We study dynamic mechanisms for optimizing revenue in repeated auctions, that are robust to heterogeneous forward-looking and learning behavior of the buyers. Typically it is assumed that the buyers are either all myopic or are all infinite lookahead, and that buyers understand and trust the mechanism. These assumptions raise the following question: is it possible to design approximately revenue optimal mechanisms when the buyer pool is heterogeneous? Facing a heterogeneous population of buyers with an unknown mixture of @math -lookahead buyers, myopic buyers, no-regret-learners and no-policy-regret learners, we design a simple state-based mechanism that achieves a constant fraction of the optimal achievable revenue.
The stream closest to our paper is the work on revenue maximization in repeated auctions @cite_22 @cite_37 @cite_6 @cite_8 @cite_24 @cite_27 @cite_0 @cite_26 @cite_29 . The main difference of our work from all of these, with the exception of @cite_0 @cite_15 , is the notion of dynamic incentive compatibility which assumes that all buyers are infinite lookahead, while we allow arbitrary mixtures of buyer attitudes. @cite_0 study the @math -buyer setting and design robust auctions when the buyers are @math -lookahead buyers or no-simple-regret learners or no-policy-regret learners. @cite_26 also study the @math -buyer setting and design mechanisms to extract more than Myerson's revenue when the buyers follow no-simple-regret learning strategies, and in particular a subset of them called mean-based bidding strategies.
@cite_37 @cite_26 @cite_22 @cite_8 @cite_29 @cite_6 @cite_24 @cite_0 @cite_27 @cite_15
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We study revenue optimization in a repeated auction between a single seller anda single buyer. Traditionally, the design of repeated auctions requires strong modeling assumptions about the bidder behavior, such as it being myopic, infinite lookahead, or some specific form of learning behavior. Is it possible to design mechanisms which are simultaneously optimal against a multitude of possible buyer behaviors? We answer this question by designing a simple state-based mechanism that is simultaneously approximately optimal against a k -lookahead buyer for all k , a buyer who is a no-regret learner, and a buyer who is a policy-regret learner. Against each type of buyer our mechanism attains a constant fraction of the optimal revenue attainable against that type of buyer. We complement our positive results with almost tight impossibility results, showing that the revenue approximation tradeoffs achieved by our mechanism for different lookahead attitudes are near-optimal. 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. In the design and analysis of revenue-maximizing auctions, auction performance is typically measured with respect to a prior distribution over inputs. The most obvious source for such a distribution is past data. The goal of this paper is to understand how much data is necessary and sufficient to guarantee near-optimal expected revenue. Our basic model is a single-item auction in which bidders' valuations are drawn independently from unknown and nonidentical distributions. The seller is given m samples from each of these distributions "for free" and chooses an auction to run on a fresh sample. How large does m need to be, as a function of the number k of bidders and e 0, so that a (1 -- e)-approximation of the optimal revenue is achievable? We prove that, under standard tail conditions on the underlying distributions, m = poly(k, 1 e) samples are necessary and sufficient. Our lower bound stands in contrast to many recent results on simple and prior-independent auctions and fundamentally involves the interplay between bidder competition, non-identical distributions, and a very close (but still constant) approximation of the optimal revenue. It effectively shows that the only way to achieve a sufficiently good constant approximation of the optimal revenue is through a detailed understanding of bidders' valuation distributions. Our upper bound is constructive and applies in particular to a variant of the empirical Myerson auction, the natural auction that runs the revenue-maximizing auction with respect to the empirical distributions of the samples. To capture how our sample complexity upper bound depends on the set of allowable distributions, we introduce α-strongly regular distributions, which interpolate between the well-studied classes of regular (α = 0) and MHR (α = 1) distributions. We give evidence that this definition is of independent interest. In this paper, we introduce a novel approach for reducing the k-item n-bidder auction with additive valuation to k-item 1-bidder auctions. This approach, called the Best-Guess reduction, can be applied to address several central questions in optimal revenue auction theory such as the relative strength of simple versus complex mechanisms, the power of randomization, and Bayesian versus dominant-strategy implementations. First, when the items have independent valuation distributions, we present a deterministic mechanism called Deterministic Best-Guess that yields at least a constant fraction of the optimal revenue by any randomized mechanism. This also gives the first simple mechanism that achieves constant fraction optimal revenue for such multi-buyer multi-item auctions. Second, if all the nk valuation random variables are independent, the optimal revenue achievable in dominant strategy incentive compatibility (DSIC) is shown to be at least a constant fraction of that achievable in Bayesian incentive compatibility (BIC). Third, when all the nk values are identically distributed according to a common one-dimensional distribution F, the optimal revenue is shown to be expressible in the closed form Θ(k(r + ∫0mr(1 − F(x)n)dx)) where r = supx≥0 x(1 − F(x)n) and m = lk nr; this revenue is achievable by a simple mechanism called 2nd-Price Bundling. All our results apply to arbitrary distributions, regular or irregular.