用博弈论让多个大模型高效协作，推理更准且省资源。
From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium
- 将多模型协作建模为不完全信息博弈，求解贝叶斯纳什均衡。
- 在6个基准上平均提升11.2%，且理论证明后悔界更优。
- 无需频繁通信，支持灵活扩展模型，适合复杂任务场景。
多智能体框架可显著提升大语言模型（LLM）的推理能力，但通常计算开销大且缺乏收敛保证。为此，本文将多LLM协调问题重新建模为不完全信息博弈，并寻求贝叶斯纳什均衡（BNE），其中每个智能体基于对其他智能体策略的信念进行最优响应。我们提出高效协同的纳什均衡方法（ECON），一种分层强化学习范式，融合分布式推理与集中式最终输出。在ECON中，每个LLM独立选择最大化其期望奖励的响应，条件是其对协作者策略的信念，无需高昂的智能体间通信。数学上证明，ECON的后悔界显著优于非均衡多智能体方案。实证显示，ECON在涵盖复杂推理与规划任务的六个基准上，平均性能提升11.2%。进一步实验表明，ECON可灵活集成更多模型，验证其可扩展性，为构建更大更强的多LLM集合铺平道路。代码已公开：https://github.com/tmlr-group/ECON。
原文摘要 · Abstract (English)
Multi-agent frameworks can substantially boost the reasoning power of large language models (LLMs), but they typically incur heavy computational costs and lack convergence guarantees. To overcome these challenges, we recast multi-LLM coordination as an incomplete-information game and seek a Bayesian Nash equilibrium (BNE), in which each agent optimally responds to its probabilistic beliefs about the strategies of others. We introduce Efficient Coordination via Nash Equilibrium (ECON), a hierarchical reinforcement-learning paradigm that marries distributed reasoning with centralized final output. Under ECON, each LLM independently selects responses that maximize its expected reward, conditioned on its beliefs about co-agents, without requiring costly inter-agent exchanges. We mathematically prove that ECON attains a markedly tighter regret bound than non-equilibrium multi-agent schemes. Empirically, ECON outperforms existing multi-LLM approaches by 11.2% on average across six benchmarks spanning complex reasoning and planning tasks. Further experiments demonstrate ECON's ability to flexibly incorporate additional models, confirming its scalability and paving the way toward larger, more powerful multi-LLM ensembles. The code is publicly available at: https://github.com/tmlr-group/ECON.
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