Fairness in Round-Robin Tournaments with Four Players and Endogenous Sequences

We examine the effects of endogenous sequences on fairness in round-robin tournaments with four players, multiple prizes, and general contest technologies. A tournament is called horizontally ex-ante fair if symmetric contestants have the same expected payoffs when the tournament starts, independent from their position in the schedule. It is called perfectly fair if the winning probabilities in each match depend only on the players’ characteristics but not on the position of the match in the course of the tournament. We show that there is no sequence that implies perfect fairness. By contrast, some endogenous sequences imply horizontal ex-ante fairness irrespective of the prize structure. In winner-take-all tournaments, additional endogenous sequences are horizontally ex-ante fair. Our findings question the prevalent use of exogenous sequences in four-player round-robin tournaments in commercial sports despite the existence of horizontally ex-ante fair alternatives.