Manipulating Single-Elimination Tournaments in the Braverman-Mossel Model

We study the power of a tournament organizer in manipulating the outcome of a single elimination tournament by fixing the initial seeding. It is not known whether the organizer can efficiently fix the outcome of the tournament even if the match outcomes are known in advance. We generalize a result from prior work by giving a new condition such that the organizer can efficiently find a tournament bracket for which the given player will win the tournament. We then use this result to show that for most tournament graphs generated by the Braverman-Mossel model, the tournament organizer can (very efficiently) make a large constant fraction of the players win, by manipulating the initial bracket. This holds for very low values of the error probability, i.e. the generated tournament graphs are almost transitive. Finally, we obtain a trade-off between the error probability and the number of players that can efficiently be made winners.