Dynamic Reserve Prices for Repeated Auctions: Learning from Bids
50 Pages Posted: 9 Jun 2014 Last revised: 31 Jan 2019
Date Written: 1 1, 2019
A large fraction of online advertisements are sold via repeated second-price auctions. In these auctions, the reserve price is the main tool for the auctioneer to boost revenues. In this work, we investigate the following question: How can the auctioneer optimize the reserve prices by learning from the previous bids, while accounting for the long-term incentives and strategic behavior of the bidders?
To this end, we consider a seller who repeatedly sells ex ante identical items via a 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. 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.
When up-front fees are permitted, we show how the seller can determine such payments based on the bids of others to obtain an approximately incentive compatible-mechanism that extracts nearly all the surplus.
JEL Classification: D44
Suggested Citation: Suggested Citation