# Stratagem: Learning Transferable Reasoning via Trajectory-Modulated Game Self-Play

arXiv: https://arxiv.org/abs/2604.17696 · HTML: https://mlsanity.com/paper/2604.17696/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 25 of its 41 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- 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, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [Exploring Large Language Models for Communication Games: An Empirical Study on Werewolf](https://mlsanity.com/paper/2309.04658/) (2023)
- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [A Survey on Large Language Model-Based Game Agents](https://mlsanity.com/paper/2404.02039/) (2024)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)
- [lmgame-Bench: How Good are LLMs at Playing Games?](https://mlsanity.com/paper/2505.15146/) (2025)
- [SPC: Evolving Self-Play Critic via Adversarial Games for LLM Reasoning](https://mlsanity.com/paper/2504.19162/) (2025)
- [Orak: A Foundational Benchmark for Training and Evaluating LLM Agents on Diverse Video Games](https://mlsanity.com/paper/2506.03610/) (2025)
- [TextArena](https://mlsanity.com/paper/2504.11442/) (2025)
- [A Survey on Self-play Methods in Reinforcement Learning](https://mlsanity.com/paper/2408.01072/) (2024)
- [Game-TARS: Pretrained Foundation Models for Scalable Generalist Multimodal Game Agents](https://mlsanity.com/paper/2510.23691/) (2025)
- [A Survey on Large Language Model-Based Social Agents in Game-Theoretic Scenarios](https://mlsanity.com/paper/2412.03920/) (2024)
- [A Survey on Game Playing Agents and Large Models: Methods, Applications, and Challenges](https://mlsanity.com/paper/2403.10249/) (2024)
- [Play to Generalize: Learning to Reason Through Game Play](https://mlsanity.com/paper/2506.08011/) (2025)
- [Game Reasoning Arena: A Framework and Benchmark for Assessing Reasoning Capabilities of Large Language Models via Game Play](https://mlsanity.com/paper/2508.03368/) (2025)
- [TextGames: Learning to Self-Play Text-Based Puzzle Games via Language Model Reasoning](https://mlsanity.com/paper/2502.18431/) (2025)
- [Think in Games: Learning to Reason in Games via Reinforcement Learning with Large Language Models](https://mlsanity.com/paper/2508.21365/) (2025)

## Abstract (arXiv)

Games offer a compelling paradigm for developing general reasoning capabilities in language models, as they naturally demand strategic planning, probabilistic inference, and adaptive decision-making. However, existing self-play approaches rely solely on terminal game outcomes, providing no mechanism to distinguish transferable reasoning patterns from game-specific heuristics. We present STRATAGEM, which addresses two fundamental barriers to reasoning transfer: domain specificity, where learned patterns remain anchored in game semantics, and contextual stasis, where static game contexts fail to cultivate progressive reasoning. STRATAGEM selectively reinforces trajectories exhibiting abstract, domain-agnostic reasoning through a Reasoning Transferability Coefficient, while incentivizing adaptive reasoning development via a Reasoning Evolution Reward. Experiments across mathematical reasoning, general reasoning, and code generation benchmarks demonstrate substantial improvements, with particularly strong gains on competition-level mathematics where multi-step reasoning is critical. Ablation studies and human evaluation confirm that both components contribute to transferable reasoning.