Associated consistency and values for TU games

Theo Driessen

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In the framework of the solution theory for cooperative transferable utility games, Hamiache axiomatized the well-known Shapley value as the unique one-point solution verifying the inessential game property, continuity, and associated consistency. The purpose of this paper is to extend Hamiache's axiomatization to the class of efficient, symmetric, and linear values, of which the Shapley value is the most important representative. For this enlarged class of values, explicit relationships to the Shapley value are exploited in order to axiomatize such values with reference to a slightly adapted inessential game property, continuity, and a similar associated consistency. The latter axiom requires that the solutions of the initial game and its associated game (with the same player set, but a different characteristic function) coincide.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente
Number of pages15
Publication statusPublished - Apr 2006

Publication series

NameMemorandum TW
PublisherDepartment of Applied Mathematics, University of Twente
ISSN (Print)0169-2690


  • MSC-91A40
  • MSC-91A12
  • Cooperative game
  • Associated game
  • Linear value
  • Shapley value
  • Consistency


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