> if the other side is in "I win, you lose" mode, none of these coping strategies really work.

If I'm dealing with a person like that, and the thing they want to "win" isn't something important for work, then I just let them "win". It's no skin off my nose. Let them have their meaningless victory.

If it is something important for work, then I just make the best factual case I can to whoever matters and roll with the results.