  We consider the problem of the optimization of bidding strategies in
prior-dependent revenue-maximizing auctions, when the seller fixes the reserve
prices based on the bid distributions. Our study is done in the setting where
one bidder is strategic. Using a variational approach, we study the complexity
of the original objective and we introduce a relaxation of the objective
functional in order to use gradient descent methods. Our approach is simple,
general and can be applied to various value distributions and
revenue-maximizing mechanisms. The new strategies we derive yield massive
uplifts compared to the traditional truthfully bidding strategy.
