On vertices of the k-additive monotone core

Abstract

Given a capacity, the set of dominating k-additive capacities is a convex polytope; 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 k-additive monotone core. Then, we characterize the vertices of the n-additive core and finally, we explore the possible translations for the k-additive case