In recent years, large language models (LLMs) have become increasingly pervasive in society. Specifically, interactions have begun to emerge in which LLMs induce changes in human behavior, and the data produced by these transformed behaviors are subsequently used to further train the LLMs. In such circumstances, the impact of LLMs’ social behaviors on society is becoming impossible to ignore. To investigate these social behaviors, previous research conducted donation games with multiple LLM agents and suggested that cooperative behavior evolved in Claude, while it did not in Gemini and GPT-4o. In this study, we examine the process by which strategic diversity and cooperative behavior become fixed in donation games. Specifically, we evaluated strategy diversity by measuring the similarity between strategy texts and assessed the temporal evolution of strategic actions. The results indicate that while Claude ’s strategic repertoire converged toward cooperative strategies and exhibited reduced diversity over successive generations, Gemini ’s strategy group tended to maintain its diversity. These findings are expected to inform our understanding of the formation of cooperation and the design of rules in a hybrid society of humans and LLM agents.