A clutter on a set X is a simple hypergraph with pairwise not-comparable hyperedges, hence in particular any set of Von Neumann-Morgenstern (VNM) -stable sets of an irreflexive simple digraph is a clutter. A clutter (X,E) is representable by VNM-stable sets or VNM if there exists an irreflexive...

Characterizations of the choice functions that select the cores or the externally stable cores induced by an underlying revealed dominance digraph are provided. Relying on such characterizations, the basic order-theoretic structure of the corresponding sets of revealed cores is also analyzed