# Fixing Knockout Tournaments With Seeds

arXiv: https://arxiv.org/abs/2204.11171 · HTML: https://mlsanity.com/paper/2204.11171/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2022.

## Built on by (most cited first, 1 of 1)

- [Parameterized Analysis of Bribery in Challenge the Champ Tournaments](https://mlsanity.com/paper/2403.17587/) (2024)

## Abstract (arXiv)

Knockout tournaments constitute a popular format for organizing sports competitions. While prior results have shown that it is often possible to manipulate a knockout tournament by fixing the bracket, these results ignore the prevalent aspect of player seeds, which can significantly constrain the chosen bracket. We show that certain structural conditions that guarantee that a player can win a knockout tournament without seeds are no longer sufficient in light of seed constraints. On the other hand, we prove that when the pairwise match outcomes are generated randomly, all players are still likely to be knockout winners under the same probability threshold with seeds as without seeds. In addition, we investigate the complexity of deciding whether a manipulation is possible when seeds are present.