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 paper examines an exchange economy with heterogeneous indivisible objects that can be substitutable or complementary. We show that a competitive equilibrium exists in such economies, provided that all the objects can be partitioned into two groups, and from the viewpoint of each agent, objects in the same group are substitutes and objects across the two groups are complements. This condition generalizes the well-known Kelso–Crawford gross substitutes condition and is called gross substitutes and complements. We also provide practical and typical examples from which substitutes and complements are both jointly observed.