Competitive Labmate

I am a first year PhD student, just started. Another student started under the same professor, and I feel like he is being extremely competitive. We share similar research interests, and I thought it would be a good idea to collaborate: if not for a research paper, just to learn. He did not seem very interested.

I am also interested in a field B, tangential to my current interests, and decided to join a seminar for that. Lo and behold, this guy signs up. I was planning on building up a rapport with the prof, but this person has already done that. A couple of other similar things have happened - where this guy tries to dominate whenever I have taken initiative. How do you deal with such a situation? Doing this for 5+ years seems exhausting.