Article ID: | iaor20043719 |
Country: | Serbia |
Volume: | 14 |
Issue: | 1 |
Start Page Number: | 33 |
End Page Number: | 40 |
Publication Date: | Jan 2004 |
Journal: | Yugoslav Journal of Operations Research |
Authors: | Lahiri Somdeb |
Keywords: | tournament games |
In this paper we obtain conditions on weak tournaments, which guarantee that every non-empty subset of alternatives admits a stable set. We also show that there exists a unique stable set for each non-empty subset of alternatives which coincides with its set of best elements, if and only if, the weak tournament is quasi-transitive. A somewhat weaker version of this result, which is also established in this paper, is that there exists a unique stable set for each non-empty subset of alternatives (which may or may not coincide with its set of best elements), if and only if the weak tournament is acyclic.