That assumes each independant only has the power to destroy his own worth. Unlike the current MAD situation irl, where I'm pretty sure any one nuclear power could destroy the planet by themselves.
That it inaccurate. On paper each of the 2 superpowers (indeed all 3 if you count China) has enough nuclear warheads to hit every major city in the world. In practice due to the way nuclear war works (there's jamming of communication, misunderstandings, shooting down missiles, people somewhere along the chain refusing to commit mass murder, etc.) most of those would actually be directed at the same places. If members of the Non Alignment League had decided to take part in a Russo-American war, most of them would be intact when the dust will have stetted, as the Superpowers would mostly try to take out each other. And then, arguably, they would become better off, on account of being able to 'pick at the carcases'.
I think I can trust them all to understand MAD theory.
MAD only works for 2 players .
Explain.
Well in a 2 player scenario, if one of the players decides to go rogue, the other will have enough vengeance to make his victory pyrrhic. However in a scenario with multiple independent actors ("independent" being the operative word, 2 alliances are roughly the same thing as 2 players, even if they can be broken) it will actually benefit the players to attack whichever combatant is weaker, as they are unlikely to recive as much retribution, and they would get a (roughly) equal piece of the destroyed player's pie. The only other special case (aside from 2 players and the trivial 1 player case) is 3 players, where the independent will attack the stronger player, since he knows he's next, reducing the problem to a 2 player case.
That assumes a rather short-sighted view. Even assuming that each player is independent, a war with a weaker power will weaken the victor as well as destroying the loser, especially if the powers are all fairly well-balanced as in this case. This opens them up to destruction, which is idiotic and makes it the very definition of a Pyrrhic victory.
You realize they aren't doing this out of spite, right? Whenever an enemy falls, there's a power vacuum where they used to be, which the attackers are best positioned to exploit. It's just that when there's 2 of you, the amount of damage you will get in response makes this not worth it. When the defender is focused elsewhere however (and people do tend to focus on one target) the benefits start to outweight the costs (if that's still not enough, you have to wonder what was the initial attacker (suffering most of that cost) tying to do?)