OP -- the GSA/DOD per diem committee sets per diem hotel rates annually. Hotels are not required to provide those rates. Many do, however, unless they are at high occupancy.
In my experience, the government rates at Marriott are cheaper than other available rates (often significantly cheaper) 90/95 percent of the time. Those rates are constant and don't depend on market condition.
Occasionally, there will be a low vacancy rate at the hotel and they will lower rates to bring in more guests (think Friday night in a business center). When that happens, the rates could be lower than the government rates which don't change. The Marriott member rates are just a slight discount off regular rates.
As a responsible government traveler seeking to be responsible with taxpayer dollars, I will check both rates and sometimes make multiple reservations, such as Sunday and Monday at a discounted non-government rate, Tuesday through Thursday at a government rate, etc. Note that when you do that and submit your voucher through DTS, you need to adjust the hotel per diem to reflect what you actually paid.