Manipulating Tournaments in Cup and Round Robin Competitions

TL;DR

This paper demonstrates that manipulating outcomes in popular sports tournaments like round robin and cup competitions can be decided and optimized efficiently using polynomial-time algorithms.

Contribution

It provides polynomial-time algorithms for deciding and minimizing manipulation in various tournament formats, extending to several variations of cup competitions.

Findings

Manipulation decision problem is solvable in polynomial time.

Minimal manipulation required can be computed efficiently.

Manipulation remains polynomial in several tournament variations.

Abstract

In sports competitions, teams can manipulate the result by, for instance, throwing games. We show that we can decide how to manipulate round robin and cup competitions, two of the most popular types of sporting competitions in polynomial time. In addition, we show that finding the minimal number of games that need to be thrown to manipulate the result can also be determined in polynomial time. Finally, we show that there are several different variations of standard cup competitions where manipulation remains polynomial.