Expressing Preferences with Price-Vector Agents in Combinatorial Auctions

Title of dissertation: EXPRESSING PREFERENCES WITH PRICE-VECTOR AGENTS IN COMBINATORIAL AUCTIONS Robert W. Day, Doctor of Philosophy, 2004 Dissertation directed by: Professor Subramanian Raghavan Decision and Information Technologies Department, The Robert H. Smith School of Business In this work, we investigate two combinatorial auction formats in which each bidding bidder may be represented by a collection of unit-demand or pricevector agents. In the first model, bidder preferences are aggregated in a Bid Table, through which a bidder in a combinatorial auction may express several forms of subadditive preferences. We show that the gross substitutes property holds for this model, and design a large-scale combinatorial auction using bid tables as a demand revelation stage, determining linear price signals for later stages. The constraints of this model coincide naturally with the restrictions of recently proposed FAA landingslot auctions, and we provide a slot auction design based on this model. In a second model, we explore the more complex behavior possible when each bidder’s collection of price-vector agents coordinate based on a bidder-specified ordering of the auction items. With this coordination each bidder is able to convey a rich set of preferences, including the ability to express both superadditive and subadditive bundle synergies (i.e., substitutes and complements). The instructions for this collection of agents are tabulated in a lower-triangular Matrix Bid, and we compare the use of matrix bids to other compact techniques for writing down a wide variety of bidding information. We show that the winner determination problem for this Matrix Bid Auction is NP-hard, provide results from a series of computational experiments, and develop IP techniques for improving run time. In addition to the results on price-vector agents, bid tables, and matrix bidding, we present a new technique for achieving bidder-Pareto-optimal core outcomes in a sealed-bid combinatorial auction. The key idea of this iterative procedure is the formulation of the separation problem for core constraints at an arbitrary point in winner payment space. EXPRESSING PREFERENCES WITH PRICE-VECTOR AGENTS IN COMBINATORIAL AUCTIONS