2007/11/30 by Felix Brandt, Felix Fischer, Paul Harrenstein +1 · 48 citations
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Combinatorics #Computer science #Economics #Game Theory and Applications #Game Theory and Voting Systems #International political economy #Law #Logic, Reasoning, and Knowledge #Macroeconomics #Mathematical economics #Mathematics #Political science #Public finance #Set (abstract data type) #Tournament #cs.CC #cs.GT #cs.MA
paper · pdf · doi:10.1007/s00355-009-0419-z
published in Social Choice and Welfare 34(4), 597-609 (Springer Science+Business Media) · 9 pages, 3 figures
arxiv created 2008/01/07 · openalex publication_date 2009/09/09 · arxiv updated 2015/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.