I've done Claude and Claude via a file, and only telling them "there is another AI agent who you can work with at XXX" and not explicitly telling them it's another Claude.
Sometimes they do work together well, sometimes they end up hating at each other and accusing the other agent of various things.
Theyre just like us!
I've done this with code review. "Another LLM reviewed the attached code and produced the attached report. What do you think?"
Lots of "the other LLM clearly hallucinated this part". To be fair, it has never accused the other, err, itself, of being incompetent; it accepts that hallucinating is just something which happens.