Descending price auctions are adopted for goods that must be sold quickly and in private values environments, for instance in flower, fish, and tobacco auctions. In this paper, we introduce efficient descending auctions for two environments: multiple non-identical items and buyers with unit-demand valuations; and multiple identical items and buyers with non-increasing marginal values. Our auctions are designed using the notion of universal competitive equilibrium (UCE) prices and they terminate with UCE prices, from which the Vickrey payments can be determined. For the unit-demand setting, our auction maintains linear and anonymous prices. For the homogeneous items setting, our auction maintains a single price and adopts Ausubel's notion of "clinching" to compute the final payments dynamically. The auctions support truthful bidding in an ex post Nash equilibrium and terminate with an efficient allocation. In simulation, we illustrate the speed and elicitation advantages of these auctions over their ascending price counterparts.
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