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Auction theory has recently revealed that multi-unit uniform-price auctions, such as those used by the U.S. Treasury for debt sales, entail demand-reduction incentives that can cause inefficient allocations. Recent experimental results show that bidders do indeed strategically reduce their bids in uniform-price auctions. The present paper extends this work, both theoretically and experimentally, to consider the effects of varying numbers of bidders. We derive several theoretical predictions, including the result that demand reduction should decrease with increasing numbers of bidders, though some demand reduction remains even in the asymptotic limit. We then examine the bidding behavior of subjects in this environment by auctioning dozens of Cal Ripken, Jr. baseball cards using both uniform-price and Vickrey auction formats. The field data are broadly consistent with the theoretical predictions of our model: most notably, demand reduction on second-unit bids becomes much smaller and harder to detect as the number of bidders increases.