Not a very practical idea though. Cause you will accept all sort of ridiculous prices by stupid people. (You can try to set a fixed range of price that is allowed, but then everyone will go for the cheapest price, which will defeat the purpose of letting people name their own price.)
I'd love to pay less for prints but I don't want to rob artists of their proper value since i would know what their works would be worth. I don't want to pay 60-80 bucks for a print but i wouldn't want to pay 5 bucks for the same print. Everything has some value and i would want to be able to give an artist what they deserve.
The only people I'd buy prints from are the "underground artists", like the ones not many people know about. They'd deserve the money for great art. I wouldn't buy prints from popular artists coz most of them would become greedy and totally overprice their art.