Values on regular games under Kirchhoff's laws

Fabien Lange (1, 2) , Michel Grabisch (1)

1 CES - Centre d'économie de la Sorbonne
2 Keleti Faculty of Economics

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.

Mots clés: Kirchhoff's laws; Regular set system; communication situation; regular game; Shapley value; Kirchhoff's laws.

Domaines: Economies et finances; Recherche opérationnelle [math.OC]

Fabien Lange, Michel Grabisch. Values on regular games under Kirchhoff's laws. Mathematical Social Sciences, 2009, 58 (3), pp.322-340. ⟨10.1016/j.mathsocsci.2009.07.003⟩. ⟨halshs-00496553⟩