Unit-demand auctions : bridging theory and practice
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Unit-demand auctions have been well studied with applications in several areas. In this dissertation, we discuss new variants of the unit-demand auction that are motivated by practical applications. We design mechanisms for these variants that have strong properties related to truthfulness, efficiency, scalability, and privacy. The main contributions of this dissertation can be divided into two parts. In the first part, we introduce a new variant of the classic sealed-bid unit-demand auction in which each item is associated with a put option; the put option of an item gives the seller the right to sell the item at a specified strike price to a specified bidder, regardless of market conditions. We motivate our unit-demand auction setting by discussing applications to the reassignment of leases, and to the design of multi-round auctions. For the classic sealed-bid unit-demand framework, the VCG mechanism provides a truthful auction with strong associated guarantees, including efficiency and envy-freedom. For an item in our auction, the strike price of the associated put imposes a lower bound on the auction price. Due to these lower bound constraints on auction prices, we find that the VCG mechanism is not suitable for our setting. Instead, our work draws on two fundamental techniques, one from the realm of mechanism design for numerical preferences -- the dynamic unit-demand approximate auction of Demange, Gale, and Sotomayor -- and one from the realm of mechanism design for ordinal preferences -- the Top Trading Cycles algorithm -- to obtain a natural auction that satisfies the lower bound constraints on auction prices. While we cannot, in general, achieve either efficiency or envy-freedom in our setting, our auction achieves suitably relaxed versions of these properties. For example, this auction is envy-free for all bidders who do not acquire an item via the exercise of a put. We provide a polynomial time implementation of this auction. By breaking ties in an appropriate manner, we are able to prove that this auction is truthful. In the second part, we specify rules for a dynamic unit-demand auction that supports arbitrary bid revision. In each round, the dynamic auction takes a tentative allocation and pricing as part of the input, and allows each bidder -- including a tentatively allocated bidder -- to submit an arbitrary unit-demand bid. Each round of our dynamic auction is implemented via a single application of the sealed-bid unit-demand auction proposed in the first part. We show that our dynamic auction satisfies strong properties related to truthfulness and efficiency. Using a certain privacy preservation property of each round of the auction, we show that the overall dynamic auction is highly resistant to shilling. We present a fast algorithm for implementing the proposed auction. Using this algorithm, the amortized cost of processing each bidding operation is upper bounded by the complexity of solving a single-source shortest paths problem on a graph with nonnegative edge weights and a node for each item in the auction. We also propose a dynamic price adjustment scheme that discourages sniping by providing bidders with incentives to bid early in the auction.