The purpose of this paper is to obtain conditions on weak tournaments, which guarantee that every non-empty subset of alternatives admits a stable set. We show that every stable set always contains the core. We also show that there exists a unique stable set for each non-empty subset of alternatives which coincides with its core if and only if the weak tournament is quasi-transitive. However, a unique stable set exists for each non-empty subset of alternatives (: which may or may not coincide with its core) if and only if the weak tournament is acyclic.
School of Economic and Business Sciences, University of Witwatersrand at Johannesburg, South Africa March 2003.