When two countries have weapons of mass destruction, then a scenario known as M.A.D happens. Mutually Assured Destruction. This essentially discourages either side from using nukes, because they know that if they launch nukes, then the other side will too, ensuring the destruction of both sides. This is why nuclear war HASN'T happened yet, and why nations are so eager to get nuclear weapons. It's because if they don't have nuclear weapons, they are at risk of nuclear annihilation.
RE: WWIII's Democratically Diverse Wasteland