Large fractions of online advertisements are sold via repeated secondprice 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 reserve prices by learning from the previous bids while accounting for the longterm incentives and strategic behavior of the bidders? To this end, we consider a seller who repeatedly sells ex ante identical items via a secondprice auction. Buyers’ valuations for each item are drawn independently and identically 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 upfront fees are permitted, we show how the seller can determine such payments based on the bids of others to obtain an approximately incentivecompatible mechanism that extracts nearly all the surplus.
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Selling to a NoRegret Buyer
We consider the problem of a single seller repeatedly selling a single item to a single buyer (specifically, the buyer has a value drawn fresh from known distribution $D$ in every round). Prior work assumes that the buyer is fully rational and will perfectly reason about how their bids today affect the seller's decisions tomorrow. In this work we initiate a different direction: the buyer simply runs a noregret learning algorithm over possible bids. We provide a fairly complete characterization of optimal auctions for the seller in this domain. Specifically:
1) If the buyer bids according to EXP3 (or any ``meanbased'' learning algorithm), then the seller can extract expected revenue arbitrarily close to the expected welfare. This auction is independent of the buyer's valuation $D$, but somewhat unnatural as it is sometimes in the buyer's interest to overbid.
2) There exists a learning algorithm $\mathcal{A}$ such that if the buyer bids according to $\mathcal{A}$ then the optimal strategy for the seller is simply to post the Myerson reserve for $D$ every round.
3) If the buyer bids according to EXP3 (or any ``meanbased'' learning algorithm), but the seller is restricted to ``natural'' auction formats where overbidding is dominated (e.g. Generalized FirstPrice or Generalized SecondPrice), then the optimal strategy for the seller is a payyourbid format with decreasing reserves over time. Moreover, the seller's optimal achievable revenue is characterized by a linear program, and can be unboundedly better than the best truthful auction yet simultaneously unboundedly worse than the expected welfare.
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 Award ID(s):
 1717899
 NSFPAR ID:
 10069457
 Date Published:
 Journal Name:
 Economics and Computation
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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