I sometimes think of game theory as being roughly divided in three parts, like Gaul. There's competitive zero-sum game theory, there's cooperative game theory, and there are games where players compete but also have some shared interest. Except this third part isn't a middle ground. It's actually better thought of as ultra-competitive game theory. Zero-sum settings are relatively harmless: you minimax and that's it. It's the variable-sum games that make you nuke your neighbour.

Could you clarify that last bit for me? You seem to have a valid point but I don't think I can glean it from that wording. I can imagine plenty of scenarios in which competitive zero-sum game theory will suggest that I nuke my neighbour. The most obvious example being if I kill them all and take their stuff and I think I can get away with it. Common interests appear not to be necessary.