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

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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

Suggested Citation

  • Michel Grabisch & Lijue Xie, 2008. "The core of games on distributive lattices: how to share benefits in a hierarchy," Documents de travail du Centre d'Economie de la Sorbonne b08077, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Sep 2009.
    • Handle: RePEc:mse:cesdoc:b08077
    DOI: 10.1007/s00186-010-0341-2
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    Cited by:

    1. Michel Grabisch, 2011. "Ensuring the boundedness of the core of games with restricted cooperation," Annals of Operations Research, Springer, vol. 191(1), pages 137-154, November.
    2. Grabisch, Michel & Sudhölter, Peter, 2014. "On the restricted cores and the bounded core of games on distributive lattices," European Journal of Operational Research, Elsevier, vol. 235(3), pages 709-717.
    3. Michel Grabisch & Lijue Xie, 2011. "The restricted core of games on distributive lattices: how to share benefits in a hierarchy," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 189-208, April.
    4. repec:hal:pseose:halshs-00950109 is not listed on IDEAS
    5. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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