The core of games on distributive lattices: how to share benefits in a hierarchy

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2008.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2008.77 - ISSN : 1955-611XFinding 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, it is not obvious to define a suitable notion of core, reflecting the team structure, and previous attempts are not satisfactory in this respect. We propose a new notion of core, which imposes efficiency of the allocation at each level of the hierarchy, 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.Trouver un concept de solution est un des problèmes centraux en théorie des jeux coopératifs, et la notion de coeur est le concept de solution le plus populaire. Dans beaucoup de situations, toutes les coalitions ne peuvent se former. Un exemple intéressant est quand les coalitions possibles sont définies à travers un ordre partiel sur les joueurs (hiérarchie). Nous proposons une notion de coeur pour cette situation