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Hart–Mas-Colell consistency and the core in convex games

Author

Listed:
  • Bas Dietzenbacher

    (Maastricht University)

  • Peter Sudhölter

    (University of Southern Denmark)

Abstract

This paper formally introduces Hart–Mas-Colell consistency for general (possibly multi-valued) solutions for cooperative games with transferable utility. This notion is used to axiomatically characterize the core on the domain of convex games. Moreover, we characterize all nonempty solutions satisfying individual rationality, anonymity, scale covariance, superadditivity, weak Hart–Mas-Colell consistency, and converse Hart–Mas-Colell consistency. This family consists of (a) the Shapley value, (b) all homothetic images of the core with the Shapley value as center of homothety and with positive ratios of homothety not larger than one, and (c) their relative interiors.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jogath:v:51:y:2022:i:2:d:10.1007_s00182-021-00798-6
    DOI: 10.1007/s00182-021-00798-6
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    More about this item

    Keywords

    Convex games; Consistency; Converse consistency; Core; Shapley value;
    All these keywords.

    JEL classification:

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

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