As Large Language Model (LLM)-based agents increasingly undertake real-world tasks and engage with human society, how well do we understand their behaviors? This study (1) investigates how LLM agents' prosocial behaviors -- a fundamental social norm -- can be induced by different personas and benchmarked against human behaviors; and (2) introduces a behavioral approach to evaluate the performance of LLM agents in complex decision-making scenarios. We explored how different personas and experimental framings affect these AI agents' altruistic behavior in dictator games and compared their behaviors within the same LLM family, across various families, and with human behaviors. Our findings reveal substantial variations and inconsistencies among LLMs and notable differences compared to human behaviors. Merely assigning a human-like identity to LLMs does not produce human-like behaviors. Despite being trained on extensive human-generated data, these AI agents cannot accurately predict human decisions. LLM agents are not able to capture the internal processes of human decision-making, and their alignment with human behavior is highly variable and dependent on specific model architectures and prompt formulations; even worse, such dependence does not follow a clear pattern.