Revenue-Maximizing Auctions: A Bidder’s Standpoint

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 whenever 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 optimization of reserve prices by the seller. In many settings, it consists in overbidding for low values, then underbidding and finally bidding truthfully. This strategy guarantees an increase in utility compared with the truthful strategy for any distribution of the competition. We generalize this result by showing that a best response for maximizing bidder’s utility in a large class of possible strategies is a simple extension of this first strategy. Our new variational approach naturally yields itself to numerical optimization and algorithms for designing or improving strategies in any given selling mechanisms. Our formulation enables the study of 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, whether the sample sizes are finite or infinite. 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 to move (here bid) and where the seller is the follower as she has no prior information on the bidder.