I could see it starting that way. One side gambles that they can nuke one city and the enemy will deescalate to avoid a full exchange. But the other side is compelled to respond in kind, knowing that they can't sit and do nothing, and hoping that that a one-for-one exchange will be the end of it. And it might be. But if not, then it must be an all-out exchange imo.
Think about it like this: someone punches you. You punch back. If they do nothing, then that's the end of it (for now). But if they do it again - are you going to stand there all day exchanging punches? You now know that they're determined to keep hitting you. Your best chance is to throw everything you have at them right now. That minimizes the damage to you. That's clearly true if you're stronger than them. But if you think about, it it's equally true if you're weaker.
FWIW, I think everyone should stop worrying about nuclear war. The US would win hands down and everyone knows it.