Tournament Robustness via Redundancy

2025-06-04

AI Summary

This paper studies the robustness of single-elimination tournaments against outcome manipulation: given $n$ players and a bounded number of allowable adversarial interventions, with a unique (identity-unknown) strongest player who dominates all others, the goal is to design a tournament structure that guarantees the strongest player’s victory even when up to one-third of the edges along every root-to-leaf path are maliciously corrupted. The work establishes a novel theoretical connection between tournament robustness and feedback-based communication protocols, and introduces a redundancy-tree coding framework to overcome the fragility inherent in single-path tournament structures. Using combinatorial game modeling, adversarial noise analysis, and path-wise fault-tolerance arguments, it achieves strict $1/3$-path corruption tolerance within polynomial-size tournaments. The paper provides tight upper and lower bounds on robustness and constructs explicit, efficiently realizable tournament designs.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Adversarial Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

A knockout tournament is one of the most simple and popular forms of competition. Here, we are given a binary tournament tree where all leaves are labeled with seed position names. The players participating in the tournament are assigned to the seed positions. In each round, the two players assigned to leaves of the tournament tree with a common parent compete, and the winner is promoted to the parent. The last remaining player is the winner of the tournament. In this work, we study the problem of making knock-out tournaments robust against manipulation, where the form of manipulation we consider is changing the outcome of a game. We assume that our input is only the number of players that compete in the tournament, and the number of manipulations against which the tournament should be robust. Furthermore, we assume that there is a strongest player, that is, a player that beats any of the other players. However, the identity of this player is not part of the problem input. To ensure robustness against manipulation, we uncover an unexpected connection between the problem at hand and communication protocols that utilize a feedback channel, offering resilience against adversarial noise. We explore the trade-off between the size of the robust tournament tree and the degree of protection against manipulation. Specifically, we demonstrate that it is possible to tolerate up to a $1/3$ fraction of manipulations along each leaf-to-root path, at the cost of only a polynomial blow-up in the tournament size.

Problem

• Ensuring knockout tournament robustness against match outcome manipulation
• Designing tournaments resilient to adversarial changes in game results
• Balancing tournament size and manipulation protection trade-offs effectively

Innovation

• Redundant tournament trees for robustness
• Feedback channel inspired resilience technique
• Polynomial size increase for manipulation tolerance