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

arXiv: https://arxiv.org/abs/2508.02076 · HTML: https://mlsanity.com/paper/2508.02076/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 67 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Builds on (most cited first, 30 of 34)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [SummEval: Re-evaluating Summarization Evaluation](https://mlsanity.com/paper/2007.12626/) (2020)
- [Why Do Multi-Agent LLM Systems Fail?](https://mlsanity.com/paper/2503.13657/) (2025)
- [AgentVerse: Facilitating Multi-Agent Collaboration and Exploring Emergent Behaviors](https://mlsanity.com/paper/2308.10848/) (2023)
- [Multi-Agent Collaboration Mechanisms: A Survey of LLMs](https://mlsanity.com/paper/2501.06322/) (2025)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)
- [A Comprehensive Capability Analysis of GPT-3 and GPT-3.5 Series Models](https://mlsanity.com/paper/2303.10420/) (2023)
- [Multi-Agent Risks from Advanced AI](https://mlsanity.com/paper/2502.14143/) (2025)
- [Multiagent Finetuning: Self Improvement with Diverse Reasoning Chains](https://mlsanity.com/paper/2501.05707/) (2025)
- [Can Large Language Models Serve as Rational Players in Game Theory? A Systematic Analysis](https://mlsanity.com/paper/2312.05488/) (2023)
- [MAPoRL: Multi-Agent Post-Co-Training for Collaborative Large Language Models with Reinforcement Learning](https://mlsanity.com/paper/2502.18439/) (2025)
- [Self-playing Adversarial Language Game Enhances LLM Reasoning](https://mlsanity.com/paper/2404.10642/) (2024)
- [Game-theoretic LLM: Agent Workflow for Negotiation Games](https://mlsanity.com/paper/2411.05990/) (2024)
- [MAgICoRe: Multi-Agent, Iterative, Coarse-to-Fine Refinement for Reasoning](https://mlsanity.com/paper/2409.12147/) (2024)
- [PREFER: Prompt Ensemble Learning via Feedback-Reflect-Refine](https://mlsanity.com/paper/2308.12033/) (2023)

## Built on by (most cited first, 4 of 4)

- [Game-Theoretic Lens on LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2601.15047/) (2026)
- [Agentic Microphysics: A Manifesto for Generative AI Safety](https://mlsanity.com/paper/2604.15236/) (2026)
- [Enactive Artificial Intelligence: A Decision-Centric Architecture for Complex Systems](https://mlsanity.com/paper/2608.03413/) (2026)
- [Compliant with Local Controls, Collectively Discriminatory. A Governance Architecture for Multi-Agent AI in Regulated Finance](https://mlsanity.com/paper/2609.27994/) (2026)

## Abstract (arXiv)

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.