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

Michel Grabisch and Lijue Xie ()
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Lijue Xie: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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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 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.

Keywords: hierarchy; Cooperative game; feasible coalition; core; Jeu coopératif; coalition réalisable; coeur; hiérarchie (search for similar items in EconPapers)
Date: 2008-10
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00344802v2
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Citations: View citations in EconPapers (10)

Published in 2008

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Related works:
Working Paper: The core of games on distributive lattices: how to share benefits in a hierarchy (2009)
Working Paper: The core of games on distributive lattices: how to share benefits in a hierarchy (2008)
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