Weakly differentially monotonic solutions for cooperative games

André Casajus () and Koji Yokote ()
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André Casajus: HHL Leipzig Graduate School of Management
Koji Yokote: Waseda Institute for Advanced Study, Waseda University

International Journal of Game Theory, 2019, vol. 48, issue 3, No 11, 979-997

Abstract: Abstract 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.

Keywords: TU game; Shapley value; Differential marginality; Weak differential marginality; 91A12 (search for similar items in EconPapers)
JEL-codes: C71 D60 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s00182-019-00669-1

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