TY - GEN

T1 - Selling to a no-regret buyer

AU - Braverman, Mark

AU - Mao, Jieming

AU - Schneider, Jon

AU - Weinberg, Matt

N1 - Funding Information:
This work is supported by NSF CAREER award (CCF-1149888), NSF CCF-1215990, NSF CCF-1525342, NSF CCF-1412958, a Packard Fellowship in Science and Engineering, the Simons Collaboration on Algorithms and Geometry and NSF CCF-1717899.
Publisher Copyright:
© 2018 Association for Computing Machinery.

PY - 2018/6/11

Y1 - 2018/6/11

N2 - 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 no-regret learning algorithm over possible bids. We provide a fairly complete characterization of optimal auctions for the seller in this domain. Specifically: • If the buyer bids according to EXP3 (or any “mean-based” 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. • There exists a learning algorithm A such that if the buyer bids according to A then the optimal strategy for the seller is simply to post the Myerson reserve for D every round. • If the buyer bids according to EXP3 (or any “mean-based” learning algorithm), but the seller is restricted to “natural” auction formats where overbidding is dominated (e.g. Generalized First-Price or Generalized Second-Price), then the optimal strategy for the seller is a pay-your-bid 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.

AB - 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 no-regret learning algorithm over possible bids. We provide a fairly complete characterization of optimal auctions for the seller in this domain. Specifically: • If the buyer bids according to EXP3 (or any “mean-based” 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. • There exists a learning algorithm A such that if the buyer bids according to A then the optimal strategy for the seller is simply to post the Myerson reserve for D every round. • If the buyer bids according to EXP3 (or any “mean-based” learning algorithm), but the seller is restricted to “natural” auction formats where overbidding is dominated (e.g. Generalized First-Price or Generalized Second-Price), then the optimal strategy for the seller is a pay-your-bid 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.

KW - Auctions

KW - Mechanism design

KW - Multi-armed bandits

KW - No-regret learning

UR - http://www.scopus.com/inward/record.url?scp=85050086319&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050086319&partnerID=8YFLogxK

U2 - 10.1145/3219166.3219233

DO - 10.1145/3219166.3219233

M3 - Conference contribution

AN - SCOPUS:85050086319

T3 - ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation

SP - 523

EP - 538

BT - ACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation

PB - Association for Computing Machinery, Inc

T2 - 19th ACM Conference on Economics and Computation, EC 2018

Y2 - 18 June 2018 through 22 June 2018

ER -