Geodesic
Stable Sets of Weak Tournaments
Yugoslav journal of operations research, Tome 14 (2004) no. 1, p. 33 .

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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.
Classification : 91B14
Keywords: Stable sets, weak tournaments, acyclic, quasi-transitive. 
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     author = {Somdeb Lahiri},
     title = {Stable {Sets} of {Weak} {Tournaments}},
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     year = {2004},
     zbl = {1058.91023},
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     url = {http://geodesic.mathdoc.fr/item/YJOR_2004_14_1_a3/}
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Somdeb Lahiri. Stable Sets of Weak Tournaments. Yugoslav journal of operations research, Tome 14 (2004) no. 1, p. 33 . http://geodesic.mathdoc.fr/item/YJOR_2004_14_1_a3/