In auctions a seller offers a commodity for sale and collects the revenue. In fair division games the object is collectively owned by the group of bidders who equally share the revenue. We run an experiment in which the participants face four types of allocation games (auctions and fair division game under two price rules, first- versus second-price rule). We collect entire bid functions rather than bids for single values and investigate price and efficiency of the different trading institutions. We find that the first-price auction is more efficient than the second-price auction, whereas economic rationality assuming heterogeneous bidders suggests the opposite. Furthermore, we study the structure of individual bid functions.