Another characterization of the Owen value without the additivity axiom

Casajus, André

doi:10.1007/s11238-009-9148-0

Cited by 15 publications

(3 citation statements)

References 16 publications

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“…It should be noted that there exist some further axiomatizations of the Shapley levels value by Calvo et al (1996), Khmelnitskaya and Yanovskaya (2007), Casajus (2010), Á lvarez-Mozos and Tejada (2011), and Besner (2019.…”

Section: The Shapley Levels Valuementioning

confidence: 99%

Harsanyi support levels solutions

Besner

2021

Theory Decis

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We introduce a new class of values for TU-games (games with transferable utility) with a level structure, called LS-games. A level structure is a hierarchical structure where each level corresponds to a partition of the player set, which becomes increasingly coarse from the trivial partition containing only singletons to the partition containing only the grand coalition. The new values, called Harsanyi support levels solutions, extend the Harsanyi solutions for LS-games. As an important subset of the class of these values, we present the class of weighted Shapley support levels values as a further result. The values from this class extend the weighted Shapley values for LS-games and contain the Shapley levels value as a special case. Axiomatizations of the studied classes are provided.

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Section: The Shapley Levels Valuementioning

confidence: 99%

Harsanyi support levels solutions

Besner

2021

Theory Decis

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“…Alternative non-efficient CS solutions have been suggested by Aumann and Drèze (1974) , Owen (1982) , and Alonso-Meijide and Fiestras-Janeiro (2002) , for example. 3 Alternative characterizations of the Owen value have been suggested by Owen (1977) himself, Hart and Kurz (1983) , Calvo et al (1996) , Hamiache (2001) , Albizuri (2008) , andCasajus (2010) , for example.…”

Section: Introductionmentioning

confidence: 99%

Second-order productivity, second-order payoffs, and the Owen value

Casajus

Takeng

2022

Ann Oper Res

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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.

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“…The research on Owen value mainly focuses on three aspects. First of all, new methods of axiomatic Owen value are proposed according to the specific application environments [4][5][6]. Second, the Owen value is improved for new application environments.…”

Section: Introductionmentioning

confidence: 99%

Matrix expression of Owen values

Zhu

Feng

Sun

2021

Asian Journal of Control

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The Owen value is investigated in this paper. It is a generation of Shapley value as a solution of cooperative games with coalition structures. First, a characteristic function of a cooperative game is expressed as a pseudo‐logical function by using semi‐tensor product of matrices. Then, a matrix formula is given for calculating Owen values. The matrix formula not only makes computing more convenient but also facilitates theoretical analysis. Therefore, an application of Owen value in distributed welfare games is presented. Utility functions of a distributed welfare game with coalition structure are designed based on Owen value. Examples are showed to illustrate the theoretical results.

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Another characterization of the Owen value without the additivity axiom

Abstract: Owen value, Additivity, Marginality, Differential marginality,

Cited by 15 publications

References 16 publications

Harsanyi support levels solutions

Harsanyi support levels solutions

Second-order productivity, second-order payoffs, and the Owen value

Matrix expression of Owen values

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