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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.
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Pacing Equilibrium in First Price Auction Markets
Mature internet advertising platforms offer high-level campaign management tools to help advertisers run their campaigns, often abstracting away the intricacies of how each ad is placed and focusing on aggregate metrics of interest to advertisers. On such platforms, advertisers often participate in auctions through a proxy bidder, so the standard incentive analyses that are common in the literature do not apply directly. In this paper, we take the perspective of a budget management system that surfaces aggregated incentives—instead of individual auctions—and compare first and second price auctions. We show that theory offers surprising endorsement for using a first price auction to sell individual impressions. In particular, first price auctions guarantee uniqueness of the steady-state equilibrium of the budget management system, monotonicity, and other desirable properties, as well as efficient computation through the solution to the well-studied Eisenberg–Gale convex program. Contrary to what one can expect from first price auctions, we show that incentives issues are not a barrier that undermines the system. Using realistic instances generated from data collected at real-world auction platforms, we show that bidders have small regret with respect to their optimal ex post strategy, and they do not have a big incentive to misreport when they can influence equilibria directly by giving inputs strategically. Finally, budget-constrained bidders, who have significant prevalence in real-world platforms, tend to have smaller regrets. Our computations indicate that bidder budgets, pacing multipliers, and regrets all have a positive association in statistical terms. This paper was accepted by Gabriel Weintraub, revenue management and market analytics. Funding: D. Panigrahi was supported in part by the National Science Foundation [Awards CCF 1535972, CCF 1750140, and CCF 1955703]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.4310 .
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- Award ID(s):
- 2147361
- PAR ID:
- 10442714
- Date Published:
- Journal Name:
- Management Science
- Volume:
- 68
- Issue:
- 12
- ISSN:
- 0025-1909
- Page Range / eLocation ID:
- 8515 to 8535
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Budget constraints are ubiquitous in online advertisement auctions. To manage these constraints and smooth out the expenditure across auctions, the bidders (or the platform on behalf of them) often employ pacing: each bidder is assigned a pacing multiplier between zero and one, and her bid on each item is multiplicatively scaled down by the pacing multiplier. This naturally gives rise to a game in which each bidder strategically selects a multiplier. The appropriate notion of equilibrium in this game is known as a pacing equilibrium. In this work, we show that the problem of finding an approximate pacing equilibrium is PPAD-complete for second-price auctions. This resolves an open question of Conitzer et al. [Conitzer V, Kroer C, Sodomka E, Stier-Moses NE (2022a) Multiplicative pacing equilibria in auction markets. Oper. Res. 70(2):963–989]. As a consequence of our hardness result, we show that the tâtonnement-style budget-management dynamics introduced by Borgs et al. [Borgs C, Chayes J, Immorlica N, Jain K, Etesami O, Mahdian M (2007) Dynamics of bid optimization in online advertisement auctions. Proc. 16th Internat. Conf. World Wide Web (ACM, New York), 531–540] are unlikely to converge efficiently for repeated second-price auctions. This disproves a conjecture by Borgs et al. [Borgs C, Chayes J, Immorlica N, Jain K, Etesami O, Mahdian M (2007) Dynamics of bid optimization in online advertisement auctions. Proc. 16th Internat. Conf. World Wide Web (ACM, New York), 531–540], under the assumption that the complexity class PPAD is not equal to P. Our hardness result also implies the existence of a refinement of supply-aware market equilibria which is hard to compute with simple linear utilities. Funding: This work was supported by National Science Foundation (CCF-1703925, IIS-1838154).more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/mnsc.2022.4310
