An Efficient Double-Track Auction for Substitutes and Complements

We propose a dynamic auction mechanism for efficiently allocating multiple heterogeneous indivisible items. These goods can be split into two distinct sets so that items in each of the two sets are substitutes but are complementary to items in the other. The seller has a reserve value for each bundle of goods. In each round of the auction, the auctioneer announces the current prices for all items, bidders respond by reporting their demands at these prices, and then the auctioneer adjusts simultaneously the prices of items in one set upwards but those of items in the other downwards. We prove that despite the fact that bidders are not assumed to be price-takers and thus can strategically exercise their market power, this dynamic auction always yields an efficient outcome and induces the bidders to bid truthfully and at the same time protects them from fully exposing their private values.