Auction Revenue Research Articles

Pricing combinatorial auctions by a set of linear price vectors

In combinatorial auctions, items are sold simultaneously. A substantial component of an auction mechanism is the pricing scheme. Prices determine the auctioneer's revenue and, ideally, justify the outcome of the auction to the bidders. Each bidder should be able to see why he won or lost a certain bundle by comparing the determined price of a bundle and his bid's value. In this paper, we pick up a non-linear anonymous pricing scheme from the literature that consists of a set of linear price vectors. We investigate whether this scheme can guarantee to find prices that support the winner allocation. Furthermore, we refine the pricing scheme by suggesting various objectives in order to evaluate different prices. We consider the computational complexity of the corresponding optimization problems and compare different objectives by means of a computational study using a well-established combinatorial auction test suite.

Improvement of Auctioneer's Revenue under Incomplete Information in Cognitive Radio Networks

Improvement of Auctioneer's Revenue under Incomplete Information in Cognitive Radio Networks

Learning algorithms for second-price auctions with reserve

Second-price auctions with reserve play a critical role in the revenue of modern search engine and popular online sites since the revenue of these companies often directly depends on the outcome of such auctions. The choice of the reserve price is the main mechanism through which the auction revenue can be influenced in these electronic markets. We cast the problem of selecting the reserve price to optimize revenue as a learning problem and present a full theoretical analysis dealing with the complex properties of the corresponding loss function. We further give novel algorithms for solving this problem and report the results of several experiments in both synthetic and real-world data demonstrating their effectiveness.

Winner Determination in Geometrical Combinatorial Auctions

We consider auctions of items that can be arranged in rows. Examples of such a setting appear in allocating pieces of land for real estate development, or seats in a theater or stadium. The objective is, given bids on subsets of items, to find a subset of bids that maximizes auction revenue (often referred to as the winner determination problem). We describe a dynamic programming algorithm which, for a k-row problem with connected and gap-free bids, solves the winner determination problem in polynomial time. We study the complexity for bids in a grid, complementing known results in literature. Additionally, we study variants of the geometrical winner determination setting. We provide a NP-hardness proof for the 2-row setting with gap-free bids. Finally, we extend this dynamic programming algorithm to solve the case where bidders submit connected, but not necessarily gap-free bids in a 2-row and a 3-row problem.

Assessing Motor Vehicle Quota Policies in China: Social Welfare Perspective

Seven cities in China employ vehicle quota policies (VQPs) to mitigate urban traffic congestion. In these cities, vehicle licenses are allocated through a lottery, auction, or a mixture of the two. This study performs a policy assessment of China’s VQP with a social welfare perspective. It is argued that the issue is relevant to the selection of different modes of resource allocation, since an auction can match the precious resource with the individuals who value it most whereas a lottery meets the social expectation of equity. From the broad perspective of urban transportation, both auction- and lottery-based VQPs can be further improved by changing supplemental policies relevant to lottery entry, auction revenue usage, and vehicle purchase timing. VQPs should be used to help but not to replace travel demand management. As more cities in China adopt VQPs, this research can inform future policy making.

A note on the continuity of the optimal auction

In the independent private values auction model I study the continuity properties of the optimal auction revenue as a function of the valuations or types distribution. I show that the optimal revenue is lowersemicontinuous for convergence in distribution. If the limit distribution is continuous, the optimal auction revenue is continuous in distribution as well.

Impact of Dependence Among Valuations on Expected Revenue in Auctions

SYNOPTIC ABSTRACTThis work studies the dependence and asymmetry among valuations in sealed-bid auctions with private valuations. In the framework of valuations with Archimedean copulas, it is found that a stronger positive dependence stochastically enhances the final price and lowers the winner’s expected rent in the two-bidder, second-price auction, and the degree of positive dependence has an opposite impact on the final price in the first-price auction. In the context of multiple bidders with valuations having proportional reversed hazards, reducing the asymmetry among negatively dependent valuations is proved to enhance the final price in the second-price auction, and a stronger (weaker) positive dependence along with less (more) asymmetry on valuations is showed to stochastically lower (increase) the final price in the first-price auction.

