There was a whole anti-ballistic missile treaty which banned the US and the USSR (and then its successor states) from developing anti-ballistic missile systems. George W. Bush withdrew the US from the treaty in 2002.
Further reading: https://en.wikipedia.org/wiki/Anti-Ballistic_Missile_Treaty
> Mutual assured destruction (MAD) is a doctrine of military strategy and national security policy ...
I'm unable to find anything about the "Assured Destruction" doctrine which isn't about MAD. If you have some links I should read to learn more, please do send them. But presumably, the US's official doctrine is that if Russia sends in a first strike, the US will retaliate with a second strike? And presumably Russia's official doctrine is the same? If that's the case, isn't that just the MAD doctrine, even if it's under a different name officially? Or has both countries officially said that a first strike won't be followed up by a second strike?
MAD is a game theory construct. It may inform doctrine, but it doesn't actually dictate how we employ forces. US doctrine can be found in the nuclear posture review : https://media.defense.gov/2018/Feb/02/2001872877/-1/-1/1/EXE...
It amounts to : the primary point of the US arsenal is deterrence. As such, we will assure that we can destroy the enemy as necessary.
Russian doctrine had explicitly contemplated the first use of nuclear weapons "in response to large-scale aggression utilizing conventional weapons in situations critical to the national security of the Russian Federation." So if they get in a war and start losing.
The critical part of MAD is a so called balance of terror. But the US doesn't use nuclear weapons because it's afraid of getting nuked in return, and Russia believes that they can win a nuclear war. So it's both not doctrine (because it's not how either military plans to use forces) and not real (because the preconditions don't exist).
Because then the solution would be to disable all of the other country's nukes simultaneously and then trigger your own.