The lattice of embedded subsets Original Research Article

In cooperative game theory, games in partition function form are real-valued function on the set of the so-called embedded coalitions, that is, pairs image where image is a subset (coalition) of the set image of players, and image is a partition of image containing image. 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.