More Like this

1. The Sample Complexity of up-to-$$\varepsilon$$ Multi-Dimensional Revenue Maximization

   Gonczarowski, Yannai A.; Weinberg, S. Matthew (January 2018, Foundations of Computer Science)

   We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multi-dimensional settings. Specifically, we study the standard model of $${n}$$ additive bidders whose values for $${m}$$ heterogeneous items are drawn independently. For any such instance and any $${\varepsilon > 0}$$, we show that it is possible to learn an $${\varepsilon}$$-Bayesian Incentive Compatible auction whose expected revenue is within $${\varepsilon}$$ of the optimal $${\varepsilon}$$-BIC auction from only polynomially many samples. Our approach is based on ideas that hold quite generally, and completely sidestep the difficulty of characterizing optimal (or near-optimal) auctions for these settings. Therefore, our results easily extend to general multi-dimensional settings, including valuations that aren't necessarily even subadditive, and arbitrary allocation constraints. For the cases of a single bidder and many goods, or a single parameter (good) and many bidders, our analysis yields exact incentive compatibility (and for the latter also computational efficiency). Although the single-parameter case is already well-understood, our corollary for this case extends slightly the state-of-the-art. 

   more » « less
2. Learning Multi-Item Auctions with (or without) Samples

   Daskalakis, Constantinos; Cai, Yang (January 2017, 58th IEEE Symposium on Foundations of Computer Science (FOCS))

   We provide algorithms that learn simple auctions whose revenue is approximately optimal in multi-item multi-bidder settings, for a wide range of valuations including unit-demand, additive, constrained additive, XOS, and subadditive. We obtain our learning results in two settings. The first is the commonly studied setting where sample access to the bidders' distributions over valuations is given, for both regular distributions and arbitrary distributions with bounded support. Our algorithms require polynomially many samples in the number of items and bidders. The second is a more general max-min learning setting that we introduce, where we are given "approximate distributions," and we seek to compute an auction whose revenue is approximately optimal simultaneously for all "true distributions" that are close to the given ones. These results are more general in that they imply the sample-based results, and are also applicable in settings where we have no sample access to the underlying distributions but have estimated them indirectly via market research or by observation of previously run, potentially non-truthful auctions. Our results hold for valuation distributions satisfying the standard (and necessary) independence-across-items property. They also generalize and improve upon recent works, which have provided algorithms that learn approximately optimal auctions in more restricted settings with additive, subadditive and unit-demand valuations using sample access to distributions. We generalize these results to the complete unit-demand, additive, and XOS setting, to i.i.d. subadditive bidders, and to the max-min setting. Our results are enabled by new uniform convergence bounds for hypotheses classes under product measures. Our bounds result in exponential savings in sample complexity compared to bounds derived by bounding the VC dimension, and are of independent interest. 

   more » « less
3. Robust Auctions for Revenue via Enhanced Competition

   https://doi.org/10.1287/opre.2019.1929  

   Roughgarden, Tim; Talgam-Cohen, Inbal; Yan, Qiqi (July 2020, Operations Research)

   Most results in revenue-maximizing mechanism design hinge on “getting the price right”—selling goods to bidders at prices low enough to encourage a sale but high enough to garner nontrivial revenue. This approach is difficult to implement when the seller has little or no a priori information about bidder valuations or when the setting is sufficiently complex, such as matching markets with heterogeneous goods. In this paper, we apply a robust approach to designing auctions for revenue. Instead of relying on prior knowledge regarding bidder valuations, we “let the market do the work” and let prices emerge from competition for scarce goods. We analyze the revenue guarantees of one of the simplest imaginable implementations of this idea: first, we enhance competition in the market by increasing demand (or alternatively, by limiting supply), and second, we run a standard second price (Vickrey) auction. In their renowned work from 1996 , Bulow and Klemperer [Bulow J, Klemperer P (1996) Auctions vs. negotiations. Amer. Econom. Rev. 86(1):180–194.] apply this method to markets with single goods. As our main result, we give the first application beyond single-parameter settings, proving that, simultaneously for many valuation distributions, this method achieves expected revenue at least as good as the optimal revenue in the original market. Our robust and simple approach provides a handle on the elusive optimal revenue in multiitem matching markets and shows when the use of welfare-maximizing Vickrey auctions is justified, even if revenue is a priority. By establishing quantitative tradeoffs, our work provides guidelines for a seller in choosing among two different revenue-extracting strategies: sophisticated pricing based on market research or advertising to draw additional bidders. 

