In another comment on this post, Eugine Nier linked to Schelling. I read that post, and the Slate page that mentions Schelling vs. Vietnam, and it became clear to me that acting moral acts as an "antidote" to these underhanded strategies that count on your opponent being rational. (It also serves as a Gödelian meta-layer to decide problems that can't be decided rationally.)

If, in Schellings example, the guy who is left with the working radio set is moral, he might reason that "the other guy doesn't deserve the money if he doesn't work for it", and from that moral strongpoint refuse to cooperate. Now if the rationalist knows he's working with a moralist, he'll also know that his immoral strategy won't work, so he won't attempt it in the first place - a victory for the moralist in a conflict that hasn't even occurred (in fact, the moralist need never know that the rationalist intended to cheat him).

This is different from simply acting irrationally in that the moralist's reaction remains predictable.

So it is possible that moral indignation helps me to prevent other people from manouevering me into a position where I don't want to be.