On complexity of single-minded auction

We consider complexity issues for a special type of combinatorial auctions, the single-minded auction, where every agent is interested in only one subset of the commodities. First, we present a matching bound on the communication complexity for the single-minded auction under a general communication model. Next, we prove that it is NP-hard to decide whether Walrasian equilibrium exists in a single-minded auction. Finally, we establish a polynomial size duality theorem for the existence of Walrasian equilibrium for the single-minded auction. r 2004 Elsevier Inc. All rights reserved.