The communication complexity of combinatorial auctions
The Hebrew University of Jerusalem
We show that any implementation of combinatorial auctions that produces efficient allocations requires an exponential amount of information transfer. The lower bound is independent of any computational complexity considerations, holds even if only an approximately efficient outcome is achieved, holds whether or not the bidder strategies are in equilibrium, and holds even if all bidder valuations have decreasing marginal utilities. This is in contrast to Ausubel's efficient auction for heterogeneous goods that applies in the case that all bidder valuations satisfy the "gross substitutes" condition. The lower bound implies that mechanisms such as AUSM, iBundle or any of the suggested variants of ascending auctions with package bids cannot, in the general case, ensure both the efficiency of the outcome and sub-exponential communication.