Values on regular games under Kirchhoff's laws

Fabien Lange () and Michel Grabisch
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Fabien Lange: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Keleti Faculty of Economics - Budapest Tech

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Abstract: The Shapley value is a central notion defining a rational way to share the total worth of a cooperative game among players. We address a general framework leading to applications to games with communication graphs, where the feasible coalitions form a poset whose all maximal chains have the same length. Considering a new way to define the symmetry among players, we propose an axiomatization of the Shapley value of these games. Borrowing ideas from electric networks theory, we show that our symmetry axiom and the efficiency axiom correspond to the two Kirchhoff's laws in the circuit associated to the Hasse diagram of feasible coalitions.

Keywords: Kirchhoff's laws; Regular set system; communication situation; regular game; Shapley value; Kirchhoff's laws. (search for similar items in EconPapers)
Date: 2009-11
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00496553v1
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Citations: View citations in EconPapers (19)

Published in Mathematical Social Sciences, 2009, 58 (3), pp.322-340. ⟨10.1016/j.mathsocsci.2009.07.003⟩

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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 (2008)
Working Paper: Values on regular games under Kirchhoff's laws (2006)
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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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-00496553

DOI: 10.1016/j.mathsocsci.2009.07.003

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