2008/03/31 by Felix Brandt
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #Combinatorics #Computer science #Discrete mathematics #Economics #Game Theory and Voting Systems #Hierarchy #Mathematical economics #Mathematics #Peroxisome Proliferator-Activated Receptors #Set (abstract data type) #Solution set #Tournament #math.CO #msc:05C20 #msc:91B14
paper · pdf · doi:10.1016/j.jet.2011.05.004
published as Journal of Economic Theory 146(4), 2011 · 29 pages, 4 figures, changed content
arxiv created 2010/09/20 · openalex publication_date 2011/05/22 · arxiv updated 2015/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, which encompasses the top cycle, the uncovered set, the Banks set, the minimal covering set, the tournament equilibrium set, the Copeland set, and the bipartisan set. Moreover, the hierarchy includes a new tournament solution, the minimal extending set, which is conjectured to refine both the minimal covering set and the Banks set.