The advances of Large Language Models (LLMs) are expanding their utility in both academic research and practical applications. Recent social science research has explored the use of these "black-box" LLM agents for simulating complex social systems and potentially substituting human subjects in experiments. Our study delves into this emerging domain, investigating the extent to which LLMs exhibit key social interaction principles, such as social learning, social preference, and cooperative behavior, in their interactions with humans and other agents. We develop a novel framework for our study, wherein classical laboratory experiments involving human subjects are adapted to use LLM agents. This approach involves step-by-step reasoning that mirrors human cognitive processes and zero-shot learning to assess the innate preferences of LLMs. Our analysis of LLM agents' behavior includes both the primary effects and an in-depth examination of the underlying mechanisms. Focusing on GPT-4, the state-of-the-art LLM, our analyses suggest that LLM agents appear to exhibit a range of human-like social behaviors such as distributional and reciprocity preferences, responsiveness to group identity cues, engagement in indirect reciprocity, and social learning capabilities. However, our analysis also reveals notable differences: LLMs demonstrate a pronounced fairness preference, weaker positive reciprocity, and a more calculating approach in social learning compared to humans. These insights indicate that while LLMs hold great promise for applications in social science research, such as in laboratory experiments and agent-based modeling, the subtle behavioral differences between LLM agents and humans warrant further investigation. Careful examination and development of protocols in evaluating the social behaviors of LLMs are necessary before directly applying these models to emulate human behavior.