They are already anchored at the maximum salary they'll pay you, and you are anchored at the minimum salary you'll accept, but neither of you knows each other's

They are already anchored at the maximum salary they'll pay you, and you are anchored at the minimum salary you'll accept, but neither of you knows each other's numbers. They want to hit somewhere above your minimum. They don't want to hit your minimum (since it may be volatile) and they really, really don't want to hit below your minimum. And they are okay with hitting their maximum. In my location it costs 15-20k to find a senior engineer you want to hire. Once that happens, you really, really don't want to lose them in salary negotiations, or to another offer. So you don't lowball them. If they give you a number they can lowball themselves, but if they don't, then you offer something near your maximum. Your advice is that you give them a number so high that you're sure it's above their anchor and that it gives them no information about your anchor. But that doesn't change their anchor, and not giving a number at all is pretty close to that, while being nearly risk-free to you. Of course, once they've asked for a number, you've refused, and they've pushed on it, it may not be risk-free to fight anymore. At that point, I'd agree: Aim for the sky.