Collinearity between the Shapley value and the egalitarian division rules for cooperative games

Irinel Dragan, Theo Driessen, Yukihiko Funaki

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

For each cooperative n-person game v and each hε{1, 2 . . . . . n}, let νh be the average worth of coalitions of size h and νih the average worth of coalitions of size h which do not contain player iε N. The paper introduces the notion of a proportional average worth game (or PAW-game), i.e., the zero-normalized game v for which there exist numbers chεℝ such that νh- νhi=chn-1-v n-1i) for all hε{2, 3 . . . . , n-1}, and iε N. The notion of average worth is used to prove a formula for the Shapley value of a PAW-game. It is shown that the Shapley value, the value representing the center of the imputation set, the egalitarian nonseparable contribution value and the egalitarian non-average contribution value of a PAW-game are collinear. The class of PAW-games contains strictly the class of k-coalitional games possessing the collinearity property discussed by Driessen and Funaki (1991). Finally, it is illustrated that the unanimity games and the landlord games are PAW-games.

Original languageEnglish
Pages (from-to)97-105
Number of pages9
JournalOR Spectrum
Volume18
Issue number2
DOIs
Publication statusPublished - 1996 Jan 1
Externally publishedYes

Keywords

  • Cooperative game
  • Egalitarian division rules
  • PAW-game
  • Shapley value
  • k-Coalitional game

ASJC Scopus subject areas

  • Management Science and Operations Research

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