Date of Award

Spring 6-3-2026

Document Type

Thesis (Undergraduate)

Department

Computer Science

First Advisor

Deeparnab Chakrabarty

Abstract

Knockout (or single game elimination) tournaments are a competition format widely used to determine a single winner from a pool of participants. However, the seeding, or the initial pairings set by the organizers of the tournament, can dramatically change each participant's probability of winning. This paper introduces stability as a property of tournaments. More specifically, a tournament is stable if no pair of players can be found such that they both wish to swap initial positions. This property is adapted from prior work on stable matchings and is therefore a well-defined structural property.

We investigate three theoretical questions on the existence, characterization, and universality of stable tournaments. We first show that under a general player strength model, a stable tournament is not always guaranteed to exist, even for tournaments as small as 4 players. We then ask what characteristics of the strength model guarantee stability. We show that an acyclicity condition is insufficient, and conjecture that a monotonic model guarantees the stability of the sorted seeding (which pairs adjacently ranked players in the first round). Our attempted proof reduces the monotonic case to bounding a certain ratio, which monotonicity alone fails to do, but is possible under the Bradley-Terry model. Thus, under a Bradley-Terry strength model, the sorted seeding is always stable. We also present some empirical findings, which show that the sorted seeding is stable under sampled monotonic and Bradley-Terry instances, and we find that the commonly used standard seeding model exhibits a low stability rate.

More broadly, this work introduces stability as a criterion for evaluating seedings in knockout tournaments, providing various stakeholders with an additional consideration with which they can evaluate knockout tournaments.

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