Are sequential round‐robin tournaments discriminatory?

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract I examine sequential round-robin tournaments with three and four symmetric players. Each player is matched once with each other player. If the matches are organized as Tullock contests (all-pay auctions), the tournament will be almost fair (highly discriminatory): subject to the position of their matches in the sequence of the tournament, the differences in players' ex-ante winning probabilities and expected payoffs will be small (large). The differing results originate from the higher discriminating power of the all-pay auction. Moreover, the resulting discouragement effect in tournaments with all-pay auctions implies lower aggregate effort than in tournaments with suitable Tullock contests. The fairness of round-robin tournaments may be improved by the use of an endogenous sequence of matches or the requirement that players fix their effort ex-ante. Terms of use: Documents in

Sequential round-robin tournaments with multiple prizes

“…2 The reason is a discouragement effect of trailing players that has been identified in most forms of dynamic contests (Konrad, 2009, Chapter 8). Sahm (2017) confirms this result for round-robin tournaments where each single match is organized as a Tullock contest. The extent of discrimination is, however, much smaller than with matches organized as all-pay auctions because the discouragement of trailing players in asymmetric intermediate stages is less pronounced due to the non-perfectly discriminating character of the Tullock contest.…”

“…0.3494 0.5000 0.6342 0.1239 0.2500 0.3674 0.2262 0.2500 0.2668 P2 0.3071 0.5000 0.6686 0.0978 0.2500 0.4161 0.2070 0.2500 0.2525 P3 0.3435 0.5000 0.6972 0.1181 0.2500 0.4547 0.2253 0.2500 0.2424 rel.SD 0.0561 0 0.0386 0.0988 0 0.0865 0.0387 0 0.0393 0.3398 0.7500 1.2383 0.6585 0.7500 0.7617 a lean-back effect. Without a second prize (a = 0), the player who skips the first match (player 3) has an (expected) disadvantage when he faces the winner of the first match that discourages him from exerting equivalent effort (Sahm, 2017). 8 Introducing a second prize mitigates this discouragement effect: With a second prize, the winner of the first match has a positive payoff even if he loses his next match and ranks second.…”

“…One reason for the popularity of round-robin tournaments might be the common wisdom that "a round-robin tournament is the fairest way to determine the champion among a known and fixed number of participants" (Wikipedia 1 , 2017). For tournaments for which the schedule of matches is sequential, however, this common wisdom is challenged by Krumer et al (2017a) and Sahm (2017). The authors investigate whether single-prize round-robin tournaments with three and four symmetric players are fair with respect to ex-ante winning probabilities and expected payoffs.…”

“…In many real world tournaments, such as the group stage of the FIFA World Cup where two teams earn a spot in the next round, the assumption of a single prize seems too narrow because the players have a positive valuation not only for ranking first. In this paper we therefore revisit the analysis of Krumer et al (2017a) and Sahm (2017) on the fairness of sequential round-robin tournaments with three and four players under the assumption of multiple prizes.…”

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

“…Third, it is almost impossible to adequately address all issues influencing match outcomes. For instance, the schedule of round-robin tournaments may result in a substantial advantage for some contestants as recent analytical (Krumer et al, 2017a(Krumer et al, , 2020Sahm, 2019) and empirical works (Krumer & Lechner, 2017) show. Similarly, even the kick-off time can affect various aspects of games such as the home advantage of the underdog team (Krumer, 2020).…”