Admissible Hierachic Sets

In this paper we present a solution concept for abstract systems called the admissible hierarchic set. The solution we propose is a refinement of the hierarchic solution, a generalization of the von Neumann and Morgenstern solution. For finite abstract systems we show that the admissible hierarchic sets and the von Neumann and Morgenstern stable sets are the only outcomes of a coalition formation procedure (Wilson, 1972 and Roth, 1984). For coalitional games we prove that the core is either a vN&M stable set or an admissible hierarchic set.