Values on regular games under Kirchhoff's laws
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.
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- Michel Grabisch & Fabien Lange, 2007.
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Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
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Cowles Foundation Discussion Papers
471R, Cowles Foundation for Research in Economics, Yale University.
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