Game theory is a branch of mathematics that studies strategic interactions among rational agents. We propose Alympics (Olympics for Agents), a systematic framework utilizing Large Language Model (LLM) agents for empirical game theory research. Alympics creates a versatile platform for studying complex game theory problems, bridging the gap between theoretical game theory and empirical investigations by providing a controlled environment for simulating human-like strategic interactions with LLM agents. In our pilot case study, the “Water Allocation Challenge”, we explore Alympics through a challenging strategic game focused on the multi-round auction of scarce survival resources. This study demonstrates the framework’s ability to qualitatively and quantitatively analyze game determinants, strategies, and outcomes. Additionally, we conduct a comprehensive human assessment and an in-depth evaluation of LLM agents in rational strategic decision-making scenarios. Our findings highlight LLM agents’ potential to advance game theory knowledge and expand the understanding of their proficiency in emulating human strategic behavior.