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The core of games on k-regular set systems

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Abstract

In the classical setting of cooperative game theory, it is always assumed that all coalitions are feasible. However in many real situations, there are restrictions on the set of coalitions, for example duo to communication, order or hierarchy on the set of players, etc. There are already many works dealing with games on restricted set of coalitions, defining many different structures for the set of feasible coalitions, called set systems. We propose in this paper to consider k-regular set systems, that is, set systems having all maximal chains of the same length k. This is somehow related to communication graphs. We study in this perspective the core of games defined on k-regular set systems. We show that the core may be unbounded and without vertices in some situations

Suggested Citation

  • Lijue Xie & Michel Grabisch, 2009. "The core of games on k-regular set systems," Documents de travail du Centre d'Economie de la Sorbonne 09055, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2009.
    • Handle: RePEc:mse:cesdoc:09055
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    1. Hans Reijnierse & Jean Derks, 1998. "Note On the core of a collection of coalitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 451-459.
    2. Honda, Aoi & Grabisch, Michel, 2008. "An axiomatization of entropy of capacities on set systems," European Journal of Operational Research, Elsevier, vol. 190(2), pages 526-538, October.
    3. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    4. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 249-266.
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    2. 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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    More about this item

    Keywords

    Cooperative game; feasible coalition; core;
    All these keywords.

    JEL classification:

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

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