Are sequential round-robin tournaments discriminatory?

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.