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
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Sylvain Béal: Université de Franche-Comté, CRESE EA3190, Universite Bourgogne Franche-Comté, F-25000 Besançon, France
Eric Rémila: ��Universite Lyon, UJM Saint-Etienne, CNRS, GATE L-SE UMR 5824, F-42023 Saint-Etienne, France‡IXXI, 46, allée d’Italie, 69007 Lyon, France
Authors registered in the RePEc Author Service: Eric Rémila and Sylvain Béal

International Game Theory Review (IGTR), 2016, vol. 18, issue 01, 1-21

Abstract: This paper studies values for cooperative games with transferable utility. Numerous such values can be characterized by axioms of Ψε-associated consistency, which require that a value is invariant under some parametrized linear transformation Ψε on the vector space of cooperative games with transferable utility. Xu et al. [(2008) Linear Algebr. Appl. 428, 1571–1586; (2009) Linear Algebr. Appl. 430, 2896–2897] Xu et al. [(2013) Linear Algebr. Appl. 439, 2205–2215], Hamiache [(2010) Int. Game Theor. Rev. 12, 175–187] and more recently Xu et al. [(2015) Linear Algebr. Appl. 471, 224–240] 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: Associated consistency; Jordan normal form; Shapley value; center of imputation set; equal allocation of nonseparable costs (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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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)
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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DOI: 10.1142/S0219198916500031

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