Even if there was a world war 3 and it went nuclear, I doubt many nuclear missiles would be fired in such a situation. Maybe half a dozen to a dozen nukes fired, tops, before everyone decides they've had enough. And that isn't going to destroy the entire world. Maybe a couple major cities pulverized, but the world would easily rebuild from the damage within a few decades.
With all the experience and history the world has with wars, I bet that such a war would only last a few days before everyone nearly unanimously decided that a third world war was the stupidest thing anyone had ever done.
Please feed the trolls. XD