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Weakly differentially monotonic solutions for cooperative games

  • 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 coex 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.

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Document Type:Article
Author:André Casajus, Koji Yokote
Chairs and Professorships:Chair of Economics and Information Systems
Parent Title (English):International journal of game theory
Year of Completion:2019
First Page:979
Last Page:997
Tag:Differential marginality; Shapley value; TU game; Weak differential marginality
Content Focus:Academic Audience
Peer Reviewed:Yes
Rankings:AJG Ranking / 2
SJR Ranking / Q2
Licence (German):License LogoUrheberrechtlich geschützt