The modified Banzhaf value for games with coalition structure: an axiomatic characterization

Ramon, Rafael Amer; Carreras, Francese; Giménez, José Miguel

doi:10.1016/s0165-4896(01)00076-2

Cited by 58 publications

(26 citation statements)

References 7 publications

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“…In this case the payoffs at both levels, that of the unions in the quotient game and that of the players within each union, are given by the Banzhaf value. This modified value was axiomatically characterized only recently, by Albizuri [1] and [2] and, independently, by Amer, Carreras and Giménez [9]. Interesting interpretations of this value as a power index when restricted to simple games can be found in Laruelle and Valenciano [37].…”

Section: A Remark and Two Examplesmentioning

confidence: 97%

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Symmetric Coalitional Binomial Semivalues

Carreras

Puente

2011

Group Decis Negot

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We introduce here a family of mixed coalitional values. They extend the binomial semivalues to games endowed with a coalition structure, satisfy the property of symmetry in the quotient game and the quotient game property, generalize the symmetric coalitional Banzhaf value introduced by Alonso and Fiestras and link and merge the Shapley value and the binomial semivalues. A computational procedure in terms of the multilinear extension of the original game is also provided and an application to political science is sketched.

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Section: A Remark and Two Examplesmentioning

confidence: 97%

“…More recently, Alonso, Carreras and Fiestras [5] apply the multilinear extension method to the Alonso-Fiestras value Π, and also to a "counterpart" value M = ϕβ m introduced by Amer, Carreras and Giménez [9]. In Puente [48] it is shown that the binomial semivalues can be computed in a way very close to that of the Banzhaf value.…”

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confidence: 99%

Symmetric Coalitional Binomial Semivalues

Carreras

Puente

2011

Group Decis Negot

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“…Even though EB-IU is a null player in the associated voting game 6 , a minority government was formed with the coalition of EAJ-PNV / EA and EB-IU. Whatever the reason for this decision could be, it suggests that null players can also play a significant role.…”

Section: Partymentioning

confidence: 99%

“…Let LSP be the least square prenucleolus (Ruiz, Valenciano and Zarzuelo, 1996). Ba (Sh) is defined and studied by Amer, Carreras and Giménez (2002). ] is the family of symmetric coalitional binomial values (Carreras and Puente, 2006).…”

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confidence: 99%

The axiomatic approach to three values in games with coalition structure

Gómez-Rúa

Vidal-Puga

2010

European Journal of Operational Research

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We study three values for transferable utility games with coalition structure, including the Owen coalitional value and two weighted versions with weights given by the size of the coalitions. We provide three axiomatic characterizations using the properties of Efficiency, Linearity, Independence of Null Coalitions, and Coordination, with two versions of Balanced Contributions inside a Coalition and Weighted Sharing in Unanimity Games, respectively.

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“…Later, Owen [20] gave another payoff index for games with a coalition structure, which is called the Banzhaf-Owen value, and discussed its axiomatic system. More researches about axiomatic characterizations of the Banzhaf-Owen value can be seen in [21,22]. Alonso-Meijide and Fiestras-Janeiro [23] pointed the Banzhaf-Owen value dissatisfies symmetry in quotient games, and gave another solution concept for games with a coalition structure, which is known as the symmetric Banzhaf value.…”

Section: ． Introductionmentioning

confidence: 99%

Cooperative Fuzzy Games with a Coalition Structure and Interval Payoffs

Meng¹,

Zhang²,

Yan³

2013

IJCIS

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Based on the extension Hukuhara difference between interval numbers, a generalized form of cooperative fuzzy games with a coalition structure and interval payoffs is proposed, which can be seen as an extension of crisp case. The interval Owen value for this kind of fuzzy games is studied, and its explicit form is given. When the fuzzy games are convex, the proposed interval Owen value is an interval population monotonic allocation function (IPMAF), and belongs to the associated core. Furthermore, we discuss a special kind of fuzzy games with a coalition structure and interval payoffs, and study the interval Owen value and the core of it. Some properties are also examined, which are coincided with the crisp case.

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The modified Banzhaf value for games with coalition structure: an axiomatic characterization

Cited by 58 publications

References 7 publications

Symmetric Coalitional Binomial Semivalues

Symmetric Coalitional Binomial Semivalues

The axiomatic approach to three values in games with coalition structure

Cooperative Fuzzy Games with a Coalition Structure and Interval Payoffs

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