My answer to this would be that people have dispositions to behavior, and these dispositions color everything we do. If one might profit by showing courage, a coward will not do as well as a courageous man.

Of course, the relative success of such people at faking in appropriate situations is perhaps an empirical question.

ETA: this makes less sense as a direct response since you edited your comment. However, I think the difference is that "being a cooperator" regards a disposition that is part of the sort of person you are (though I think the above comment uses it more narrowly as a disposition that might only affect this one action), while a precommitment... well, I'm not sure actual people really do have those, if they're immutable.