Round‐Robin Tournaments with a Dominant Player

Abstract

We analyze the subgame perfect equilibrium of the round‐robin tournament with one strong (dominant) and two weak players, and we compare this tournament and the one‐stage contest with respect to the players' expected payoffs, expected total effort, and their probabilities of winning. We find that if the contest designer's goal is to maximize the players' expected total effort, then – if the asymmetry between the players is relatively low – the one‐stage contest should be used. However, if the asymmetry is relatively high, then the round‐robin tournament should be used.

Are sequential round‐robin tournaments discriminatory?

“…One might thus additionally require some kind of vertical fairness: a player who is stronger (due to higher ability or higher valuation of the prize) should have a higher ex ante winning probability and expected payoff. The analysis of Krumer, Megidish, and Sela () suggests that most results on discrimination in round‐robin tournaments with symmetric players will also hold with asymmetric players.…”

Optimal Tournament Design: Lessons From the Men’s Handball Champions League

“…It should be recognized that there are always some unavoidable trade-offs between the goals of a tournament designer, and they cannot be achieved simultaneously as recent theoretical results show (Krumer et al, 2017b). For example, while format Dð8 þ 6Þ is better at selecting stronger teams to be the winner, decreasing the chances that a weaker team plays against a stronger one can be detrimental for gradually improving the squad of the former.…”

Format and schedule proposals for a FIFA World Cup with 12 four-team groups

“…This paper belongs to a large literature on tournament design of sports competitions that can be found in many academic fields such as economics, operational research, computer and sport sciences. Previous studies have investigated various issues related to tournament design such as collusion (Duggan & Levitt, 2002;Elaad et al, 2018;Guyon, 2018), incentives to lose (Csato, 2019;Csato, 2020a;Csato, 2020b;Csato, 2022;Dagaev & Sonin, 2018;Guyon, 2022;Haugen & Krumer, 2021;Vong, 2017), scheduling (Alarcón et al, 2017;Durán et al, 2017;Goller & Krumer, 2020;Ermakov & Krumer, 2022;Krumer, 2020;Krumer et al, 2017a;Krumer & Lechner, 2017;Scoppa, 2015;Van Bulck et al, 2019), optimal seeding (Cea et al, 2020;Guyon, 2015;Groh et al, 2012;Krumer et al, 2017b;Nissim & Sela, 2020;Sziklai et al, 2022), tie-breaking rules (Berker, 2014), number of prizes (Krumer et al, 2020), number of teams in the tournament (Di Mattia & Krumer, 2023), etc. 6 This paper also relates to a growing literature on the 2026 FWC.…”