Selling to a No-Regret Buyer
Mark Braverman, Jieming Mao, Jon Schneider, S. Matthew Weinberg

TL;DR
This paper studies repeated auctions with a buyer using no-regret learning algorithms, revealing how different buyer strategies influence the seller's optimal auction design and achievable revenue.
Contribution
It characterizes optimal seller strategies under buyer no-regret learning, including scenarios with mean-based algorithms and natural auction formats, and provides revenue bounds.
Findings
Buyer using EXP3 can extract near-welfare revenue.
Optimal seller strategy with certain algorithms is to post Myerson reserve.
Revenue can be unboundedly better or worse than truthful auction.
Abstract
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 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 , but somewhat unnatural as it is sometimes in the buyer's interest to overbid. - There exists a learning…
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