On the vertices of the k-additive core

dc.contributor.authorGrabisch, Michel
dc.contributor.authorMiranda Menéndez, Pedro
dc.description.abstractThe 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.
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
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dc.journal.titleDiscrete Mathematics
dc.publisherElsevier Science
dc.rights.accessRightsrestricted access
dc.subject.keywordCooperative games
dc.subject.keywordk-additive games
dc.subject.ucmTeoría de Juegos
dc.subject.unesco1207.06 Teoría de Juegos
dc.titleOn the vertices of the k-additive core
dc.typejournal article
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