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Stable Sets of Weak Tournaments

Somdeb Lahiri (lahiris***at***sebs.wits.ac.za)

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

Category 1: Other Topics (Game Theory )

Category 2: Applications -- OR and Management Sciences (Other )

Category 3: Other Topics (Multi-Criteria Optimization )

Citation: School of Economic and Business Sciences, University of Witwatersrand at Johannesburg, South Africa March 2003.

Download: [PDF]

Entry Submitted: 03/09/2003
Entry Accepted: 03/11/2003
Entry Last Modified: 04/17/2003

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