Sticking to trade wars, let's say country A is the current leader and country B is catching up. A might start a trade war knowing that it will be worse off right now, but B will lose more, and A will remain the leader. The competition from a stronger B could be even more costly to A than the trade war.

And also, yes, some consider relative wealth more important than absolute wealth; "I'd rather have $100 and my neighbor $10, than I have $150 and my neighbor $140."