Stable sets of weak tournaments

Stable sets of weak tournaments

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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:
Keywords: tournament games
Abstract:

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.

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