Associated consistency characterization of two linear values for TU games by matrix approach

G. Xu, J.R. van den Brink, G. van der Laan, H. Sun

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

Hamiache assigns to every TU game a so-called associated game and then shows that the Shapley value is characterized as the unique solution for TU games satisfying the inessential game property, continuity and associated consistency. The latter notion means that for every game the Shapley value of the associated game is equal to the Shapley value of the game itself. In this paper we show that also the EANS-value as well as the CIS-value is characterized by these three properties for appropriately modified notions of the associated game. This shows that these three values only differ with respect to the associated game. The characterization is obtained by applying the matrix approach as the pivotal technique for characterizing linear values of TU games in terms of associated consistency.
Original languageEnglish
Pages (from-to)224-240
JournalLinear Algebra and its Applications
Volume471
Issue numberApril
DOIs
Publication statusPublished - 2015

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title = "Associated consistency characterization of two linear values for TU games by matrix approach",
abstract = "Hamiache assigns to every TU game a so-called associated game and then shows that the Shapley value is characterized as the unique solution for TU games satisfying the inessential game property, continuity and associated consistency. The latter notion means that for every game the Shapley value of the associated game is equal to the Shapley value of the game itself. In this paper we show that also the EANS-value as well as the CIS-value is characterized by these three properties for appropriately modified notions of the associated game. This shows that these three values only differ with respect to the associated game. The characterization is obtained by applying the matrix approach as the pivotal technique for characterizing linear values of TU games in terms of associated consistency.",
author = "G. Xu and {van den Brink}, J.R. and {van der Laan}, G. and H. Sun",
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Associated consistency characterization of two linear values for TU games by matrix approach. / Xu, G.; van den Brink, J.R.; van der Laan, G.; Sun, H.

In: Linear Algebra and its Applications, Vol. 471, No. April, 2015, p. 224-240.

Research output: Contribution to JournalArticleAcademicpeer-review

TY - JOUR

T1 - Associated consistency characterization of two linear values for TU games by matrix approach

AU - Xu, G.

AU - van den Brink, J.R.

AU - van der Laan, G.

AU - Sun, H.

PY - 2015

Y1 - 2015

N2 - Hamiache assigns to every TU game a so-called associated game and then shows that the Shapley value is characterized as the unique solution for TU games satisfying the inessential game property, continuity and associated consistency. The latter notion means that for every game the Shapley value of the associated game is equal to the Shapley value of the game itself. In this paper we show that also the EANS-value as well as the CIS-value is characterized by these three properties for appropriately modified notions of the associated game. This shows that these three values only differ with respect to the associated game. The characterization is obtained by applying the matrix approach as the pivotal technique for characterizing linear values of TU games in terms of associated consistency.

AB - Hamiache assigns to every TU game a so-called associated game and then shows that the Shapley value is characterized as the unique solution for TU games satisfying the inessential game property, continuity and associated consistency. The latter notion means that for every game the Shapley value of the associated game is equal to the Shapley value of the game itself. In this paper we show that also the EANS-value as well as the CIS-value is characterized by these three properties for appropriately modified notions of the associated game. This shows that these three values only differ with respect to the associated game. The characterization is obtained by applying the matrix approach as the pivotal technique for characterizing linear values of TU games in terms of associated consistency.

U2 - 10.1016/j.laa.2014.12.036

DO - 10.1016/j.laa.2014.12.036

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EP - 240

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

IS - April

ER -