A Banzhaf value for games with a proximity relation among the agents

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

doi:10.1016/j.ijar.2017.05.010

Cited by 5 publications

(8 citation statements)

References 18 publications

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“…The following axiom is an extension of the group symmetry axiom for games with a priori unions. This is the main difference between this Banzhaf value and that introduced in [10].…”

Section: The Banzhaf-myerson Valuementioning

confidence: 65%

“…Another one was given in [9]. Fernández et al [10] defined an extension of the non-symmetric version of the Banzhaf value to the Casajus model. In this paper we consider a cooperation value consisting of applying the Banzhaf value in the first step and the Myerson value in the second step in order to get a symmetric version.…”

Section: A Priori Unionsmentioning

confidence: 99%

“…Fernandez et al [10] defined a Banzhaz value following [6] for the Casajus model [8]. However, this value fails in an important condition for a value: the symmetry for groups as we can see in [7] (a priori unions are particular cases of the Casajus model).…”

Section: The Banzhaf-myerson Valuementioning

confidence: 99%

“…It is defined an axiomatized in Fernández et al [9]. Later Fernández et al [10] introduced a Banzhaf value from the Owen version to the Casajus model. Now we define in this paper another Banzhaf solution for games in the Casajus model but from the Alonso-Meijide and Fiestras-Janeiro point of view, this in taking into account the symmetry in groups.…”

Section: Introductionmentioning

confidence: 99%

“…They introduced the concept of fuzzy communication structure in a particular version and defined the Choquet by graphs partition of a fuzzy graph with the purpose of constructing values in this context; see [14][15][16]. Later the analyzed games with a proximity relation among the players, the Shapley value [9] and the Banzhaf value [10] (following the Owen version). Now we use the symmetric version introduced in this same paper to get another Banzhaf value for games with a proximity relation among the agents.…”

Section: Introductionmentioning

confidence: 99%

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A Symmetric Banzhaf Cooperation Value for Games with a Proximity Relation among the Agents

et al. 2020

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A cooperative game represents a situation in which a set of agents form coalitions in order to achieve a common good. To allocate the benefits of the result of this cooperation there exist several values such as the Shapley value or the Banzhaf value. Sometimes it is considered that not all communications between players are feasible and a graph is introduced to represent them. Myerson (1977) introduced a Shapley-type value for these situations. Another model for cooperative games is the Owen model, Owen (1977), in which players that have similar interests form a priori unions that bargain as a block in order to get a fair payoff. The model of cooperation introduced in this paper combines these two models following Casajus (2007). The situation consists of a communication graph where a two-step value is defined. In the first step a negotiation among the connected components is made and in the second one players inside each connected component bargain. This model can be extended to fuzzy contexts such as proximity relations that consider leveled closeness between agents as we proposed in 2016. There are two extensions of the Banzhaf value to the Owen model, because the natural way loses the group symmetry property. In this paper we construct an appropriate value to extend the symmetric option for situations with a proximity relation and provide it with an axiomatization. Then we apply this value to a political situation.

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“…The following axiom is an extension of the group symmetry axiom for games with a priori unions. This is the main difference between this Banzhaf value and that introduced in [10].…”

Section: The Banzhaf-myerson Valuementioning

confidence: 65%

Section: A Priori Unionsmentioning

confidence: 99%

Section: The Banzhaf-myerson Valuementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%