Authors: Michel Grabisch Lijue Xie
Publish Date: 2011/01/15
Volume: 73, Issue: 2, Pages: 189-208
Abstract
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 TUgames 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
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