Game-theory behaviour of large language models: The case of Keynesian beauty contests

The growing adoption of large language models (LLMs) presents potential for deeper understanding of human behaviours within game theory frameworks. This paper examines 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 in previous studies. However, they do display a similar convergence pattern towards Nash Equilibrium choice in repeated settings. Through simulations that vary the group composition of agent types, I found that environments with a lower strategic uncertainty enhance convergence for LLM-based agents, and environments with mixed strategic types accelerate convergence for all. Results with simulated agents not only convey insights into potential human behaviours in competitive settings, but also prove valuable for understanding strategic interactions among algorithms.