Strategic Behavior in Large Language Models Depends Critically on Game Structure

Large language models (LLMs) are increasingly deployed as strategic agents. However, it remains unclear how their strategic behavior changes with game structure. To address this question, we conduct self-play experiments with 15 LLMs across 10 complete information games, 4 complex incomplete information environments, and an electricity-sector carbon-market bidding game. We find that strategic behavior depends critically on game structure. Equilibrium attainment in sequential games averages 63.2%, about 18 percentage points higher than simultaneous games, and 12 of 15 models perform better in sequential games. Moreover, attaining equilibrium does not imply selecting the Pareto-optimal equilibrium. In complex incomplete information environments, outcome-based metrics alone are insufficient, as models can achieve high scores while exhibiting low-quality interaction processes. To diagnose such failures, we propose Strategic Failure Detection (SFD), which decomposes strategic behavior into planning, coordination, action validity, and outcome. Applying SFD to the carbon-market game improves planning and coordination and raises welfare and terminal payoff achievement rate for DeepSeek-V3 and GPT-4o. These results show that process-level detection can make strategic behavior more observable and easier to improve.