I’ll note though that you may want to make it at least somewhat easier to make the new threat, so that the other player has an incentive to use the new threat rather than the old threat, in cases where they would have used the old threat (rather than being indifferent between the two).
This does mean it is no longer a Pareto improvement, but it still seems like this sort of unilateral commitment can significantly help in expectation.
Yeah, this seems right.
I’ll note though that you may want to make it at least somewhat easier to make the new threat, so that the other player has an incentive to use the new threat rather than the old threat, in cases where they would have used the old threat (rather than being indifferent between the two).
This does mean it is no longer a Pareto improvement, but it still seems like this sort of unilateral commitment can significantly help in expectation.