The shapley value on some lattices of monotonic games

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8 Scopus citations

Abstract

It is shown that the restriction of the Shapley value to the lattice of all monotonic games whose range is contained in an arbitrary set of non-negative real numbers (which contains 0) can be uniquely characterized by the axioms that were given by Dubey (in order to characterize the Shapley value on the class of monotonic simple games). We also derive formulas for the Shapley-Shubik and Banzhaf power indices in terms of the minimal winning coalitions of the game.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalMathematical Social Sciences
Volume15
Issue number1
DOIs
StatePublished - 1 Jan 1988
Externally publishedYes

Keywords

  • Banzhaf value
  • Monotonic game
  • Shapley value
  • simple game
  • valuation

ASJC Scopus subject areas

  • Sociology and Political Science
  • General Social Sciences
  • General Psychology
  • Statistics, Probability and Uncertainty

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