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The core of games on ordered structures and graphs

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  • Michel Grabisch

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In many situations, this assumption is too strong and one has to deal with some unfeasible coalitions. Defining a game on a subcollection of the power set of the set of players has many implications on the mathematical structure of the core, depending on the precise structure of the subcollection of feasible coalitions. Many authors have contributed to this topic, and we give a unified view of these different results.

Suggested Citation

  • Michel Grabisch, 2013. "The core of games on ordered structures and graphs," PSE - Labex "OSE-Ouvrir la Science Economique" hal-00803233, HAL.
    • Handle: RePEc:hal:pseose:hal-00803233
    DOI: 10.1007/s10479-012-1265-4
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    Keywords

    TU-game; Solution concept; Core; Feasible coalition; Communication graph; Partially ordered set;
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