Recognizing Members of the Tournament Equilibrium Set is NP-hard

Abstract

A recurring theme in the mathematical social sciences is how to select the "most desirable" elements given a binary dominance relation on a set of alternatives. Schwartz's tournament equilibrium set (TEQ) ranks among the most intriguing, but also among the most enigmatic, tournament solutions that have been proposed so far in this context. Due to its unwieldy recursive definition, little is known about TEQ. In particular, its monotonicity remains an open problem up to date. Yet, if TEQ were to satisfy monotonicity, it would be a very attractive tournament solution concept refining both the Banks set and Dutta's minimal covering set. We show that the problem of deciding whether a given alternative is contained in TEQ is NP-hard.

9 pages, 3 figures

Cited by in corpus (6)

• Minimal Stable Sets in Tournaments
• On the Structure of Stable Tournament Solutions
• A tournament of order 24 with two disjoint TEQ-retentive sets
• Approval Voting with Intransitive Preferences
• A Further Step Towards an Understanding of the Tournament Equilibrium Set
• The Complexity of Computing Minimal Unidirectional Covering Sets