Truthful learning mechanisms for multi-slot sponsored search auctions with externalities

Sponsored Search Auctions (SSAs) constitute one of the most successful applications of microeconomic mechanisms. In mechanism design, auctions are usually designed to incentivize advertisers to bid their truthful valuations and, at the same time, to guarantee both the advertisers and the auctioneer a non-negative utility. Nonetheless, in sponsored search auctions, the Click–Through–Rates (CTRs) of the advertisers are often unknown to the auctioneer and thus standard truthful mechanisms cannot be directly applied and must be paired with an effective learning algorithm for the estimation of the CTRs. This introduces the critical problem of designing a learning mechanism able to estimate the CTRs at the same time as implementing a truthful mechanism with a revenue loss as small as possible compared to the mechanism that can exploit the true CTRs. Previous work showed that, when dominant-strategy truthfulness is adopted, in single-slot auctions the problem can be solved using suitable exploration–exploitation mechanisms able to achieve a cumulative regret (on the auctioneer's revenue) of order O˜(T23), where T is the number of times the auction is repeated. It is also known that, when truthfulness in expectation is adopted, a cumulative regret (over the social welfare) of order O˜(T12) can be obtained. In this paper we extend the results available in the literature to the more realistic case of multi-slot auctions. In this case, a model of the user is needed to characterize how the CTR of an ad changes as its position in the allocation changes. In particular, we adopt the cascade model, one of the most popular models for sponsored search auctions, and we prove a number of novel upper bounds and lower bounds on both auctioneer's revenue loss and social welfare w.r.t. the Vickrey–Clarke–Groves (VCG) auction. Furthermore, we report numerical simulations investigating the accuracy of the bounds in predicting the dependency of the regret on the auction parameters.

Intermediaries as Information Aggregators: An Application to U.S. Treasury Auctions

According to most theories of nancial intermediation, intermediaries diversify risk, transform maturity or liquidity, and screen or monitor borrowers. In U.S. Treasury auctions, none of these rationales apply. Intermediaries submit their customer bids without transforming liquidity or maturity, and they do not screen and monitor borrowers or diversify scal policy risk. Yet, most end investors place their Treasury auction bids through an intermediary rather than submit them directly. Motivated by this evidence, we explore a new information aggregation model of intermediation. Intermediaries observe each client’s order ow, aggregate that information across clients, and use it to advise their clients as a group. In contrast to underwriting theories in which intermediaries, by acting as gatekeepers, extract rents but reduce revenue variance, information aggregators increase expected auction revenue, but also make the revenue more sensitive to changes in asset value. We use the model to examine current policy questions, such as the optimal number of intermediaries, the eect of non-intermediated bids, and minimum bidding requirements.

Unlicensed Operations in the Lower Spectrum Bands: Why is No One Using the TV White Space and What Does That Mean for the FCCCs Order on the 600 MHz Guard Bands?

