I actually don't think that game theory helps with winning friends. It's useful to prevent other people from bullying yourself but it doesn't make people like you.

Game Theory per-se won't help with winning friends, but it does wonders at helping one analyze and plan strategies about political landscapes in the general sense, including the tribal and clique networks of highschool in the specific.

Dealing with negative shenanigans is definitely its primary strongpoint, but that in itself can be counted as removing obstacles or negative influences on winning friends. Which, in my interpretation, is equivalent to pouncing on those opportunity costs and making a profit.