Maximizing Value in Challenge the Champ Tournaments

TL;DR

This paper explores how to maximize the overall value generated in Challenge the Champ tournaments by analyzing different match representations and the complexity of optimizing player sequences.

Contribution

It extends previous work on value maximization from DAGs to general strength graphs in Challenge the Champ tournaments, providing complexity characterizations.

Findings

Characterizes the computational complexity of value maximization.

Extends analysis from DAGs to general strength graphs.

Provides insights into match value representations.

Abstract

A tournament is a method to decide the winner in a competition, and describes the overall sequence in which matches between the players are held. While deciding a worthy winner is the primary goal of a tournament, a close second is to maximize the value generated for the matches played, with value for a match measured either in terms of tickets sold, television viewership, advertising revenue, or other means. Tournament organizers often seed the players -- i.e., decide which matches are played -- to increase this value. We study the value maximization objective in a particular tournament format called Challenge the Champ. This is a simple tournament format where an ordering of the players is decided. The first player in this order is the initial champion. The remaining players in order challenge the current champion; if a challenger wins, she replaces the current champion. We model the outcome of a match between two players using a complete directed graph, called a strength graph, with each player represented as a vertex, and the direction of an edge indicating the winner in a match. The value-maximization objective has been recently explored for knockout tournaments when the strength graph is a directed acyclic graph (DAG). We extend the investigation to Challenge the Champ tournaments and general strength graphs. We study different representations of the value of each match, and completely characterize the computational complexity of the problem.