Reduced Game Property of Linear Values with Equal Treatment Property

  • Tsuneyuki Namekata
  • Theo S.H. Driessen
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 43)


A transferable utility game deals with problems of how to allocate the total benefit among players by considering contributions of various coalitions of players to the total benefit. A value for games is an allocation of the total benefit among them. Many values such as the Shapley value and the prenucleolus are introduced by their own equity consideration. Thus a consistency in terms of a reduced game is a useful tool to compare various solutions in a unified way, because it expresses the differences in solutions as those in associated reduced games. This paper axiomatizes linear values with Equal Treatment Property by the consistency in terms of a reduced game.


TU-game consistency reduced game Shapley value Solidarity value. 


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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Tsuneyuki Namekata
    • 1
  • Theo S.H. Driessen
    • 2
  1. 1.Department of Information and Management ScienceOtaru University of CommerceOtaru HokkaidoJapan
  2. 2.Faculty of Mathematical SciencesUniversity of TwenteEnschedeThe Netherlands

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