Stable sets of weak tournaments
DOI:
https://doi.org/10.2298/YJOR0401033LKeywords:
stable sets, weak tournaments, acyclic, quasi-transitiveAbstract
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.References
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