Title: Strategic Interactions between Large Language Models-based Agents in Beauty Contests

Abstract: The growing adoption of large language models (LLMs) presents substantial potential for deeper understanding of human behaviours within game theory frameworks through simulations. Leveraging on the diverse pool of LLM types and addressing the gap in research on competitive games, this paper examines the strategic interactions among multiple types of LLM-based agents in a classical game of beauty contest. Drawing parallels to experiments involving human subjects, LLM-based agents are assessed similarly in terms of strategic levels. They demonstrate varying depth of reasoning that falls within a range of level-0 and 1, and show convergence in actions in repeated settings. Furthermore, I also explore how variations in group composition of agent types influence strategic behaviours, where I found higher proportion of fixed-strategy opponents enhances convergence for LLM-based agents, and having a mixed environment with agents of differing relative strategic levels accelerates convergence for all agents. There could also be higher average payoffs for the more intelligent agents, albeit at the expense of the less intelligent agents. These results not only provide insights into outcomes for simulated agents under specified scenarios, it also offer valuable implications for understanding strategic interactions between algorithms.