 2019. "Consistency, anonymity, and the core on the domain of convex games," Discussion Papers on Economics 13/2019, University of Southern Denmark, Department of Economics.
    • Handle: RePEc:hhs:sdueko:2019_013
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    References listed on IDEAS

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    1. Dragan, I. & Potters, J.A.M. & Tijs, S.H., 1989. "Superadditivity for solutions of coalitional games," Other publications TiSEM 283e2594-e3a0-418d-ae5e-2, Tilburg University, School of Economics and Management.
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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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    More about this item

    Keywords

    Convex TU game; core;

    JEL classification:

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

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