On the computational power of demand queries

We study the computational power of iterative combinatorial auctions. Most existing iterative combinatorial auctions are based on repeatedly suggesting prices for bundles of items and querying the bidders for their "demand" under these prices. We prove several results regarding such auctions that use a polynomial number of demand queries: (1) that such auctions can simulate several other natural types of queries; (2) that they can approximate the optimal allocation as well as generally possible using polynomial communication or computation, while weaker types of queries cannot do so; (3) that such auctions that use only item prices may solve allocation problems in communication cost that is exponentially lower than the cost incurred by auctions that use prices for bundles. For the latter result, we initiate the study of how prices of bundles can be represented when they are not linear and show that the "default" representation has severe limitations. Our results hold for any series of demand queries with polynomial length, without any additional restrictions on the queries (e.g., to ascending prices).