Weakly differentially monotonic solutions for cooperative games

André Casajus*, Koji Yokote

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


The principle of differential monotonicity for cooperative games states that the differential of two players’ payoffs weakly increases whenever the differential of these players’ marginal contributions to coalitions containing neither of them weakly increases. Together with the standard efficiency property and a relaxation of the null player property, differential monotonicity characterizes the egalitarian Shapley values, i.e., the convex mixtures of the Shapley value and the equal division value for games with more than two players. For games that contain more than three players, we show that, cum grano salis, this characterization can be improved by using a substantially weaker property than differential monotonicity. Weak differential monotonicity refers to two players in situations where one player’s change of marginal contributions to coalitions containing neither of them is weakly greater than the other player’s change of these marginal contributions. If, in such situations, the latter player’s payoff weakly/strictly increases, then the former player’s payoff also weakly/strictly increases.

Original languageEnglish
Pages (from-to)979-997
Number of pages19
JournalInternational Journal of Game Theory
Issue number3
Publication statusPublished - 2019 Sept 1
Externally publishedYes


  • Differential marginality
  • Shapley value
  • TU game
  • Weak differential marginality

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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