Thresholding at the monopoly price: an agnostic way to improve bidding strategies in revenue-maximizing auctions

We address the problem of improving bidders' strategies in prior-dependent revenue-maximizing auctions. We introduce a simple and generic method to design novel bidding strategies if the seller uses past bids to optimize her mechanism. This strategy works with general value distributions, with asymmetric bidders and for different revenue-maximizing mechanisms. Furthermore, it can be made robust to sample approximation errors on the seller part. This results in a large increase in utility for bidders whether they have a full or partial knowledge of their competitors. In the case where the buyer has no information about the competition, we propose a simple and agnostic strategy that is robust to mechanism changes and local (as opposed to global) optimization of e.g. reserve prices by the seller. In textbook-style examples, for instance with uniform 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 no reserves. In the i.i.d symmetric case, we show existence and uniqueness of a Nash equilibrium in the class of strategy we consider for lazy second price auctions, as well as the corresponding explicit shading strategies. Our approach also works for Myerson auctions for instance. At this Nash equilibrium, buyer's utility is the same as in a second price auction with no reserve. Our approach also yields optimal solutions when buyer are constrained in the class of shading strategies they can use, a realistic constraint in practical applications. The heart 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