Why do people throw term "tragedy of commons" at every problem involving group? This issue has nothing to do with "tragedy of commons" which deals with exhaustible resources, not nuclear weaponry control.
Also, as I remember US bombed major cities using nuclear bombs, world didn't end.
The moment after the US bombed Nagasaki, there were no more usable nucler weapons left in the world. There was no such thing as an ICBM. Right now most of the world is pre-targeted by thousands of nukes mounted to space vehicles spread across half a dozen countries and on strike submarines. In the modern era if a country believes it may be under nuclear attack by another nuclear power, they have less than 2 minutes to decide whether to launch because their retaliatory capability would be crushed after that point. There is nothing remotely comparable about nukes in the ww2 era vs the post cold war era.
Also, as I remember US bombed major cities using nuclear bombs, world didn't end.