The Simple Empirics of Optimal Online Auctions
We study reserve prices computed to maximize the expected profit of the seller based on historical observations of incomplete bid data typically available to the auction designer in online auctions for advertising or e-commerce. This direct approach to computing reserve prices circumvents the need to fully recover distributions of bidder valuations. We derive asymptotic results and also provide a new bound, based on the empirical Rademacher complexity, for the number of historical auction observations needed in order for revenue under the estimated reserve price to approximate revenue under the optimal reserve arbitrarily closely. This simple approach to estimating reserves may be particularly useful for auction design in Big Data settings, where traditional empirical auctions methods may be costly to implement. We illustrate the approach with e-commerce auction data from eBay. We also demonstrate how this idea can be extended to estimate all objects necessary to implement the Myerson (1981) optimal auction.
We thank Isa Chaves, Han Hong, Dan Quint, Evan Storms, and Anthony Zhang for helpful comments. Coey and Sweeney were employees of eBay Research Labs while working on this project, and Larsen was a part-time consultant for eBay Research Labs when the project was started. eBay had the right to review the paper before it was circulated, but did not attempt to influence the research in any way. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.