# The lattice of embedded subsets

## Author Info

• Michel Grabisch

()

(CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

## 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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File URL: https://hal.archives-ouvertes.fr/hal-00457827/document

## 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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 Length: Date of creation: Mar 2010 Date of revision: Publication status: Published in Discrete Applied Mathematics, Elsevier, 2010, 158 (5), pp.479-488. <10.1016/j.dam.2009.10.015> Handle: RePEc:hal:cesptp:hal-00457827 DOI: 10.1016/j.dam.2009.10.015 Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00457827 Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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