It's great if the other party gives a number first, but this binary, on-of-us-has-to-be-a-looser game can be a pain in the ass. Have a fall-back strategy, like giving a high number first, or even better, simply be very pragmatic, i.e. know what you're worth (or want), say that number first and don't ever budge. When pressed, point out that you understand it's bad negotiating strategy to give a number first, but you're not playing games here, you being very straight up.