An axiomatic characterization of the Owen–Shapley spatial power index

Peters, Hans; Zarzuelo, José Manuel

doi:10.1007/s00182-016-0544-8

Cited by 9 publications

(9 citation statements)

References 18 publications

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“…Then ϕ 5 is a power index satisfying ISP and SPID, but not EPC. (This example is analogous to an example in Peters and Zarzuelo (2017)).…”

Section: Strong Issue Dependence (Sid) For Allmentioning

confidence: 78%

“…For instance, Owen (1971) and later Owen and Shapley (1989) add to the simple game a vector of positions of players in two-dimensional Euclidean space, and use this to obtain a variant of the Shapley-Shubik index, called the Owen-Shapley spatial power index, which takes these positions into consideration. See Peters and Zarzuelo (2017) for an axiomatic characterization of this index. As will become clear below, the approach in the present paper is based on a similar idea as the Owen-Shapley spatial power index.…”

Section: Introductionmentioning

confidence: 99%

“…Equal power changeFor our last characterization, we consider a condition which is closely related to the familiar condition of additivity for solutions of cooperative games(Shapley 1953), and more specifically to the transfer property for solutions of simple games(Dubey 1975;Dubey et al 2005). Compared to the other axioms, this condition (which is also used inPeters and Zarzuelo (2017)) is concerned with the simple game in an issue game, rather than the issue profile.…”

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confidence: 99%

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An issue based power index

Kong

Peters

2020

Int J Game Theory

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An issue game is a combination of a monotonic simple game and an issue profile. An issue profile is a profile of linear orders on the player set, one for each issue within the set of issues: such a linear order is interpreted as the order in which the players will support the issue under consideration. A power index assigns to each player in an issue game a nonnegative number, where these numbers sum up to one. We consider a class of power indices, characterized by weight vectors on the set of issues. A power index in this class assigns to each player the weighted sum of the issues for which that player is pivotal. A player is pivotal for an issue if that player is a pivotal player in the coalition consisting of all players preceding that player in the linear order associated with that issue. We present several axiomatic characterizations of this class of power indices. The first characterization is based on two axioms: one says how power depends on the issues under consideration (Issue Dependence), and the other one concerns the consequences, for power, of splitting players into several new players (no advantageous splitting). The second characterization uses a stronger version of Issue Dependence, and an axiom about symmetric players (Invariance with respect to Symmetric Players). The third characterization is based on a variation on the transfer property for values of simple games (Equal Power Change), besides Invariance with respect to Symmetric Players and another version of Issue Dependence. Finally, we discuss how an issue profile may arise from preferences of players about issues.

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“…Then ϕ 5 is a power index satisfying ISP and SPID, but not EPC. (This example is analogous to an example in Peters and Zarzuelo (2017)).…”

Section: Strong Issue Dependence (Sid) For Allmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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An issue based power index

Kong

Peters

2020

Int J Game Theory

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“…Hinich, 1984, 1990;Grofman et al, 1987). A well-known adaptation of the Shapley value to the spatial context is the Owen-Shapley spatial power index (Owen and Shapley, 1989;Martin et al, 2014;Peters and Zarzuelo, 2016).…”

Section: An Application Of the Infinite Case: A Spatial Power Indexmentioning

confidence: 99%

Effectivity and power

Karos

Peters

2018

Games and Economic Behavior

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People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

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“…For instance, Owen [49] and later Owen and Shapley [50] add to the simple game a vector of positions of players in two-dimensional Euclidean space, and use this to obtain a variant of the Shapley-Shubik index, called the Owen-Shapley spatial power index, which takes these positions into consideration. See Peters and Zarzuelo [54] for an axiomatic characterization of this index. As will become clear below, the approach in the present chapter is based on a similar idea as the Owen-Shapley spatial power index.…”

Section: Introductionmentioning

confidence: 99%

Power indices, claims games and core selection

Kong¹

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People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

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An axiomatic characterization of the Owen–Shapley spatial power index

Cited by 9 publications

References 18 publications

An issue based power index

An issue based power index

Effectivity and power

Power indices, claims games and core selection

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