The rules for this exercise are that every nation has one and only one nuclear missile. As to the range of this missile, let’s assume this missile can hit any target on the world accurately.
The first problem is whether or not to give failed states a tactical missile and who decides such things. We will, for this argument, give a missile to every contry that has a stable government (for a hassle free definition, I give to you this chart. Every state from 21 on up will get one and only one nuke.)
I propose that this will create worldwide stability.
Of course, North Korea must give up any nukes it has. Assume it is so.
I don’t want to get into “what if a state becomes suitable/unsuitable for having a nuke?” Let’s assume the world stays at this level.