Values on regular games under Kirchhoff's laws

Fabien Lange () and Michel Grabisch
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Fabien Lange: CEntre de Recherche en Mathématiques, Statistique et Economie Mathématique (CERMSEM)

Cahiers de la Maison des Sciences Economiques from Université Panthéon-Sorbonne (Paris 1)

Abstract: In cooperative game theory, the Shapley value is a central notion defining a rational way to share the total worth of a game among players. In this paper, we address a general framework, namely regular set systems, where the set of feasible coalitions forms a poset where all maximal chains have the same length. We first show that previous definitions and axiomatizations of the Shaphey value proposed by Faigle and Kern and Bilbao and Edelman still work. our main contribution is then to propose a new axiomatization avoiding the hierarchical strength axiom of Faigle and Kern, and considering a new way to define the symmetry among players. Borrowing ideas from electric networks theory, we show that our symmetry axiom and the classical efficiency axiom correspond actually to the two Kirchhoff's laws in the resistor circuit associated to the Hasse diagram of feasible coalitions. We finally work out a weak form of the monotonicity axiom which is satisfied by the proposed value

Keywords: Regular set systems; regular games; Shapley value; probalistic efficient values; regular values; Kirchhoff's laws (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2006-12
New Economics Papers: this item is included in nep-gth and nep-net
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Published in Journal Mathematical Social Sciences, Elsevier, 2009, 58 (3), pp.322-340

Downloads: (external link)
https://halshs.archives-ouvertes.fr/halshs-00130449 (application/pdf)
https://doi.org/10.1016/j.mathsocsci.2009.07.003

Related works:
Journal Article: Values on regular games under Kirchhoff's laws (2009)
Working Paper: Values on regular games under Kirchhoff's laws (2009)
Working Paper: Values on regular games under Kirchhoff's laws (2009)
Working Paper: Values on regular games under Kirchhoff’s laws (2008)
Working Paper: Values on regular games under Kirchhoff's laws (2006)
Working Paper: Values on regular games under Kirchhoff's laws (2006)
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