CAMBO: Combinatorial Auctions using Matrix Bids with Order

Since combinational auctions allow bidders to bid on any combination of goods, bid data can be of exponential size. To combat this problem, restrictions have been proposed limiting the number of bundles a bidder is allowed to bid on (as in FCC Auction #31). We describe a new combinatorial auction format that restricts bidders to submit a fixed number of “matrix bids with order”. The advantage of this approach is that it provides bidders a mechanism to compactly express bids on every possible bundle. We describe many different types of preferences that can be modeled using matrix bids and show that matrix bids are quite flexible, supporting additive, subadditive, and superadditive preferences simultaneously. We model the NP-hard winner determination problem for CAMBO as a polynomiallysized integer program, and discuss computational techniques for solving this problem. Our results suggest that CAMBO is an easy to use format. Further, the winner determination can be rapidly achieved for at least 50 goods, indicating that this model may be well suited for practical implementation.