On the Computational Power of Iterative Auctions I: Demand Queries

We study the computational power and limitations 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 such auctions can solve linear programming relaxations of winner determination problems; (3) that they can approximate the optimal allocation as well as generally possible using polynomial communication or computation, while weaker types of queries can not do so. We also initiate the study of how can the prices of bundles be represented when they are not linear, and show that the ``default'' representation has severe limitations.