I've read Schelling's Strategy of Conflict so I have done some reading on this. Once again you are assuming players are always rational which is a simplistic assumption. The game doesn't work if one side doesn't care about iterative rounds, chooses to signal erratic behaviour or doesn't understand the implications of their actions.

A good example is Nixon's "madman theory" during the Vietnam conflict.

Trump is erratic and can't be assumed to act rationally , so his use of a nuclear weapon would massively increase the chance that Russia would use one in response on the basis that the US is willing to kill the leaders of other countries in a sneak attack.

MAD is not set in stone and can break down in certain circumstances.