Auctions with Buyer Preferences

Auctions and exchanges are one of the most important market mechanisms for price determination and allocation of goods. In this paper we consider the case when each buyer has a limited budget and wishes to buy at most one item in multi-item auctions. We show the limitations of two known mechanisms { sequence of single-item auctions and recently introduced XOR double auctions { and introduce a new mechanism, so called XOR (double) auction with buyer preferences (XOR-(D)ABP), which avoids these limitations. In the proposed mechanism buyers specify preferences on the items on which they bid. We seek allocations of the items to the buyers which are stable with respect to buyer's preferences, i.e., items which are preferable to the item allocated to a buyer are sold for a price higher or equal to what she o ered for them. In the case of double auctions, the allocation should also ensure fairness to the sellers: if an item received a bid with a higher value than the allocated price then the buyer who placed that bid gets a more or equally preferable item. We rst show that in an XOR auction with no ties in buyer preferences and bid values both buyers and sellers are better o than in an XOR auction. Second, we show that nding stable allocations with maximum revenue or buyer satisfaction can be done eÆciently in an XOR-DABP without ties, and that the problem is NP-hard problem when ties are allowed. We propose a practical heuristic for nding maximum stable allocations in the presence of ties, and report promising experimental results. Finally, we give an eÆcient algorithm for the special case when all bids for an item have the same value.