Say the market is showing you between $X-$Y.
Consider it a form of late-binding. You want to be dynamic. So make that range both realistic and wide.
This is beneficial to you for a number of reasons. It will eliminate companies that can't get there. Win. It doesn't commit you to a specific number. Win. You don't have to ruin the rapport with an unnecessary game of chicken over who says the first number. Win. And most importantly, you have a wide open range to negotiate in when your offers come in. You can say... hey, I was upfront about my range, and I really feel like I'm <here> in that range for <these reasons>.
Using this strategy has worked beautifully for me.