Matrix approach to consistency of the additive efficient normalization of semivalues

Genjiu Xu, Theo Driessen, Hao Sun

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Abstract

In fact the Shapley value is the unique efficient semivalue. This motivated Ruiz et al. to do additive efficient normalization for semivalues. In this paper, by matrix approach we derive the relationship between the additive efficient normalization of semivalues and the Shapley value. Based on the relationship, we axiomatize the additive efficient normalization of semivalues as the unique solution verifying covariance, symmetry, and reduced game property with respect to the $p-$reduced game.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente
Number of pages12
Publication statusPublished - Oct 2007

Publication series

NameMemorandum Department of Applied Mathematics
PublisherUniversity of Twente
No.1854
ISSN (Print)1874-4850

Keywords

  • MSC-91A12
  • MSC-15A18

Cite this

Xu, G., Driessen, T., & Sun, H. (2007). Matrix approach to consistency of the additive efficient normalization of semivalues. (Memorandum Department of Applied Mathematics; No. 1854). Enschede: University of Twente.