Relationally equal treatment of equals and affine combinations of values for TU games

Koji Yokote, Takumi Kongo*, Yukihiko Funaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We axiomatize the set of affine combinations between the Shapley value, the equal surplus division value, and the equal division value in cooperative games with transferable utilities. The set is characterized by efficiency, linearity, the balanced contributions property for equal contributors and outsiders, and the differential null player out property. The balanced contributions property for equal contributors and outsiders requires the balance of contributions between two players who contribute the same amount to the grand coalition and whose singleton coalitions earn the same worth. The differential null player out property requires that an elimination of a null player affects the other players identically. These two relational axioms are obtained by investigating Myerson’s (Int J Game Theory 9:169–182, 1980) balanced contributions property and Derks and Haller’s (Int Game Theory Rev 1:301–314, 1999) null player out property, respectively, from the perspective of a principle of Aristotle’s distributive justice, whereby “equals should be treated equally”.

Original languageEnglish
Pages (from-to)197-212
Number of pages16
JournalSocial Choice and Welfare
Volume53
Issue number2
DOIs
Publication statusPublished - 2019 Aug 1

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

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