A note on generalized stable sets

A solution concept is introduced that is able to deal with cyclic relations. The concept is a generalization of the Von Neumann-Morgenstern solution concept of stable set and is therefore called the concept of generalized stable set. Its point of departure is the transitive closure of an asymmetric relation. A characterization theorem and an existence theorem are presented.The author would like to thank Thom Bezembinder, Maurice Salles and Harrie de Swart for their useful comments.