Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/308955 
Year of Publication: 
2022
Citation: 
[Journal:] Annals of Operations Research [ISSN:] 1572-9338 [Volume:] 320 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2022 [Pages:] 1-13
Publisher: 
Springer US, New York, NY
Abstract: 
We introduce the concepts of the components' second-order productivities in cooperative games with transferable utility (TU games) with a coalition structure (CS games) and of the components' second-order payoffs for one-point solutions for CS games as generalizations of the players' second-order productivities in TU games and of the players' second-order payoffs for one-point solutions for TU games (Casajus in Discrete Appl Math 304:212–219, 2021). The players' second-order productivities are conceptualized as second-order marginal contributions, that is, how one player affects another player's marginal contributions to coalitions containing neither of them by entering these coalitions. The players' second-order payoffs are conceptualized as the effect of one player leaving the game on the payoff of another player. Analogously, the components' second-order productivities are conceptualized as their second-order productivities in the game between components; the components' second-order payoffs are conceptualized as their second-order payoffs in the game between components. We show that the Owen value is the unique efficient one-point solution for CS games that reflects the players' and the components' second-order productivities in terms of their second-order payoffs.
Subjects: 
TU game
Shapley value
Owen value
Second-order marginal contributions
Second-order payoffs
JEL: 
C71
D60
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version

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