Axiomatizations of the proportional division value

Zhengxing Zou*, René van den Brink, Youngsub Chun, Yukihiko Funaki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We present axiomatic characterizations of the proportional division value for TU-games, which distributes the worth of the grand coalition in proportion to the stand-alone worths of the players. First, a new proportionality principle, called proportional-balanced treatment, is introduced by strengthening Shapley’s symmetry axiom, which states that if two players make the same contribution to any nonempty coalition, then they receive the amounts in proportion to their stand-alone worths. We characterize the family of values satisfying efficiency, weak linearity, and proportional-balanced treatment. We also show that this family is incompatible with the dummy player property. However, we show that the proportional division value is the unique value in this family that satisfies the dummifying player property. Second, we propose appropriate monotonicity axioms, and obtain axiomatizations of the proportional division value without both weak linearity and the dummifying player property. Third, from the perspective of a variable player set, we show that the proportional division value is the only one that satisfies proportional standardness and projection consistency. Finally, we provide a characterization of proportional standardness.

Original languageEnglish
Pages (from-to)35-62
Number of pages28
JournalSocial Choice and Welfare
Issue number1
Publication statusPublished - 2021 Jul

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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