RT Journal Article T1 On the vertices of the k-additive core A1 Grabisch, Michel A1 Miranda Menéndez, Pedro AB The core of a game upsilon on N, which is the set of additive games phi dominating upsilon such that phi(N) = upsilon(N), is a central notion in cooperative game theory, decision making and in combinatorics, where it is related to submodular functions, matroids and the greedy algorithm. In many cases however, the core is empty, and alternative solutions have to be found. We define the k-additive core by replacing additive games by k-additive games in the definition of the core, where k-additive games are those games whose Mobius transform vanishes for subsets of more than k elements. For a sufficiently high value of k, the k-additive core is nonempty, and is a convex closed polyhedron. Our aim is to establish results similar to the classical results of Shapley and Ichiishi on the core of convex games (corresponds to Edmonds' theorem for the greedy algorithm). which characterize the vertices of the core. PB Elsevier Science SN 0012-365X YR 2008 FD 2008 LK https://hdl.handle.net/20.500.14352/50183 UL https://hdl.handle.net/20.500.14352/50183 LA eng DS Docta Complutense RD 29 abr 2025