This paper examines strategic interactions among multiple types of LLM-based agents in a beauty contest game. They demonstrate varying depth of reasoning that fall within level-0 to 1, which is lower than experimental results conducted with human subjects, but they do display similar convergence pattern towards Nash Equilibrium (NE) choice in repeated setting. 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 of different agent types could accelerate learning. The results from game play with simulated agents not only convey insights on potential human behaviours, they also offer valuable understanding of strategic interactions among algorithms.