People will pay whatever amount they value the item, not what the game values the item. Since everyone values items differently, the price cannot be constant* or people will stop buying (if algorithm prices it too high) or selling (if algorithm prices it too low). From there, everyone will move to manual trading and the whole AH system would die.
(*even if the price could vary over time, people would wait until the price is right.)

There is a game which had implemented this; all items have a price (which even extended to trades as well) and they change everyday slightly depending on how many have been sold. This went on for a while and people found workarounds, eventually they removed the system and allowed free trading again.

tldr
It won't work