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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Reducing inefficiency in carbon auctions with imperfect competition.
We study auctions for carbon licenses, a policy tool used to control the social cost of pollution. Each identical license grants the right to produce a unit of pollution. Each buyer (i.e., firm that pollutes during the manufacturing process) enjoys a decreasing marginal value for licenses, but society suffers an increasing marginal cost for each license distributed. The seller (i.e., the government) can choose a number of licenses to put up for auction, and wishes to maximize the societal welfare: the total economic value of the buyers minus the social cost. Motivated by emission license markets deployed in practice, we focus on uniform price auctions with a price floor and/or price ceiling. The seller has distributional information about the market, and their goal is to tune the auction parameters to maximize expected welfare. The target benchmark is the maximum expected welfare achievable by any such auction under truthtelling behavior. Unfortunately, the uniform price auction is not truthful, and strategic behavior can significantly reduce (even below zero) the welfare of a given auction configuration.
We describe a subclass of “safeprice” auctions for which the welfare at any BayesNash equilibrium will approximate the welfare under truthtelling behavior. We then show that the better of a safeprice auction, or a truthful auction that allocates licenses to only a single buyer, will approximate the target benchmark. In particular, we show how to choose a number of licenses and a price floor so that the worstcase welfare, at any equilibrium, is a constant approximation to the best achievable welfare under truthtelling after excluding the welfare contribution of a single buyer.
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 Award ID(s):
 1903037
 NSFPAR ID:
 10471374
 Editor(s):
 Vidick, T.
 Publisher / Repository:
 LIPIcs
 Date Published:
 Journal Name:
 11th Innovations in Theoretical Computer Science Conference, ITCS 2020
 Volume:
 151
 Page Range / eLocation ID:
 15:1–15:21
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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