Large Language Models (LLMs) have demonstrated remarkable general capabilities, yet they falter in domains requiring deep strategic reasoning. A primary obstacle is the need to navigate a game tree that grows exponentially with search depth, a task for which their generative nature is ill-suited. To address this, we introduce Generative Gamer (GenGamer), a framework that trains LLMs to reason like an expert player. Instead of attempting an exhaustive search, GenGamer learns to generate a compact, pruned reasoning trajectory termed as a Dynamic Deduction. This is achieved by integrating three key strategies: action pruning based on policy confidence, state pruning via value estimation, and branch pruning inspired by alpha-beta principles. Furthermore, to train the model effectively, we propose the Deduction Tree Reward (DTR), a process-oriented mechanism that provides step-by-step feedback on the quality of the reasoning process, rather than relying solely on the final game outcome. Experiments on complex games such as Tic-Tac-Toe and Leduc Poker demonstrate that GenGamer significantly enhances the strategic capabilities of LLMs, enabling them to achieve performance that surpasses current state-of-the-art language models.

Strategic reasoning is a complex yet essential capability for intelligent agents. It requires Large Language Model (LLM) agents to adapt their strategies dynamically in multi-agent environments. Unlike static reasoning tasks, success in these contexts depends on anticipating other agents’ beliefs and actions while continuously adjusting strategies to achieve individual goals. LLMs and LLM agents often struggle with strategic reasoning due to the absence of a reasoning framework that enables them to dynamically infer others’ perspectives and adapt to changing environments. Inspired by the Level-K framework from game theory and behavioral economics, which extends reasoning from simple reactions to structured strategic depth, we propose a novel framework: “K-Level Reasoning with Large Language Models (K-R).” This framework employs recursive mechanisms to enable LLMs to achieve varying levels of strategic depth, allowing agents to form higher order beliefs—beliefs about others’ beliefs. We validate this framework through rigorous testing on four testbeds: two classical game theory problems and two social intelligence tasks. The results demonstrate the advantages of K-R in strategic reasoning. Our work presents the first recursive implementation of strategic depth in large language models (LLMs). It establishes a foundation for future research into theory of mind and strategic reasoning in LLMs.