Incentive-Compatible Learning of Reserve Prices for Repeated Auctions

Motivated by online advertising market, we consider a seller who repeatedly sells ex ante identical items via the second-price auction. Buyers’ valuations for each item are drawn i.i.d. from a distribution F that is unknown to the seller. We find that if the seller attempts to dynamically update a common reserve price based on the bidding history, this creates an incentive for buyers to shade their bids, which can hurt revenue. When there is more than one buyer, incentive compatibility can be restored by using personalized reserve prices, where the personal reserve price for each buyer is set using the historical bids of other buyers. In addition, we use a lazy allocation rule, so that buyers do not benefit from raising the prices of their competitors. Such a mechanism asymptotically achieves the expected revenue obtained under the static Myerson optimal auction for F. Further, if valuation distributions differ across bidders, the loss relative to the Myerson benchmark is only quadratic in the size of such differences. We extend our results to a contextual setting where the valuations of the buyers depend on observed features of the items.