Coincidence of the Shapley value with other solutions satisfying covariance

Koji Yokote*, Yukihiko Funaki, Yoshio Kamijo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We identify the necessary and sufficient condition under which the Shapley value coincides with the prenucleolus for general TU games. For 0-normalized 3-person games, the coincidence holds if and only if the game is symmetric or satisfies the PS property (Kar et al., 2009). We also identify the necessary and sufficient coincidence condition in the following allocation problems: the airport games (Littlechild and Owen, 1973), the bidder collusion games (Graham et al., 1990) and the polluted river games (Ni and Wang, 2007). The coincidence between the Shapley value and the CIS and ENSC values is discussed as well.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalMathematical social sciences
Publication statusPublished - 2017 Sept


  • Coincidence condition
  • Prenucleolus
  • Shapley value
  • TU games

ASJC Scopus subject areas

  • Sociology and Political Science
  • Social Sciences(all)
  • Psychology(all)
  • Statistics, Probability and Uncertainty


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