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We model multi-unit auctions in which bidders’ valuations are multidimensional private information. We show that the last accepted bid uniform-pricing rule admits a unique equilibrium with a simple characterization; in comparison, the commonly-studied first rejected bid uniform-pricing rule admits many equilibria, many of which provide zero expected revenue. In a natural example, equilibrium strategies in the last accepted bid auction are constructed from familiar strategies for single-unit first price auctions. In contrast with the information pooling we prove to arise in the first rejected bid and pay as bid auctions, the unique equilibrium of the last accepted bid auction is fully revealing.
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