Compromising between the proportional and equal division values

Zhengxing Zou, René van den Brink, Yukihiko Funaki

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce a family of values for TU-games that offers a compromise between the proportional and equal division values. Each value, called an α-mollified value, is obtained in two steps. First, linear functions are defined that associate a real number to every TU-game. Second, the weight assigned by this function is used to weigh proportionality and equality principles in allocating the worth of the grand coalition. We provide an axiomatic characterization of this family, and show that this family contains the affine combinations of the equal division value and the equal surplus division value as the only linear values. Further, we identify the proportional division value and the affine combinations of the equal division value and the equal surplus division value as those members of this family, that satisfy projection consistency.

Original languageEnglish
Article number102539
JournalJournal of Mathematical Economics
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Consistency
  • Cooperative game
  • Equal division value
  • Proportional division value

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics

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