# SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning

arXiv: https://arxiv.org/abs/2506.24119 · HTML: https://mlsanity.com/paper/2506.24119/

## Key facts

- Cited by 100 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 52 of its 71 references that are in the map.
- First posted on arXiv 30 Jun 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)
- Synthetic data and self-improvement for LLMs / [Self-play RL for reasoning](https://mlsanity.com/synth/self-play-rl-for-reasoning/)

## Builds on (most cited first, 30 of 52)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [RAGEN: Understanding Self-Evolution in LLM Agents via Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2504.20073/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligence](https://mlsanity.com/paper/2406.11931/) (2024)
- [Way Off-Policy Batch Deep Reinforcement Learning of Implicit Human Preferences in Dialog](https://mlsanity.com/paper/1907.00456/) (2019)
- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)
- [Exploring Large Language Models for Communication Games: An Empirical Study on Werewolf](https://mlsanity.com/paper/2309.04658/) (2023)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search](https://mlsanity.com/paper/2408.08152/) (2024)
- [Language Agents with Reinforcement Learning for Strategic Play in the Werewolf Game](https://mlsanity.com/paper/2310.18940/) (2023)
- [BALROG: Benchmarking Agentic LLM and VLM Reasoning On Games](https://mlsanity.com/paper/2411.13543/) (2024)

## Built on by (most cited first, 30 of 100)

- [The Landscape of Agentic Reinforcement Learning for LLMs: A Survey](https://mlsanity.com/paper/2509.02547/) (2025)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [A Survey of Self-Evolving Agents: What, When, How, and Where to Evolve on the Path to Artificial Super Intelligence](https://mlsanity.com/paper/2507.21046/) (2025)
- [SPICE: Self-Play In Corpus Environments Improves Reasoning](https://mlsanity.com/paper/2510.24684/) (2025)
- [Agent0: Unleashing Self-Evolving Agents from Zero Data via Tool-Integrated Reasoning](https://mlsanity.com/paper/2511.16043/) (2025)
- [Parallel-R1: Towards Parallel Thinking via Reinforcement Learning](https://mlsanity.com/paper/2509.07980/) (2025)
- [Multi-Agent Evolve: LLM Self-Improve through Co-evolution](https://mlsanity.com/paper/2510.23595/) (2025)
- [RLVE: Scaling Up Reinforcement Learning for Language Models with Adaptive Verifiable Environments](https://mlsanity.com/paper/2511.07317/) (2025)
- [LLM Collaboration With Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2508.04652/) (2025)
- [Dr. Zero: Self-Evolving Search Agents without Training Data](https://mlsanity.com/paper/2601.07055/) (2026)
- [Language Self-Play For Data-Free Training](https://mlsanity.com/paper/2509.07414/) (2025)
- [Vision-Zero: Scalable VLM Self-Improvement via Strategic Gamified Self-Play](https://mlsanity.com/paper/2509.25541/) (2025)
- [Reinforcement Learning Meets Large Language Models: A Survey of Advancements and Applications Across the LLM Lifecycle](https://mlsanity.com/paper/2509.16679/) (2025)
- [Tool-R0: Self-Evolving LLM Agents for Tool-Learning from Zero Data](https://mlsanity.com/paper/2602.21320/) (2026)
- [Beyond Trajectory-Level Attribution: Graph-Based Credit Assignment for Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.26684/) (2026)
- [SPELL: Self-Play Reinforcement Learning for Evolving Long-Context Language Models](https://mlsanity.com/paper/2509.23863/) (2025)
- [Stronger-MAS: Multi-Agent Reinforcement Learning for Collaborative LLMs](https://mlsanity.com/paper/2510.11062/) (2025)
- [On Predictability of Reinforcement Learning Dynamics for Large Language Models](https://mlsanity.com/paper/2510.00553/) (2025)
- [GEM: A Gym for Agentic LLMs](https://mlsanity.com/paper/2510.01051/) (2025)
- [FrontierCS: Evolving Challenges for Evolving Intelligence](https://mlsanity.com/paper/2512.15699/) (2025)
- [Magentic Marketplace: An Open-Source Environment for Studying Agentic Markets](https://mlsanity.com/paper/2510.25779/) (2025)
- [From Context to Skills: Can Language Models Learn from Context Skillfully?](https://mlsanity.com/paper/2604.27660/) (2026)
- [World Action Verifier: Self-Improving World Models via Forward-Inverse Asymmetry](https://mlsanity.com/paper/2604.01985/) (2026)
- [On-Policy Self-Distillation without Any Supervision](https://mlsanity.com/paper/2608.06296/) (2026)
- [MARSHAL: Incentivizing Multi-Agent Reasoning via Self-Play with Strategic LLMs](https://mlsanity.com/paper/2510.15414/) (2025)
- [Position: Agentic Evolution is the Path to Evolving LLMs](https://mlsanity.com/paper/2602.00359/) (2026)
- [Dr. MAS: Stable Reinforcement Learning for Multi-Agent LLM Systems](https://mlsanity.com/paper/2602.08847/) (2026)
- [SPADE: Self-Play in Adaptive Synthetic Executable Environments](https://mlsanity.com/paper/2608.19197/) (2026)
- [V-Zero: Self-Improving Multimodal Reasoning with Zero Annotation](https://mlsanity.com/paper/2601.10094/) (2026)
- [R-Diverse: Mitigating Diversity Illusion in Self-Play LLM Training](https://mlsanity.com/paper/2602.13103/) (2026)

## Abstract (arXiv)

Recent advances in reinforcement learning have shown that language models can develop sophisticated reasoning through training on tasks with verifiable rewards, but these approaches depend on human-curated problem-answer pairs and domain-specific reward engineering. We introduce SPIRAL, a self-play framework where models learn by playing multi-turn, zero-sum games against continuously improving versions of themselves, generating an automatic curriculum of stronger opponents, and eliminating the need for human supervision. To enable this self-play training at scale, we implement a fully online, multi-turn, multi-agent reinforcement learning system for LLMs and propose role-conditioned advantage estimation (RAE) to stabilize multi-agent training. SPIRAL produces reasoning capabilities that transfer broadly, improving performance by up to 10% across a suite of 8 reasoning benchmarks on 4 different models spanning Qwen and Llama model families, outperforming supervised fine-tuning on 25,000 expert game trajectories. Multi-game training (TicTacToe, Kuhn Poker, Simple Negotiation) yields the strongest results, with improvements observed across both base and instruction-tuned models. Analysis of chain-of-thought traces reveals that games develop distinct cognitive patterns that transfer to improve reasoning performance, with different games developing complementary strengths. Even models which have already been trained on reasoning tasks using RLVR, like DeepSeek-R1-Distill-Qwen-7B, still benefit from our approach. These results demonstrate that zero-sum games naturally develop transferable reasoning capabilities across diverse model architectures and training stages, highlighting a promising direction for autonomous reasoning development. Our code can be found in https://github.com/spiral-rl/spiral.