A Nuclear exchange is not really to make the other side concede. Both sides know if they fire nukes the other side will respond in minutes with their own massive salvo. The initial strike is essentially to render as much of the enemies military ineffective especially their nukes. Surviving for a second strike is not a given. In the event of a nuclear strike I think both sides understand that there wont be very many people or leadership to concede. Hence the term Mutually Assured Destruction.