  With the increasing use of auctions in online advertising, there has been a
large effort to study seller revenue maximization, following Myerson's seminal
work, both theoretically and practically. We take the point of view of the
buyer in classical auctions and ask the question of whether she has an
incentive to shade her bid even in auctions that are reputed to be truthful,
when aware of the revenue optimization mechanism.
  We show that in auctions such as the Myerson auction or a VCG with reserve
price set as the monopoly price, the buyer who is aware of this information has
indeed an incentive to shade. Intuitively, by selecting the revenue maximizing
auction, the seller introduces a dependency on the buyers' distributions in the
choice of the auction. We study in depth the case of the Myerson auction and
show that a symmetric equilibrium exists in which buyers shade non-linearly
what would be their first price bid. They then end up with an expected payoff
that is equal to what they would get in a first price auction with no reserve
price.
  We conclude that a return to simple first price auctions with no reserve
price or at least non-dynamic anonymous ones is desirable from the point of
view of both buyers, sellers and increasing transparency.
