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You make a good point. Let's look at the payouts from the NK point of view:
US first strike -> NK crushed, US not damaged
NK first strike -> US harmed, NK crushed
nobody shoots -> NK not crushed, US not damaged
NK first strike outperforms US first strike. If you give them different negative weights and assign 0 to nobody shoots you can solve for the probability of US first strike where NK is indifferent to shooting. Above that probability of US first strike, NK first strike is the winning move.
Right. I think we agree then. Let's look at the payouts from the NK point of view:
US first strike -> NK crushed, US not damaged
NK first strike -> US harmed, NK crushed
nobody shoots ->
NK not crushed, US not damaged
The bolded is key. Kim's ultimate payoff is to not be crushed AND stay in power. I think the game theory calculation here is how many threats (e.g., Trump tweets) and salami tactics (e.g., sanctions that punish NK but don't necessarily trigger an NK first strike) can the NK regime absorb before Kim calculates that NK first strike is > nobody shoots.
I think that's the Trump miscalculation, which is what the article you cited pointed out. Every Trump threat, etc. is presumably pushing Kim to a place where he cannot survive "nobody shoots" outcomes. Someone else pointed it out, but the way out of this is to give Kim an ability not to shoot AND to save face so that he gets his payoff from nobody shoots scenarios.