Is this different from the question "Can groups cooperate rationally?"

Could groups commit to CEV somehow, so that it could better prevent conflict?

I have a sense that this is what people who join the intelligence services do. The intelligence services lie both to keep secrets and to manipulate people into doing things they don't really want to do. The group of people in those services who believe in what they are doing believe they are doing right, that the things they are preserving are more valuable than the lesser values of telling the truth and not killing "innocent" people. Within the intelligence services it would appear conflict is largely avoided, with rare but spectacular exceptions like Snowden.

Indeed, this group value I am noticing would appear to apply to the police and the military. Anywhere where getting things done relies upon contravening the simple values of not using physical force against other people.

Is this the kind of thing you mean to be asking about?

It depends on how many groups and how many people in each. The Tobin tax would have been great to avoid some international financial catastrophes. The Kyoto protocol and all other sorts of tragedy of the common problems indicate that this type of commitment is hard to make and harder to keep. An interesting book mixing this with transhumanism and bioethics is "Unfit for the future" by Julian Savulescu.