While large language models (LLMs) have demonstrated remarkable capabilities in understanding human languages, this study explores how they translate this understanding into social exchange contexts that capture certain essences of real world human interactions. Three LLMs - ChatGPT-4, Claude, and Bard - were placed in economic trust games where players balance self-interest with trust and reciprocity, making decisions that reveal their social preferences and interactive reasoning abilities. Our study shows that LLMs deviate from pure self-interest and exhibit trust and reciprocity even without being prompted to adopt a specific persona. In the simplest one-shot interaction, LLMs emulated how human players place trust at the beginning of such a game. Larger human-machine divergences emerged in scenarios involving trust repayment or multi-round interactions, where decisions were influenced by both social preferences and interactive reasoning. LLMs responses varied significantly when prompted to adopt personas like selfish or unselfish players, with the impact outweighing differences between models or game types. Response of ChatGPT-4, in an unselfish or neutral persona, resembled the highest trust and reciprocity, surpassing humans, Claude, and Bard. Claude and Bard displayed trust and reciprocity levels that sometimes exceeded and sometimes fell below human choices. When given selfish personas, all LLMs showed lower trust and reciprocity than humans. Interactive reasoning to the actions of counterparts or changing game mechanics appeared to be random rather than stable, reproducible characteristics in the response of LLMs, though some improvements were observed when ChatGPT-4 responded in selfish or unselfish personas.