  We consider the "Offline Ad Slot Scheduling" problem, where advertisers must
be scheduled to "sponsored search" slots during a given period of time.
Advertisers specify a budget constraint, as well as a maximum cost per click,
and may not be assigned to more than one slot for a particular search.
  We give a truthful mechanism under the utility model where bidders try to
maximize their clicks, subject to their personal constraints. In addition, we
show that the revenue-maximizing mechanism is not truthful, but has a Nash
equilibrium whose outcome is identical to our mechanism. As far as we can tell,
this is the first treatment of sponsored search that directly incorporates both
multiple slots and budget constraints into an analysis of incentives.
  Our mechanism employs a descending-price auction that maintains a solution to
a certain machine scheduling problem whose job lengths depend on the price, and
hence is variable over the auction. The price stops when the set of bidders
that can afford that price pack exactly into a block of ad slots, at which
point the mechanism allocates that block and continues on the remaining slots.
To prove our result on the equilibrium of the revenue-maximizing mechanism, we
first show that a greedy algorithm suffices to solve the revenue-maximizing
linear program; we then use this insight to prove that bidders allocated in the
same block of our mechanism have no incentive to deviate from bidding the fixed
price of that block.
