  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.
