Stratagem: Learning Transferable Reasoning via Trajectory-Modulated Game Self-Play
Authors: name: Xiachong Feng, name: Deyi Yin, name: Xiaocheng Feng, name: Yi Jiang, name: Libo Qin, name: Yangfan Ye, name: Lei Huang, name: Weitao Ma, name: Qiming Li, name: Yuxuan Gu, name: Bing Qin, name: Lingpeng Kong
Organization: The University of Hong Kong

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.