I have to say, I have seen several cases where they keep countering in a fully transparent way where everyone has access to the same information. I find it far more excruciating. The biggest problem is the winning buyer feels completely used by the system at the end. The seller ends up with a bitter buyer who is looking to get their pound of flesh back and in nearly every case the transaction explodes on everyone.
In the “best and final” system, I tell clients to pick the number you are comfortable with and can be satisifed with “win or lose”. So yes it does work for my buyers too. Its not perfect but I find its better than the alternative above.