There are three major conditions where MAD fails:
1) When there are lots of actors. As the number of potential threats go up, the probability that someone will act "irrationally" goes up combinatorially. This is why monopolies always act to benefit themselves, oligopolies usually act in their own interest, but competitive markets always have some defector that triggers a price war.
2) When one of the actors is dead anyway. MAD relies on total annihilation being a negative consequence. If total annihilation is what's going to happen to you anyway, you have no incentive not to launch the missiles.
3) When the responsible party for a launch can't be identified. If you launch but your other enemy gets blamed for it, you've killed two birds with one stone.
Note that the U.S. government has very strong doctrines in place to avert each of these conditions. Nuclear non-proliferation, strong sanctions or military action on countries that are developing nuclear weapons, and nuclear secrecy are all to avert #1. American reliance on soft-power and us keeping dictators in power even when we don't like them are to avert #2. U.S. intelligence agencies are to avert #3.
Despite all this, all three of these conditions are fraying. I'm not all that optimistic that we'll avert nuclear armageddon. The game theorists at RAND corporation knew what they were doing, though.