In the previous post, Mutually-Assured Destruction, we looked at the payoff matrix for MAD, motivated by Iran's desire to acquire nuclear weapons.
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However, the Iran case is quite asymmetric and the payoff matrix looks something like the above.
If the US does nothing, then Iran gets the bomb and scores +5, while the US has to deal with the negative foreign policy implications and scores -x (how big is x?).
The US therefore prefers Iran not to get the bomb, which motivates a first strike. If the US gets away with it, Iran scores -5 and the US scores +1 as its foreign policy problem has now gone away.
If however Iran retaliates: massive destabilisation in Iraq; attacks on Israel by Hezbollah in Lebanon; or more generally via a wider Islamic/world reaction against the US; then Iran would get battered again and scores -10 but the US has a negative outcome of -y.
Given a credible posture that Iran would retaliate, the US has to figure out whether -y is worse than -x, and Iran has to persuade the US that it would not take an attack lying down. The latter case is a lot easier to make than second-strike retaliation in the MAD case, although Iran would no doubt come off even worse if it retaliated.
For the US there are no stable good outcomes, and it's still a case of a "subgame perfect Nash equilibrium".
Arguably, there is the missing option where 'the West' persuades Iran not to acquire nuclear weapons, and 'play nice'. But that's a different game.
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