  Signaling is an important topic in the study of asymmetric information in
economic settings. In particular, the transparency of information available to
a seller in an auction setting is a question of major interest. We introduce
the study of signaling when conducting a second price auction of a
probabilistic good whose actual instantiation is known to the auctioneer but
not to the bidders. This framework can be used to model impressions selling in
display advertising. We study the problem of computing a signaling scheme that
maximizes the auctioneer's revenue in a Bayesian setting. While the general
case is proved to be computationally hard, several cases of interest are shown
to be polynomially solvable. In addition, we establish a tight bound on the
minimum number of signals required to implement an optimal signaling scheme and
show that at least half of the maximum social welfare can be preserved within
such a scheme.
