 On a class of vertices of the coreMichel Grabisch and Peter Sudhölter No 5/2016, Discussion Papers on Economics from University of Southern Denmark, Department of Economics Abstract: It is known that for supermodular TU-games, the vertices of the core are the marginal vectors, and this result remains true for games where the set of feasible coalitions is a distributive lattice. Such games are induced by a hierarchy (partial order) on players. We propose a larger class of vertices for games on distributive lattices, called min-max vertices, obtained by minimizing or maximizing in a given order the coordinates of a core element. We give a simple formula which does not need to solve an optimization problem to compute these vertices, valid for connected hierarchies and for the general case under some restrictions. We find under which conditions two different orders induce the same vertex for every game, and show that there exist balanced games whose core has vertices which are not min-max vertices if and only if n > 4. Keywords: TU games; restricted cooperation; game with precedence constraints; core; vertex (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hhs:sdueko:2016_005 Access Statistics for this paper More papers in Discussion Papers on Economics from University of Southern Denmark, Department of Economics Department of Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark. Contact information at EDIRC. |
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