A computational analysis of the tournament equilibrium set

Authors:
Felix Brandt;Felix Fischer;Paul Harrenstein;Maximilian Mair
Affiliations:
Institut für Informatik, Universität München, Germany;Institut für Informatik, Universität München, Germany;Institut für Informatik, Universität München, Germany;Mathematisches Institut, Universität München, Germany
Venue:
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Year:
2008

Citing 7
Cited 1

Introduction to algorithms

Introduction to algorithms
On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games

Artificial Intelligence
Computational properties of argument systems satisfying graph-theoretic constraints

Artificial Intelligence
The computational complexity of choice sets

TARK '07 Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge
Computing slater rankings using similarities among candidates

AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Improved bounds for computing Kemeny rankings

AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Computational aspects of covering in dominance graphs

AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1

Nonmanipulable selections from a tournament

IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence

Quantified Score

Hi-index	0.00

Visualization

Abstract

A recurring theme in AI and multiagent systems 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 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 to date. Yet, if TEQ were to satisfy monotonicity, it would be a very attractive 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. Furthermore, we propose a heuristic that significantly outperforms the naive algorithm for computing TEQ. Early experimental results support the conjecture that TEQ is indeed monotonic.