How to optimize Challenge the Champ tournament seeding?
Maximizing Value in Challenge the Champ Tournaments
February 19, 2025
https://arxiv.org/pdf/2502.12569This paper explores how to maximize "value" in "Challenge the Champ" tournaments, a simplified tournament format where a champion is challenged by a sequence of contenders. "Value" can represent ticket sales, viewership, or other metrics. The paper analyzes the computational complexity of finding the optimal seeding (order of challengers) to maximize value under different value functions, including those based on player popularity, win counts, and pairwise match values.
For LLM-based multi-agent systems, this research offers insights into:
- Agent Sequencing/Scheduling: The "seeding" problem is analogous to finding the optimal order for LLMs to interact in a collaborative or competitive setting.
- Value Functions: The various value functions explored (popularity, win-count, pairwise) provide a framework for defining success in multi-agent scenarios. For example, "popularity" could translate to an LLM's persuasiveness or knowledge base, influencing the outcome of interactions.
- Computational Complexity: The hardness results presented highlight the potential difficulties in finding optimal solutions for agent coordination, emphasizing the need for heuristics or approximations in practical LLM-based multi-agent applications. Especially interesting is that maximizing value in Challenge the Champ tournaments is, at times, more computationally complex than maximizing value in knockout tournaments, despite the seemingly simpler structure of the former. This suggests that even minor changes in interaction structures can significantly impact the difficulty of optimization problems in multi-agent systems.