A Banzhaf value for games with fuzzy communication structure: Computing the power of the political groups in the European Parliament

Gallego, Inés; Fernández, Julio R.; Jiménez-Losada, Andrés; Ordóñez, Manuel

doi:10.1016/j.fss.2013.12.012

Cited by 10 publications

(5 citation statements)

References 16 publications

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“…We use the matrix representation of γ, to obtain the fuzzy graphs γ k and the crisp graphs g k . The time complexity of cg-partition algorithm is O m 2 (Gallego et al 2014), where…”

Section: Theorem 2 the Cg-average Tree Value Is The Only Cycle-free Fuzzy Communication Value Satisfying Fuzzy Efficiency By Components Amentioning

confidence: 99%

The cg-average tree value for games on cycle-free fuzzy communication structures

Fernández

Gallego

Jiménez-Losada

et al. 2019

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The main goal in a cooperative game is to obtain a fair allocation of the profit due the cooperation of the involved agents. The most known of these allocations is the Shapley value. This allocation considers that the communication among the players is complete. The Myerson value is a modification of the Shapley value considering a communication structure which determines the feasible bilateral relationships among the agents. This allocation of the profit is not always a stable solution. Another payoff allocation for games with a communication structure from the definition of the Shapley value is the average tree value. This one is a stable solution for any game using a cycle-free communication structure. Later fuzzy communication structures were introduced. In a fuzzy communication structure, the membership of the agents and the relationships among them are leveled. The Myerson value was extended in several different ways depending on the behavior of the agents. In this paper, the average tree value is extended to games with fuzzy communication structures taking one particular version: the Choquet by graphs (cg). We present an application to the management of an electrical network with an algorithmic implementation.

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“…We use the matrix representation of γ, to obtain the fuzzy graphs γ k and the crisp graphs g k . The time complexity of cg-partition algorithm is O m 2 (Gallego et al 2014), where…”

Section: Theorem 2 the Cg-average Tree Value Is The Only Cycle-free Fuzzy Communication Value Satisfying Fuzzy Efficiency By Components Amentioning

confidence: 99%

The cg-average tree value for games on cycle-free fuzzy communication structures

Fernández

Gallego

Jiménez-Losada

et al. 2019

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“…The Banzhaf value 9 for cooperative games can be used as a solution concept and to evaluate the cooperation existing among players. To name a few, the application of the Banzhaf value to communication situations has been given by Alonso-Meijide and Fiestras-Janeiro 10 , Gallego et al 11 to Compute the power of the political groups in the European Parliament, and Fragnelli and Pusillo 12 applied the Banzhaf value for detecting abnormally expressed genes.…”

Section: Introductionmentioning

confidence: 99%

An Application of the Banzhaf Values for Cooperating Among Producers of Waste Processing in the Al-Mahmudiya Factory

Hadi

Abbas

2023

Baghdad Sci.J

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The game theory has been applied to all situations where agents’ (people or companies) actions are utility-maximizing, and the collaborative offshoot of game theory has proven to be a robust tool for creating effective collaboration strategies in a broad range of applications. In this paper first, we employ the Banzhaf values to show the potential cost to waste producers in the case of a cooperation and to reduce the overall costs of processing non-recyclable waste during cooperation between producers. Secondly, we propose an application of the methodology to study a case for five waste producers' waste management in the Al-Mahmudiya factory with the aim of displaying the potential cost to waste producers in case of cooperation. Lastly, the obtained results of the proposed framework will strongly help professionals to formulate and improve well-organized strategies for the waste management system of the future.

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“…The notion of fuzzy game was first introduced by Aubin (1974) and since then different fuzzy approaches to cooperative games have been profusely developed in various directions by many scholars Borkotokey (2008); Meng et al (2017); Jana and Roy (2019); Bhaumik et al (2020). It is remarkable that a notion of the Banzhaf index in the context of uncertainty is provided in Gallego et al (2014).…”

Section: Introductionmentioning

confidence: 99%

An Appropriate Way to Extend the Banzhaf Index for Multiple Levels of Approval

Freixas

Pons

2021

Group Decis Negot

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The Banzhaf power index for games admits several extensions if the players have more than two ordered voting options. In this paper we prove that the most intuitive and recognized extension of the index fails to preserve the desirability relation for games with more than three ordered input levels of approval, a failure that undermines the index to be a good measure of power. This leads us to think of an alternative to the Banzhaf index for several input levels of approval. We propose a candidate for which it is proved that: 1) coincides with the Banzhaf index for simple games, 2) it is proportional to its known extension for three levels of approval, and 3) preserves the desirability relation regardless of the number of input levels of approval. This new index is based on measuring the total capacity the player has to alter the outcome. In addition, it can be expressed through a very appropriate mathematical formulation that greatly facilitates its computation.Defining extensions of well-established notions in a wider context requires a careful analysis. Different extensions can provide complementary nuances and, when this occurs, none of them can be considered to be 'the' extension. As shown in this paper, this situation applies when trying to extend the Banzhaf power index from simple games to the broader context of games with several ordered input levels of approval. KeywordsExtensions of the Banzhaf index • Several ordered levels of input approval • Preservation of the desirability relation • Forms of criticality • Total criticality

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A Banzhaf value for games with fuzzy communication structure: Computing the power of the political groups in the European Parliament

Cited by 10 publications

References 16 publications

The cg-average tree value for games on cycle-free fuzzy communication structures

The cg-average tree value for games on cycle-free fuzzy communication structures

An Application of the Banzhaf Values for Cooperating Among Producers of Waste Processing in the Al-Mahmudiya Factory

An Appropriate Way to Extend the Banzhaf Index for Multiple Levels of Approval

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