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

Bas Dietzenbacher, Peter Sudhölter

Research output: Contribution to journalArticleAcademicpeer-review


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.
Original languageEnglish
Number of pages17
JournalInternational Journal of Game Theory
Publication statusE-pub ahead of print - 6 Oct 2021

JEL classifications

  • c71 - Cooperative Games


  • Shapley value
  • consistency
  • converse consistency
  • convex games
  • core
  • Convex games
  • Consistency
  • Converse consistency
  • Core

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