  Motivated by sponsored search auctions, we study multi-unit auctions with
budget constraints. In the mechanism we propose, Sort-Cut, understating budgets
or values is weakly dominated. Since Sort-Cut's revenue is increasing in
budgets and values, all kinds of equilibrium deviations from true valuations
turn out to be beneficial to the auctioneer. We show that the revenue of
Sort-Cut can be an order of magnitude greater than that of the natural Market
Clearing Price mechanism, and we discuss the efficiency properties of its
ex-post Nash equilibrium.
