Deferred-Acceptance Auctions for Multiple Levels of Service

Deferred-acceptance (DA) auctions} are mechanisms that are based on backward-greedy algorithms and possess a number of remarkable incentive properties, including implementation as an obviously-strategyproof ascending auction. All existing work on DA auctions considers only binary single-parameter problems, where each bidder either ``wins'' or ``loses.'' This paper generalizes the DA auction framework to non-binary settings, and applies this generalized framework to obtain approximately welfare-maximizing DA auctions for a number of basic mechanism design problems: multiunit auctions, problems with polymatroid constraints or multiple knapsack constraints, and the problem of scheduling jobs to minimize their total weighted completion time. Our results require the design of novel backward-greedy algorithms with good approximation guarantees.