Stable Sets of Weak Tournaments
U of Witwatersrand at Johannesburg, School of Economic and Business Sciences Working Paper
8 Pages Posted: 28 Feb 2003
There are 2 versions of this paper
Stable Sets of Weak Tournaments
Stable Sets of Weak Tournaments
Date Written: March 2003
Abstract
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.
Keywords: stable sets, core
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