An algorithm for finding the vertices of the k-additive monotone core

Pedro Miranda (1) , Michel Grabisch (2, 3)

1 UCM - Universidad Complutense de Madrid = Complutense University of Madrid [Madrid]
2 CES - Centre d'économie de la Sorbonne
3 PSE - Paris School of Economics

Given a capacity, the set of dominating k-additive capacities is a convex polytope called the k-additive monotone core; thus, it is defined by its vertices. In this paper we deal with the problem of deriving a procedure to obtain such vertices in the line of the results of Shapley and Ichiishi for the additive case. We propose an algorithm to determine the vertices of the n-additive monotone core and we explore the possible translations for the k-additive case.

Mots clés: polyhedra; Capacities; k-additivity; Dominance; Core

Domaines: Mathématique discrète [cs.DM]; Economies et finances

Pedro Miranda, Michel Grabisch. An algorithm for finding the vertices of the k-additive monotone core. Discrete Applied Mathematics, 2012, 160 (4-5), pp.628-639. ⟨10.1016/j.dam.2011.11.013⟩. ⟨hal-00806905⟩