caa a22 4500 445839783 CHVBK 20180317145340.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00186-010-0341-2 doi (NATIONALLICENCE)springer-10.1007/s00186-010-0341-2 The restricted core of games on distributive lattices: how to share benefits in a hierarchy [Elektronische Daten] [Michel Grabisch, Lijue Xie] Finding a solution concept is one of the central problems in cooperative game theory, and the notion of core is the most popular solution concept since it is based on some rationality condition. In many real situations, not all possible coalitions can form, so that classical TU-games cannot be used. An interesting case is when possible coalitions are defined through a partial ordering of the players (or hierarchy). Then feasible coalitions correspond to teams of players, that is, one or several players with all their subordinates. In these situations, the core in its usual formulation may be unbounded, making its use difficult in practice. We propose a new notion of core, called the restricted core, which imposes efficiency of the allocation at each level of the hierarchy, is always bounded, and answers the problem of sharing benefits in a hierarchy. We show that the core we defined has properties very close to the classical case, with respect to marginal vectors, the Weber set, and balancedness. Springer-Verlag, 2011 Cooperative game nationallicence Feasible coalition nationallicence Core nationallicence Hierarchy nationallicence Grabisch Michel Paris School of Economics, University of Paris I—Panthéon-Sorbonne, 106-112, Bd de l'Hôpital, 75013, Paris, France aut Xie Lijue Centre d'Economie de la Sorbonne, University of Paris I—Panthéon-Sorbonne, 106-112, Bd de l'Hôpital, 75013, Paris, France aut Mathematical Methods of Operations Research Springer-Verlag 73/2(2011-04-01), 189-208 1432-2994 73:2<189 2011 73 186 https://doi.org/10.1007/s00186-010-0341-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00186-010-0341-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Grabisch Michel Paris School of Economics, University of Paris I—Panthéon-Sorbonne, 106-112, Bd de l'Hôpital, 75013, Paris, France aut NATIONALLICENCE 700 1- Xie Lijue Centre d'Economie de la Sorbonne, University of Paris I—Panthéon-Sorbonne, 106-112, Bd de l'Hôpital, 75013, Paris, France aut NATIONALLICENCE 773 0- Mathematical Methods of Operations Research Springer-Verlag 73/2(2011-04-01), 189-208 1432-2994 73:2<189 2011 73 186 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer