Counterexample:
A man seduces a female movie star into a one night stand and secretly records a sex tape. He would prefer to blackmail the movie star for lots of money, but if that fails he would rather release the tape to the press for a smaller amount of money + prestige than he would just do nothing. The movie star's preference ordering is for nothing to happen, for her to pay out, then lastly for the press to find out. The optimal choice is for her to pay out, because if she pre-commits to not give in to blackmail, she will receive the worst possible outcome.
This seems to fall squarely under blackmail, yet requires no pre-committment, iteration, or bluffing.
That's a promise, not a threat, by Schelling's terminology. Once the movie start upholds her end of the bargain, the man has no incentive to keep his promise, and every incentive to break it.
Is there something game-theoretic about blackmail that makes it an identifiable subset of the group threats + promises? Note that Schelling also describes a negotiating position that is neither threat nor promise, but the combination of the two. And that's not exactly blackmail either. I suspect you could come up with a blackmail scenario that fits any of the three groupings.
From the last thread:
Meta: