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

The growing adoption of large language models (LLMs) presents potential for deeper understanding of human behaviours within game theory frameworks. Addressing research gap on multi-player competitive games, this paper examines the strategic interactions among multiple types of LLM-based agents in a classical beauty contest game. LLM-based agents demonstrate varying depth of reasoning that fall within a range of level-0 to 1, which are lower than experimental results conducted with human subjects, but they do display similar convergence pattern towards Nash Equilibrium (NE) choice in repeated setting. Further, through variation in group composition of agent types, I found environment with lower strategic uncertainty enhances convergence for LLM-based agents, and having a mixed environment comprises of LLM-based agents of differing strategic levels accelerates convergence for all. Higher average payoffs for the more intelligent agents are usually observed, albeit at the expense of less intelligent agents. The results from game play with simulated agents not only convey insights on potential human behaviours under specified experimental set-ups, they also offer valuable understanding of strategic interactions among algorithms.