  In a single-parameter mechanism design problem, a provider is looking to sell
a service to a group of potential buyers. Each buyer $i$ has a private value
$v_i$ for receiving the service and a feasibility constraint restricts which
sets of buyers can be served simultaneously. Recent work in economics
introduced clock auctions as a superior class of auctions for this problem, due
to their transparency, simplicity, and strong incentive guarantees. Subsequent
work focused on evaluating the social welfare approximation guarantees of these
auctions, leading to strong impossibility results: in the absence of prior
information regarding the buyers' values, no deterministic clock auction can
achieve a bounded approximation, even for simple feasibility constraints with
only two maximal feasible sets.
  We show that these negative results can be circumvented by using prior
information or by leveraging randomization. We provide clock auctions that give
a $O(\log\log k)$ approximation for general downward-closed feasibility
constraints with $k$ maximal feasible sets for three different information
models, ranging from full access to the value distributions to complete absence
of information. The more information the seller has, the simpler these auctions
are. Under full access, we use a particularly simple deterministic clock
auction, called a single-price clock auction, which is only slightly more
complex than posted price mechanisms. In this auction, each buyer is offered a
single price and a feasible set is selected among those who accept their
offers. In the other extreme, where no prior information is available, this
approximation guarantee is obtained using a complex randomized clock auction.
In addition to our main results, we propose a parameterization that
interpolates between single-price clock auctions and general clock auctions,
paving the way for an exciting line of future research.
