Honestly I tried this every time I was interviewed. Never could get them to give the first number. I probably should have been firmer but usually the pressure of the situation led to me giving a number I would be happy with.
"I've actually done a few of these calls at this point and i know what the best practice / right move / way to play this is, so instead of me telling you what i'm looking for i'd like you to tell me the range on your hiring document:)" and just be totally silent.
Worked twice for me now.
Most people want to fill the audio void and will talk. Extensively.
Usually that comes with the offer letter, or comes with the numbers that the recruiter reads to you before the offer letter.
But this is usually much before offer letter.
Now I ask back with “what is the total compensation for this position/role?”. I almost always get an answer, often above my expectations. I used to give my range (mistake)
When they answer "no, we want you to give a number first", I'm at loss about what to do, so I usually give them a number. Answering "no, you" feels kinda puerile.
I assume you have to be the first to do the power play?