Values on regular games under Kirchhoff’s laws

Fabien Lange () and Michel Grabisch

No 807, Working Paper Series from Óbuda University, Keleti Faculty of Business and Management

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 leading to applications to games with communication graphs, 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 Shapley value proprosed 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; probabilistic efficient values; regular values; Kirchhoff’s laws. (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2006, Revised 2008-11
New Economics Papers: this item is included in nep-cdm and nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (27)

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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 (2009)
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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