THE NUMBER OF POTENTIAL WINNERS IN BRADLEY-TERRY MODEL IN RANDOM ENVIRONMENT

• 成果类型: Article
• 署名作者: Chetrite, Raphael; Diel, Roland; Lerasle, Matthieu
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Ton Duc Thang University; Ton Duc Thang University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1231
• 发表日期: 2017
• 页码: 1372-1394
• 关键词: paired-comparison experiments; TIES

摘要

We consider a Bradley-Terry model in random environment where each player faces each other once. More precisely, the strengths of the players are assumed to be random and we study the influence of their distributions on the asymptotic number of potential winners. First, we prove that under moment and convexity conditions, the asymptotic probability that the best player wins is 1. The convexity condition is natural when the distribution of strengths is unbounded and, in the bounded case, when this convexity condition fails the number of potential winners grows at a rate depending on the tail of the distribution. We also study the minimal strength required for an additional player to win in this last case.