Tournament Robustness via Redundancy

TL;DR

This paper investigates making knockout tournaments resistant to manipulation by changing game outcomes, revealing a connection to communication protocols with feedback channels and analyzing the trade-offs between robustness and tournament size.

Contribution

It introduces a novel approach linking tournament robustness to communication protocols, providing bounds on robustness against manipulations with polynomial size increases.

Findings

Robust tournament structures can tolerate up to 1/3 manipulation along each path.

A polynomial increase in tournament size achieves significant robustness.

A new connection between tournament manipulation and feedback communication protocols.

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.