The Fragility of Strategic Thinking in Large Language Models

Large Language Models (LLMs) are increasingly applied to domains that require reasoning about other agents' behavior, such as negotiation, policy design, and market simulation. However, can we trust LLMs to think strategically in complex situations? Existing research mostly evaluates LLMs' adherence to equilibrium play or their exhibited depth of reasoning, leaving open whether they display strategic thinking meant as the ability to form coherent conjectures about other agents, to evaluate possible actions conditional on those conjectures, and to best respond to them. We develop a framework to identify this ability by disentangling belief formation, evaluation, and choice in static complete-information games across a series of non-cooperative environments. By jointly analyzing models' revealed choices and reasoning traces, and introducing a new context-free game to rule out imitation from memorization, we show that strategic thinking in current frontier LLMs is real but fragile: models execute best responses to exogenous conjectures and form opponent-contingent conjectures when left unconstrained. Yet under increasing complexity explicit recursion gives way to model-specific logic shifts and heuristic rules of choice, both within and outside equilibrium reasoning. Further, these heuristics do not map directly onto the systematic biases typically observed in human strategic behavior. These findings, already emerging in noiseless settings, warrant caution in the application of LLMs as strategic agents in complex environments.