A Computational Analysis of the Tournament Equilibrium Set

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.

Authors

• Felix Brandt Technical University of Munich
• Paul Harrenstein

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