  We address the problem of improving bidders' strategies in prior-dependent
revenue-maximizing auctions and introduce a simple and generic method to design
novel bidding strategies if the seller uses past bids to optimize her
mechanism. We propose a simple and agnostic strategy, independent of the
distribution of the competition, that is robust to mechanism changes and local
(as opposed to global) optimization of e.g. reserve prices by the seller. This
strategy guarantees an increase in utility compared to the truthful strategy
for any distribution of the competition. In textbook-style examples, for
instance with uniform [0,1] value distributions and two bidders, this
no-side-information and mechanism-independent strategy yields an enormous 57%
increase in buyer utility for lazy second price auctions with monopoly
reserves. When the bidder knows the distribution of the highest bid of the
competition, we show how to optimize the tradeoff between reducing the reserve
price and beating the competition. Our formulation enables to study some
important robustness properties of the strategies, showing their impact even
when the seller is using a data-driven approach to set the reserve prices. In
this sample-size setting, we prove under what conditions, thresholding bidding
strategies can still improve the buyer's utility. The gist of our approach is
to see optimal auctions in practice as a Stackelberg game where the buyer is
the leader, as he is the first one to move (here bid) when the seller is the
follower as she has no prior information on the bidder.
