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The lattice of embedded subsets

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  • Michel Grabisch

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

Abstract

In cooperative game theory, games in partition function form are real-valued function on the set of so-called embedded coalitions, that is, pairs $(S,\pi)$ where $S$ is a subset (coalition) of the set $N$ of players, and $\pi$ is a partition of $N$ containing $S$. Despite the fact that many studies have been devoted to such games, surprisingly nobody clearly defined a structure (i.e., an order) on embedded coalitions, resulting in scattered and divergent works, lacking unification and proper analysis. The aim of the paper is to fill this gap, thus to study the structure of embedded coalitions (called here embedded subsets), and the properties of games in partition function form.

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number hal-00457827.

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Date of creation: Mar 2010
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Publication status: Published, Discrete Applied Mathematics, 2010, 158, 5, 479-488
Handle: RePEc:hal:cesptp:hal-00457827

Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00457827
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Related research

Keywords: Partition; Embedded subset; Game; Valuation; k-monotonicity;

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Cited by:
  1. Michel Grabisch & Yukihiko Funaki, 2012. "A coalition formation value for games in partition function form," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00690696, HAL.
  2. repec:hal:journl:halshs-00690696 is not listed on IDEAS

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