# The lattice of embedded subsets

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.
Keywords :
Document type :
Journal articles
Domain :

Cited literature [21 references]

https://hal.archives-ouvertes.fr/hal-00457827
Contributor : Michel Grabisch <>
Submitted on : Friday, February 19, 2010 - 6:01:37 PM
Last modification on : Tuesday, March 27, 2018 - 11:48:05 AM
Long-term archiving on : Friday, June 18, 2010 - 9:21:17 PM

### Files

dam09.pdf
Files produced by the author(s)

### Citation

Michel Grabisch. The lattice of embedded subsets. Discrete Applied Mathematics, Elsevier, 2010, 158 (5), pp.479-488. ⟨10.1016/j.dam.2009.10.015⟩. ⟨hal-00457827⟩

Record views