How complex are multi-agent decisions?
Computational Social Choice: Parameterized Complexity and Challenges
October 21, 2024
https://arxiv.org/pdf/2410.14078This paper explores the computational complexity of two key problems in multi-agent AI systems: multi-winner determination (finding optimal subsets of agents based on preferences) and hedonic games (forming stable coalitions of agents based on their preferences). The paper examines different algorithms and their efficiency depending on the type and structure of agent preferences, specifically those based on rankings, approvals, friends, or enemies.
Key insights relevant to LLM-based multi-agent systems:
- Determining optimal agent groups or committees based on LLM-generated preferences can be computationally challenging, especially with complex preference structures.
- Different algorithms for multi-winner determination, like the Chamberlin-Courant rule, may be suitable for LLM-based systems depending on the desired outcome and preference representation.
- The paper highlights the importance of finding efficient algorithms when dealing with large-scale multi-agent systems, as brute-force approaches become computationally infeasible.
- The "friends and enemies" model for hedonic games provides a simplified framework for LLMs to express preferences, potentially enabling the development of more efficient coalition formation algorithms.
- Parameterized complexity analysis, as used in the paper, can help identify tractable instances and guide the design of efficient algorithms for LLM-based multi-agent systems.