Maximizing Value in Challenge the Champ Tournaments

2025-02-18

AI Summary

This paper studies the spectator-value maximization problem under the “Challenge the Champ” single-elimination tournament format—i.e., sequencing challengers to maximize total match value (e.g., box-office revenue or viewership). We model选手 pairwise strength relations as a directed graph, where each edge encodes win-probability advantage; this representation unifies arbitrary strength structures, including non-DAG cases. We are the first to systematically extend value maximization to this format and provide a complete computational complexity classification across general match-value functions: polynomial-time algorithms exist for certain function classes, while most are NP-hard. For NP-hard cases, we devise exact algorithms and supply rigorous hardness proofs. Our key contribution is breaking prior structural constraints on the strength graph, establishing the first comprehensive complexity landscape framework applicable to *any* directed strength graph.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• Security and Privacy: Large-scale security measurements

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.

Problem

• Maximizing value in tournaments
• Optimizing player seeding for revenue
• Analyzing Challenge the Champ format

Innovation

• Challenge the Champ format
• Strength graph modeling
• Value maximization complexity