Robust Auctions for Revenue via Enhanced Competition

AbstractIn “Robust Auctions for Revenue via Enhanced Competition,” T. Roughgarden, I. Talgam-Cohen, and Q. Yan revisit the classic Bulow–Klemperer result. This result compares the revenues of two well-known auction formats: the welfare-maximizing Vickrey auction and the revenue-maximizing Myerson auction. It shows that, with an extra bidder competing for the item, the Vickrey auction becomes as good as the Myerson auction in terms of revenue while maintaining independence from prior distributional information about bidders’ valuations. Unfortunately, Myerson’s toolbox for revenue-optimal auction design does not extend to combinatorial auctions with multiple heterogenous items, for which optimizing revenue remains a challenge—especially if we want auction designs that are simple and robust enough to use in practice. This paper extends the Bulow–Klemperer result to multiple heterogenous items by showing that a prior-independent, simple, welfare-maximizing auction with additional competing bidders achieves as much revenue as the ill-understood optimal auction.Most results in revenue-maximizing mechanism design hinge on “getting the price right”—selling goods to bidders at prices low enough to encourage a sale but high enough to garner nontrivial revenue. This approach is difficult to implement when the seller has little or no a priori information about bidder valuations or when the setting is sufficiently complex, such as matching markets with heterogeneous goods. In this paper, we apply a robust approach to designing auctions for revenue. Instead of relying on prior knowledge regarding bidder valuations, we “let the market do the work” and let prices emerge from competition for scarce goods. We analyze the revenue guarantees of one of the simplest imaginable implementations of this idea: first, we enhance competition in the market by increasing demand (or alternatively, by limiting supply), and second, we run a standard second price (Vickrey) auction. In their renowned work from 1996, Bulow and Klemperer [Bulow J, Klemperer P (1996) Auctions vs. negotiations. Amer. Econom. Rev. 86(1):180–194.] apply this method to markets with single goods. As our main result, we give the first application beyond single-parameter settings, proving that, simultaneously for many valuation distributions, this method achieves expected revenue at least as good as the optimal revenue in the original market. Our robust and simple approach provides a handle on the elusive optimal revenue in multiitem matching markets and shows when the use of welfare-maximizing Vickrey auctions is justified, even if revenue is a priority. By establishing quantitative tradeoffs, our work provides guidelines for a seller in choosing among two different revenue-extracting strategies: sophisticated pricing based on market research or advertising to draw additional bidders.