We study round-robin tournaments with either three or four symmetric players whose values of winning are common knowledge. In the round-robin tournament with three players there are three stages, each of which includes one match between two players. The player who wins in two matches wins the tournament. We characterize the sub-game perfect equilibrium and show that each player maximizes his expected payo¤ and his probability to win if he competes in the …rst and the last stages of the tournament. In the round-robin tournament with four players there are three rounds, each of which includes two sequential matches where each player plays against a di¤erent opponent in every round. We characterize the sub-game perfect equilibrium and show that a player who plays in the …rst match of each of the …rst two rounds has a …rst-mover advantage as re ‡ected by a signi…cantly higher winning probability as well as a signi…cantly higher expected payo¤ than his opponents.

Judo is a combat sport with seven different weight categories. In this article, we examined data from 1,902 men's and 1,400 women's fights at the eight most prestigious judo tournaments during the period 2010-2013. Using a single fight as the unit of observation, we found that the probability for the favorite to win against the underdog in the men's half-lightweight category is significantly lower than in most other categories. Moreover, in fights in which only European and/or Asian judokas participate, we found that the men's half-lightweight category is significantly more balanced than all other men's categories. For women, there is no consistent evidence that any one weight category is more balanced than any of the others. Our results indicate that in choosing the members of a national team, it is to some extent reasonable for national coaches to select a lower ranked judoka in the men's halflightweight category over a higher ranked judoka in several other weight categories. We also found that the home advantage increases the probability of winning a single fight for both genders. This result implies that it might be worthwhile for national judo associations to bid to host international tournaments in order to improve the world rankings of their domestic judokas.

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