Associated Consistency Characterization of Two Linear Values for Tu Games by Matrix Approach

Tinbergen Institute Discussion Paper 12-105/II

22 Pages Posted: 9 Oct 2012

See all articles by Genjiu Xu

Genjiu Xu

Northwestern Polytechnical University, China

René van den Brink

VU University Amsterdam - Department of Economics; Tinbergen Institute; Tinbergen Institute

Gerard van der Laan

Vrije Universiteit Amsterdam, School of Business and Economics; Tinbergen Institute

Hao Sun

Northwestern Polytechnical University, China

Date Written: October 8, 2012

Abstract

Hamiache (2001) 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 are 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.

Keywords: TU games, Shapley value, EANS-value, CIS-value, associated consistency, matrix approach

JEL Classification: C71

Suggested Citation

Xu, Genjiu and van den Brink, J.R. (René) and van der Laan, Gerard and Sun, Hao, Associated Consistency Characterization of Two Linear Values for Tu Games by Matrix Approach (October 8, 2012). Tinbergen Institute Discussion Paper 12-105/II, Available at SSRN: https://ssrn.com/abstract=2158737 or http://dx.doi.org/10.2139/ssrn.2158737

Genjiu Xu (Contact Author)

Northwestern Polytechnical University, China ( email )

127# YouYi Load
Xi'an, Shaanxi 710072
China

J.R. (René) Van den Brink

VU University Amsterdam - Department of Economics ( email )

De Boelelaan 1105
1081 HV Amsterdam
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Gerard Van der Laan

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Department of Econometrics and Tinbergen Institute
1081 HV Amsterdam
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Hao Sun

Northwestern Polytechnical University, China ( email )

127# YouYi Load
Xi'an, Shaanxi 710072
China

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