# Multi-LLM Collaborative Alignment via Stackelberg Games

arXiv: https://arxiv.org/abs/2609.39076 · HTML: https://mlsanity.com/paper/2609.39076/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 46 of its 54 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 30 of 46)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
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- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [AlpacaFarm: A Simulation Framework for Methods that Learn from Human Feedback](https://mlsanity.com/paper/2305.14387/) (2023)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [Skywork-Reward: Bag of Tricks for Reward Modeling in LLMs](https://mlsanity.com/paper/2410.18451/) (2024)
- [Gemma 4 Technical Report](https://mlsanity.com/paper/2607.02770/) (2026)
- [Nash Learning from Human Feedback](https://mlsanity.com/paper/2312.00886/) (2023)
- [GraphRouter: A Graph-based Router for LLM Selections](https://mlsanity.com/paper/2410.03834/) (2024)
- [LAB-Bench: Measuring Capabilities of Language Models for Biology Research](https://mlsanity.com/paper/2407.10362/) (2024)
- [Aya Expanse: Combining Research Breakthroughs for a New Multilingual Frontier](https://mlsanity.com/paper/2412.04261/) (2024)
- [Modular Pluralism: Pluralistic Alignment via Multi-LLM Collaboration](https://mlsanity.com/paper/2406.15951/) (2024)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [Multiagent Finetuning: Self Improvement with Diverse Reasoning Chains](https://mlsanity.com/paper/2501.05707/) (2025)
- [BixBench: a Comprehensive Benchmark for LLM-based Agents in Computational Biology](https://mlsanity.com/paper/2503.00096/) (2025)
- [In-the-Flow Agentic System Optimization for Effective Planning and Tool Use](https://mlsanity.com/paper/2510.05592/) (2025)
- [NVIDIA Nemotron 3: Efficient and Open Intelligence](https://mlsanity.com/paper/2512.20856/) (2025)
- [Pangea: A Fully Open Multilingual Multimodal LLM for 39 Languages](https://mlsanity.com/paper/2410.16153/) (2024)

## Abstract (arXiv)

A pool of language models can collaborate and improve collectively by learning from one another's responses. These interactions depend on the instructions used during training. Existing methods typically sample instructions uniformly, even though their usefulness may change as the models improve: an instruction on which models' responses once differed in quality may later be answered equally well, while a previously difficult instruction may begin to provide a useful learning signal. We propose Stackelberg Alignment, a game-theory-inspired leader-follower framework that turns instruction selection into an adaptive curriculum. An EXP3 bandit acts as the leader, allocating a fixed sampling budget across instructions and updating its sampling distribution using a reward that combines instruction difficulty and response discriminability. The language models act as followers: they respond to the selected instructions, evaluate one another's responses, and learn from the resulting preference signals through DPO or GRPO. The framework uses Elo-style reputation-weighted peer judgment and reputation-based opponent matching to support reliable and competitive model interactions. Experiments across three heterogeneous model pools and 12 benchmarks spanning scientific discovery, reasoning, code, instruction following, and knowledge show that Stackelberg Alignment achieves the highest macro-average across three diverse model pools, outperforming the strongest training-time baseline by up to 7.4% and the best static inference baseline by 12-25%. Analysis confirms that the adaptive leader concentrates duels on the most informative instructions, and ablations show that both reputation-weighted judgment and reputation-based matching improve the effectiveness of multi-LLM evolution.