Everyone Contributes! Incentivizing Strategic Cooperation in Multi-LLM Systems via Sequential Public Goods Games

• URL: http://arxiv.org/abs/2508.02076v1
• Date: Mon, 04 Aug 2025 05:36:07 GMT
• Title: Everyone Contributes! Incentivizing Strategic Cooperation in Multi-LLM Systems via Sequential Public Goods Games
• Authors: Yunhao Liang, Yuan Qu, Jingyuan Yang, Shaochong Lin, Zuo-Jun Max Shen,
• Abstract summary: Multi-Agent Cooperation Sequential Public Goods Game (MAC-SPGG)<n>We introduce a novel, game-theoretically grounded reinforcement learning framework, to systematically incentivize cooperation in multi-LLM ensembles.<n>Our results highlight the power of structured, incentive-aligned MAC-SPGG cooperation for scalable and robust multi-agent language generation.
• Score: 4.3891974840097925
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Coordinating multiple large language models (LLMs) to solve complex tasks collaboratively poses a fundamental trade-off between the computation costs and collective performance compared with individual model. We introduce a novel, game-theoretically grounded reinforcement learning (RL) framework, the Multi-Agent Cooperation Sequential Public Goods Game (MAC-SPGG), to systematically incentivize cooperation in multi-LLM ensembles. In MAC-SPGG, LLM agents move in sequence, observing predecessors' outputs and updating beliefs to condition their own contributions. By redesigning the public-goods reward, effortful contributions become the unique Subgame Perfect Nash Equilibrium (SPNE), which eliminates free-riding under traditional SPGG or PGG. Its sequential protocol replaces costly round-based information exchanges with a streamlined decision flow, cutting communication overhead while retaining strategic depth. We prove the existence and uniqueness of the SPNE under realistic parameters, and empirically show that MAC-SPGG-trained ensembles outperform single-agent baselines, chain-of-thought prompting, and other cooperative methods, even achieving comparable performance to large-scale models across reasoning, math, code generation, and NLP tasks. Our results highlight the power of structured, incentive-aligned MAC-SPGG cooperation for scalable and robust multi-agent language generation.

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