Characterizations of three linear values for TU games by associated consistency: simple proofs using the Jordan normal form

Sylvain Béal, Eric Rémila and Philippe Solal

No 2015-05, Working Papers from CRESE

Abstract: This article studies values for cooperative games with transferable utility. Numerous such values can be characterized by axioms of associated consistency, which require that a value is invariant under some parametrized linear transformation on the vector space of cooperative games with transferable utility. Xu et al. (2008, 2009, Linear Algebra Appl.), Xu et al. (2013, Linear Algebra Appl.), Hamiache (2010, Int. Game Theory Rev.) and more recently Xu et al. (2015, Linear Algebra Appl.) follow this approach by using a matrix analysis. The main drawback of these articles is the heaviness of the proofs to show that the matrix expression of the linear transformations is diagonalizable. By contrast, we provide quick proofs by relying on the Jordan normal form of the previous matrix.

Keywords: TU-games; associated consistency; linear transformation; matrix approach; Jordan normal form; Shapley value; center of gravity of imputation set; equal allocation of non-separable contributions. (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Pages: 15 pages
Date: 2015-03
New Economics Papers: this item is included in nep-gth
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Related works:
Journal Article: Characterizations of Three Linear Values for TU Games by Associated Consistency: Simple Proofs Using the Jordan Normal Form (2016)
Working Paper: Characterizations of three linear values for TU games by associated consistency: simple proofs using the Jordan normal form (2016)
Working Paper: Characterizations of three linear values for TU games by associated consistency: simple proofs using the Jordan normal form (2015)
Working Paper: Characterizations of three linear values for TU games by associated consistency: simple proofs using the Jordan normal form (2015)
Working Paper: Characterizations of three linear values for TU games by associated consistency: simple proofs using the Jordan normal form (2015)
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