The lattice of embedded subsets
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.
|Date of creation:||Mar 2010|
|Publication status:||Published in Discrete Applied Mathematics, Elsevier, 2010, 158 (5), pp.479-488. <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/|