Sequential round-robin tournaments with multiple prizes

• 成果类型: Article
• 署名作者: Laica, Christoph; Lauber, Arne; Sahm, Marco
• 署名单位: Otto Friedrich University Bamberg; Leibniz Association; Ifo Institut
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2021.06.012
• 发表日期: 2021
• 页码: 421-448
• 关键词: Round-robin tournament; Multiple prizes; fairness; intensity; Tullock contest; all-pay auction

摘要

We examine the fairness and intensity of sequential round-robin tournaments with multiple prizes and heterogeneous players. A tournament is called fair if the winning probabilities in each match depend only on the players' characteristics but not on the sequence of matches. We show that tournaments with three players will be fair if and only if the second prize is valued half of the first prize. The optimal prize structure may, however, be subject to a trade-off between fairness and intensity (measured by the players' expected aggregate effort). By contrast, there is no prize structure for which tournaments with more than three players will be fair if the sequence of matches is exogenously fixed. Our analysis suggests that many tournaments of major sporting events are inherently unfair. (C) 2021 Elsevier Inc. All rights reserved.