Standard studies of multiple unit auctions generally overlook the stra
tegic role of bidders' quantity decisions. Using a simple equilibrium
model of bidding I analyze bidders' incentives to choose quantities in
discriminatory and competitive auctions. The main result is that bidd
ers have a stronger strategic incentive to bid for fewer units in comp
etitive auctions. Since under competition a bidder pays the lowest acc
epted price for each unit she gets, she may benefit from dropping her
quantity to let lower-valuing bidders enter the set of winners. This p
rediction is consistent with empirical observations from foreign curre
ncy and spectrum auctions.