Inside the building there would be a menu where you could put items for sale and ask what you want in return, then people could bid on your item (maybe giving more than you asked so they have a higher chance of winning) and you accept the bid that you like most, switching the items automatically.
After the bid is closed, the ones who didn't win have their items returned to their owners.
Bids can stay open for 7 days, if nothing happens the items are returned to their owners.
EDIT: after thinking about it for a few days I think this is a bad idea. It's more fun when this kind of stuff is run by players instead of being automated
I'll leave this up in case people still want to discuss it