# Instructing LLMs to Negotiate using Reinforcement Learning with Verifiable Rewards

arXiv: https://arxiv.org/abs/2604.09855 · HTML: https://mlsanity.com/paper/2604.09855/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 41 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 20 of 20)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Deal or No Deal? End-to-End Learning for Negotiation Dialogues](https://mlsanity.com/paper/1706.05125/) (2017)
- [Improving Language Model Negotiation with Self-Play and In-Context Learning from AI Feedback](https://mlsanity.com/paper/2305.10142/) (2023)
- [Qwen2.5-1M Technical Report](https://mlsanity.com/paper/2501.15383/) (2025)
- [How Well Can LLMs Negotiate? NegotiationArena Platform and Analysis](https://mlsanity.com/paper/2402.05863/) (2024)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)
- [Human-inspired Episodic Memory for Infinite Context LLMs](https://mlsanity.com/paper/2407.09450/) (2024)
- [Evaluating Language Model Agency through Negotiations](https://mlsanity.com/paper/2401.04536/) (2024)
- [Measuring Bargaining Abilities of LLMs: A Benchmark and A Buyer-Enhancement Method](https://mlsanity.com/paper/2402.15813/) (2024)
- [Let's Negotiate! A Survey of Negotiation Dialogue Systems](https://mlsanity.com/paper/2212.09072/) (2022)
- [STRIDE: A Tool-Assisted LLM Agent Framework for Strategic and Interactive Decision-Making](https://mlsanity.com/paper/2405.16376/) (2024)
- [The Automated but Risky Game: Modeling and Benchmarking Agent-to-Agent Negotiations and Transactions in Consumer Markets](https://mlsanity.com/paper/2506.00073/) (2025)
- [SAGE: Multi-Agent Self-Evolution for LLM Reasoning](https://mlsanity.com/paper/2603.15255/) (2026)

## Built on by (most cited first, 7 of 7)

- [Strategic Bargaining in Multi-Buyer Markets: Reinforcement Learning from Verifiable Rewards for LLM Negotiations](https://mlsanity.com/paper/2607.05863/) (2026)
- [Robust Data-Collection Policy Learning for Low-Variance Online Policy Evaluation](https://mlsanity.com/paper/2608.24146/) (2026)
- [OR-Transformer: Scaling Real-Time Decision-Making to 1,000 Items](https://mlsanity.com/paper/2609.01933/) (2026)
- [IB-RL: Isolated Bilateral Reinforcement Learning for Strategic Dialogue Agents](https://mlsanity.com/paper/2608.06735/) (2026)
- [From Passive Delegates to Strategic Negotiators: Reinforcing Social Reasoning in Small Language Models with SocialRL](https://mlsanity.com/paper/2608.13787/) (2026)
- [Pessimistic Minimax Learning for Public-Private Information Games under Unilateral Coverage](https://mlsanity.com/paper/2610.04997/) (2026)
- [Parallelism or Concession? Concurrency-Aware Procurement Negotiation for Agentic Commerce](https://mlsanity.com/paper/2610.06017/) (2026)

## Abstract (arXiv)

The recent advancement of Large Language Models (LLMs) has established their potential as autonomous interactive agents. However, they often struggle in strategic games of incomplete information, such as bilateral price negotiation. In this paper, we investigate if Reinforcement Learning from Verifiable Rewards (RLVR) can effectively teach LLMs to negotiate. Specifically, we explore the strategic behaviors that emerge during the learning process. We introduce a framework that trains a mid-sized buyer agent against a regulated LLM seller across a wide distribution of real-world products. By grounding reward signals directly in the maximization of economic surplus and strict adherence to private budget constraints, we reveal a novel four-phase strategic evolution. The agent progresses from naive bargaining to using aggressive starting prices, moves through a phase of deadlock, and ultimately develops sophisticated persuasive skills. Our results demonstrate that this verifiable training allows a 30B agent to significantly outperform frontier models over ten times its size in extracting surplus. Furthermore, the trained agent generalizes robustly to stronger counterparties unseen during training and remains effective even when facing hostile, adversarial seller personas.