A matrix approach to associated consistency of the Shapley value for games in generalized characteristic function form

Yuan Feng, Theo S.H. Driessen, Georg Still

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Abstract

The paper is devoted to the Shapley value for cooperative games in generalized characteristic function form in which the players of coalitions are supposed to be ordered. An axiomatization of the generalized Shapley value is presented in terms of three properties, namely continuity, associated consistency, and inessential game property. The proof of the characterization of the Shapley value is based on a matrix representation of so-called associated games. We analyze the dimension of the eigenspaces of this matrix and show that the matrix is diagonalizable.
Original languageEnglish
Pages (from-to)4279-4295
Number of pages17
JournalLinear algebra and its applications
Volume438
Issue number11
DOIs
Publication statusPublished - 2013

Keywords

  • Shapley value
  • Orders
  • Diagonalization
  • Cooperative game
  • Associated consistency

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