   more » « less
4. When Bidders Are DAOs

   https://doi.org/10.4230/LIPIcs.AFT.2023.21  

   Bahrani, Maryam; Garimidi, Pranav; Roughgarden, Tim (January 2023, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Bonneau, Joseph; Weinberg, S Matthew (Ed.)

   In a typical decentralized autonomous organization (DAO), people organize themselves into a group that is programmatically managed. DAOs can act as bidders in auctions (with ConstitutionDAO being one notable example), with a DAO’s bid typically treated by the auctioneer as if it had been submitted by an individual, without regard to any details of the internal DAO dynamics. The goal of this paper is to study auctions in which the bidders are DAOs. More precisely, we consider the design of two-level auctions in which the "participants" are groups of bidders rather than individuals. Bidders form DAOs to pool resources, but must then also negotiate the terms by which the DAO’s winnings are shared. We model the outcome of a DAO’s negotiations through an aggregation function (which aggregates DAO members' bids into a single group bid) and a budget-balanced cost-sharing mechanism (that determines DAO members' access to the DAO’s allocation and distributes the aggregate payment demanded from the DAO to its members). DAOs' bids are processed by a direct-revelation mechanism that has no knowledge of the DAO structure (and thus treats each DAO as an individual). Within this framework, we pursue two-level mechanisms that are incentive-compatible (with truthful bidding a dominant strategy for each member of each DAO) and approximately welfare-optimal. We prove that, even in the case of a single-item auction, the DAO dynamics hidden from the outer mechanism preclude incentive-compatible welfare maximization: No matter what the outer mechanism and the cost-sharing mechanisms used by DAOs, the welfare of the resulting two-level mechanism can be a ≈ ln n factor less than the optimal welfare (in the worst case over DAOs and valuation profiles). We complement this lower bound with a natural two-level mechanism that achieves a matching approximate welfare guarantee. This upper bound also extends to multi-item auctions in which individuals have additive valuations. Finally, we show that our positive results cannot be extended much further: Even in multi-item settings in which bidders have unit-demand valuations, truthful two-level mechanisms form a highly restricted class and as a consequence cannot guarantee any non-trivial approximation of the maximum social welfare. 

   more » « less
5. Increasing Revenue in Efficient Combinatorial Auctions by Learning to Generate Artificial Competition

   https://doi.org/10.1609/aaai.v39i13.33482  

   Balcan, Maria-Florina; Prasad, Siddharth; Sandholm, Tuomas (April 2025, Proceedings of the AAAI Conference on Artificial Intelligence)

   The design of multi-item, multi-bidder auctions involves a delicate balancing act of economic objectives, bidder incentives, and real-world complexities. Efficient auctions, that is, auctions that allocate items to maximize total bidder value, are practically desirable since they promote the most economically beneficial use of resources. Arguably the biggest drawback of efficient auctions, however, is their potential to generate very low revenue. In this work, we show how the auction designer can artificially inject competition into the auction to boost revenue while striving to maintain efficiency. First, we invent a new auction family that enables the auction designer to specify competition in a precise, expressive, and interpretable way. We then introduce a new model of bidder behavior and individual rationality to understand how bidders act when prices are too competitive. Next, under our bidder behavior model, we use our new competitive auction class to derive the globally revenue-optimal efficient auction under two different knowledge models for the auction designer: knowledge of full bidder value distributions and knowledge of bidder value quantiles. Finally, we study a third knowledge model for the auction designer: knowledge of historical bidder valuation data. In this setting we present sample and computationally efficient learning algorithms that find high-revenue probably-efficient competitive auctions from bidder data. Our learning algorithms are instance adaptive and can be run in parallel across bidders, unlike most prior approaches to data-driven auction design. 

   more » « less