Cooperation among agents with a proximity relation

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

doi:10.1016/j.ejor.2015.09.029

Cited by 16 publications

(13 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With the purpose of obtaining an axiomatization we introduce some axioms. The first four axioms also appear in the axiomatization of the Myerson-Owen value in [9]. We will also prove that this value is a coalitional value of Banzhaf.…”

Section: The Banzhaf-myerson Valuementioning

confidence: 76%

“…Casajus defined a value using the Shapley value in the first step and the Myerson value in the second step and gave an axiomatization. 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.…”

Section: A Priori Unionsmentioning

confidence: 99%

“…If we compare the axiomatizations of the Myerson-Owen value in [9] and the Banzhaf-Myerson value, the latter differs from the first in the fact that connected efficiency and component merging replace efficiency. This seems a logical consequence from the axiomatizations of the Shapley value and the Banzhaf value presented before.…”

Section: Connected Efficiency a Cooperation Value F Satisfies Connected Efficiency Ifmentioning

confidence: 99%

“…The Myerson-Owen value is a two-step value like the Owen value that applies the Shapley value among the components and the Myerson value inside each component. 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.…”

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%

See 4 more Smart Citations

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

et al. 2020

View full text Add to dashboard Cite

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.

show abstract

Section: The Banzhaf-myerson Valuementioning

confidence: 76%

Section: A Priori Unionsmentioning

confidence: 99%

Section: Connected Efficiency a Cooperation Value F Satisfies Connected Efficiency Ifmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%