In-context learning (ICL) enables large language model (LLM) agents to improve decisions using interaction history, yet it remains unclear whether such improvement reflects refined internal reasoning or mere extrapolation of statistical patterns. To disentangle these mechanisms, we study LLM agents in multi-agent incomplete-information games that require recursive belief reasoning. By constructing a public goods game and manipulating the statistical structure of historical feedback, we evaluate decision quality against a history-independent rational expectations equilibrium (REE) benchmark. Our experiments reveal that when historical statistical patterns are disrupted, the benefits of longer context largely vanish, degrading decision quality to the no-context baseline in a way sharply amplified by stronger strategic interdependence. These results suggest that, in such strategic environments, ICL behavior is more consistent with statistical extrapolation than with strategic reasoning. Our work extends the mechanistic study of ICL to strategic multi-agent settings, introduces REE as a diagnostic tool for distinguishing reasoning from extrapolation, and provides a reusable framework for probing the boundaries of LLM reasoning in recursive belief tasks.

With the rapid expansion of large language model (LLM) applications, there is an emerging shift in the role of LLM-based AI chatbots from serving merely as general inquiry tools to acting as professional service agents. However, current studies often overlook a critical aspect of professional service agents: the act of communicating in a manner consistent with their professional identities. This is of particular importance in the healthcare sector, where effective communication with patients is essential for achieving professional goals, such as promoting patient well-being by encouraging healthy behaviors. To bridge this gap, we propose LAPI (LLM-based Agent with a Professional Identity), a novel framework for designing professional service agent tailored for medical question-and-answer (Q&A) services, ensuring alignment with a specific professional identity. Our method includes a theory-guided task planning process that decomposes complex professional tasks into manageable subtasks aligned with professional objectives and a pragmatic entropy method designed to generate professional and ethical responses with low uncertainty. Experiments on various LLMs show that the proposed approach outperforms baseline methods, including few-shot prompting, chain-of-thought prompting, across key metrics such as fluency, naturalness, empathy, patient-centricity, and ROUGE-L scores. Additionally, the ablation study underscores the contribution of each component to the overall effectiveness of the approach.