We propose a new Walrasian tâtonnement process called a double-track procedure for efficiently allocating multiple heterogeneous indivisible items in two distinct sets to many buyers who view items in the same set as substitutes but items across the two sets as complements. In each round of the process, a Walrasian auctioneer first announces the current prices for all items, buyers respond by reporting their demands at these prices, and then the auctioneer adjusts simultaneously the prices of items in one set upward but those of items in the other set downward. It is shown that this procedure converges globally to a Walrasian equilibrium in finitely many rounds.

This article proposes an efficient and incentive compatible dynamic auction for selling multiple complementary goods. The seller has reserve prices. The auctioneer announces a current price for every bundle of goods and a supply set of goods, every bidder responds with a set of goods demanded at these prices, and the auctioneer adjusts prices. We prove that even when bidders can exercise their market power strategically, this dynamic auction always induces them to bid truthfully, resulting in an efficient allocation, its supporting Walrasian equilibrium price for every bundle of goods, and a generalized Vickrey-Clarke-Groves payment for every bidder.