1975/05/01 by Willi Maurer · 1 citation
Computer Science · Decision Sciences · Mathematics · #Artificial Intelligence in Games #Data Management and Algorithms #Auction Theory and Applications #Tournament #Mathematics #Competitor analysis #Econometrics #Mathematical economics #Statistics #Marketing #Business #Combinatorics
paper · pdf · doi:10.1214/aos/1176343135
openalex publication_date 1975/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/26
Let Ωn denote a set of n players, pij the probability that player i defeats player j and Γ the class of preference matrices (pij) with p1j \geqq (1)/(2), j > 2. Under the assumption that the outcomes of games are independent and distributed according to (pij) ∈ Γ, the effectiveness (relative to (pij)) of a tournament plan, together with a rule to select a winner, is measured by the probability that player 1 (the "best" player) wins the tournament. A k.o. plan is a tournament plan in which a player is eliminated from the tournament if he loses one game. It is shown that there are no plans on Ωn with n - 1 games that are more effective than k.o. plans relative to all matrices contained in certain reasonable subclasses of Γ. Among the k.o. plans for 2m + k, 0 \leqq k < 2m, players, those which consist of a preliminary round of k games followed by a "symmetric" k.o. tournament on the remaining 2m players are more effective than all other plans relative to the preference matrices contained in two large subclasses of Γ. In order to prove these assertions, the tournament plans are interpreted as mappings with directed digraphs as domain and range.