None of the big US brands do that. They each have a best price guarantee that gives you a free night or 50% off or something if you are able to reserve for cheaper than on their official website.

The only thing they might engage in is opaque pricing, which is Priceline and hotwire auction. But that is different since it's not a publicly advertised price, the buyer puts in how much they want to pay and they are stuck with whatever hotel Priceline or hotwire give them.

But reputable hotels don't resort to that since that attracts price sensitive guests that aren't desirable anyway, such as prostitutes and drug dealers.