The entire mutually-assured destruction (MAD) concept is based on game theory and mutual belief.
Suppose we have two states (A and B) with massive nuclear arsenals which together suffice to plunge the world into a nuclear holocaust. If State A believes State B will retaliate massively to a nuclear strike, State A is disincentivized from using nuclear weapons, and vice-versa. It is a deterrence strategy to prevent nuclear war from starting. Per this doctrine, it is thus in the interest of all parties involved to give the appearance (publicly) that they would retaliate massively to a nuclear strike.
However, it is not clear why actually adhering to this retaliation policy in the event of a nuclear strike is in the interest of the targeted party.
Let us consider a thought experiment where State A has already launched a massive nuclear barrage at State B. State B is thus doomed. State B's destruction is, at that point, a fait accompli. There is no victory to be had for State B as it will likely cease to exist as a functioning state. Its leadership (presumably hiding in bunkers somewhere safe) has a limited amount of time to decide on retaliatory action.
At that point, it is not clear why it is in State B's interest to retaliate. The leadership and elites of State B may be better served by not retaliating or if anything retaliating in a very limited manner. This could facilitate their survival in the post-nuclear war, for instance. It could be in the interest of the limited surviving population of State B, as one major country (State B) being subject to nuclear devastation would have a lesser impact on the global economy, supply lines and climate than two major countries (State A and State B) being subject to nuclear devastation. Perhaps most importantly, the possibility of human extinction could be significantly mitigated if the target state refuses to retaliate. Surely the weight of human extinction would be a reason not to strike back.
Conversely, the benefits of actually retaliating are unclear. As far as I can tell, retaliation accomplishes little for State B, which, again, is already doomed. It just seems to fulfill the primal human desire for "revenge" or "retaliation" but lacks any sound logical or strategic basis.
Are there potential benefits to retaliating that my analysis misses?
If not, then could this potentially undermine the MAD doctrine?
Have such questions been studied before?