The lattice of embedded subsets

Michel Grabisch (1)

1 CES - Centre d'économie de la Sorbonne

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.

Mots clés: Partition; Embedded subset; Game; Valuation; k-monotonicity

Domaines: Mathématique discrète [cs.DM]; Informatique et théorie des jeux [cs.GT]; Economies et finances

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