I had a similar relationship in my physics class a couple years ago with a friend who tests as INTJ. We were frequently paired up for group assignments and would often argue and compete quite a bit. Overall it remained relatively cordial because we both respected each other as far as physics goes and were used to butting heads at that point (we argued a lot in regards to more personal topics the year or so before then, and it got heated at times). An outsider might think we were fighting for real, as we tend to use a lot of "what the fuck are you talking about? You're fucking stupid" but it actually really helped us both be productive and correct (neither of us wanted to be the one that screwed up).
At times he'd seem to take that tension between us pretty seriously and would sometimes act on it when I saw him around. Sometimes it was as innocuous as just being kind of cold in conversation and other times he'd say and do things that seemed like he was actively trying to attack me. During that time, I didn't really have much to do about it besides try and ignore it and if he directly tried to confront me then I'd snap back and we'd argue (looking back, I kind of miss when it was relatively acceptable (almost expected) to be an argumentative cunt. High School was a truly... actually fuck it, high school sucked).
He and I never really resolved our differences until the next year when we had English together (neither of us really cared about that subject) and we'd just fuck around with our teacher (who seemed to care as little as we did). After that we were a couple regular old pals. Chums, even.
Anyway, that was a lot of unnecessary information but I already wrote it all out so I guess I'll keep it. Advice; If you can't get distance from the thing you guys are competing at (which I assume is a school/work thing and therefore hard/impossible to do avoid him while doing it) then try and ignore whatever he's doing that's bothering you. If he does something to actively sabotage you or crosses a line in any overtly inappropriate way, then I'd just be honest with him (or her, I guess. You weren't gender specific) about what he's doing that's bothering you and try and hash it out with direct, honest conversation.