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:
1) 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.
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 ``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.
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This content will become publicly available on November 13, 2024
Coasian Equilibria in Sequential Auctions
We study stationary equilibria in a sequential auction setting. A seller runs
a sequence of standard first-price or second-price auctions to sell an indivisible
object to potential buyers. The seller can commit to the rule of the auction and
the reserve price of the current period but not to reserve prices of future periods.
We prove the existence of stationary equilibria and establish a uniform Coase
conjecture—at any point in time and in any stationary equilibrium, the seller’s
profit from running sequential auctions converges to the profit of running an
efficient auction as the period length goes to zero.
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- Award ID(s):
- 1824328
- NSF-PAR ID:
- 10482400
- Publisher / Repository:
- SSRN
- Date Published:
- Journal Name:
- SSRN Electronic Journal
- ISSN:
- 1556-5068
- Subject(s) / Keyword(s):
- ["Coase conjecture, auctions with limited commitment, sequential auctions"]
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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