In 2008, the FCC authorized unlicensed use of vacant channels in the TV bands (TV white space) following the digital TV transition. Supporters of the FCC action asserted that giving unlicensed devices access to the lower bands would forestall congestion at 2.4 GHz and 5 GHz, provide mobile broadband coverage to underserved areas, and power a new wave of innovation (Google’s CEO famously said TV white space would bring about “Wi-Fi on steroids”). We were among a small minority who countered that the TV white space could not support effective unlicensed operations both because the limited bandwidth would make it inferior to 2.4 GHz and 5 GHz for Wi-Fi-type applications, and because the necessarily stringent power limits and lack of interference protection would preclude most long-range applications. We also argued that the TV white space could be used for licensed services, generating billions of dollars in auction revenue. In this paper we analyze a) the impact to date of the FCC’s TV white space policy and b) the implications of this for the FCC’s 2014 proposal to allow unlicensed operations in 600 MHz guard bands following the incentive auction, which is an extension of the TV white space policy.The FCC’s TV white space policy to date has been a flop, as evidenced by the anemic market response. The FCC has approved only nine products for operation in the TV white space, and none of the major manufacturers of Wi-Fi routers or Wi-Fi chips fields a product that can be used there. Nor does any major smartphone or tablet vendor offer a product with the capability to use TV white space. As another indicator, users in this country have registered fewer than 600 individual devices (registrations are a proxy for sales), in contrast to the tens of millions predicted. Although regulatory uncertainty may be a factor, the market’s anemic response to the TV white space has far more to do with fundamentals, in particular the predictably slow data rates for short-range, Wi-Fi-type applications. The maximum data rates for TV white space devices range from 3.25-16 megabits per second (Mbps), which is below the FCC’s new threshold for what constitutes broadband, compared to 600 Mbps to 1.7 gigabits per second for unlicensed devices that operate at 2.4 GHz and 5 GHz. For long-range applications, TV white space faces other challenges (key are the 4 watt power limit and the risk of interference from short-range devices), making licensed spectrum a superior choice.The FCC’s decision to allow unlicensed operations in the (post-auction) 600 MHz guard bands is likely to meet the same fate. For short-range applications, because of limitations on bandwidth (six megahertz) and transmit power (40 milliwatts), unlicensed devices operating in the 600 MHz guard bands will have a data rate that is one-tenth to one-hundredth that of a Wi-Fi device operating at 2.4 GHz and 5 GHz. That handicap will trump almost any propagation advantages that the 600 MHz band may offer. For long-range voice and data communications, unlicensed operations in the 600 MHz guard bands will have even less to offer. With a power limit of 40 milliwatts, unlicensed guard band devices will simply not be capable of providing rural broadband access and other long-range communication services on any meaningful scale.

Auction 97 and the Value of Spectrum

Using econometric methods and data from prior spectrum auctions, this paper evaluates the design of the FCC's Auction 97. We find that the elements of the auction's design, including the size of license areas, reduced auction revenues by as much as $21 billion.

Multi-Item Spectrum Auction for Recall-Based Cognitive Radio Networks With Multiple Heterogeneous Secondary Users

In this paper, we consider a spectrum auction system among heterogeneous secondary users (SUs) with various quality-of-service (QoS) requirements and a recall-based primary base station (PBS) that could recall channels after auction to deal with a sudden increase in its own demand. Beginning with proposing a recall-based single-winner spectrum auction (RSSA) algorithm, we further extend our work to allow multiple winners in order to improve the spectrum utilization and propose a recall-based multiple-winner spectrum auction (RMSA) algorithm. A combinatorial auction model is then formulated, and Vickrey-Clarke-Groves (VCG) mechanism is applied in the payment function. Moreover, the proposed RMSA algorithm focuses on a fair spectrum allocation among heterogeneous SUs and the increase in the PBS's auction revenue. Both theoretical and simulation results show that the proposed spectrum auction algorithm can improve the spectrum utilization with guarantees on SUs' heterogeneous QoS requirements.

Spectrum auction designs and revenue variations

This study examines a sample of 93 national 3G spectrum auctions for the period 2000–2011 to identify the sources of substantial revenue variations. An implied reduced-form econometric model that recognises the censored nature of the sample relates per capita winning bid (per Mhz, per million populations) values to regulator-determined auction design characteristics, auction competitiveness, mobile wireless market conditions and spectrum package attributes identified from tender documents. The analysis reveals that among other factors, all auction design characteristics independently impact on realized 3G spectrum auction revenues.

Are auction revenues affected by rising art buyers’ premia? The case of early American art

The steady rise in the premiums charged to art buyers at auction (above hammer price) has been underway since 1992. This article, using a stable and bounded sample of repeat purchase of American works created before 1950, reveals that this tact has reduced hammer prices for that art. However, renewed and hyper-competitive efforts to bring more and higher quality art to market by the two main houses, Sotheby’s and Christie’s, have resulted in general profitability. Nevertheless, we calculate that a rise in buyers’ premia at Sotheby’s, a publically traded company, has reduced revenues and profits below their potential in the absence of such increases.

Multi-object auctions with resale: Theory and experiment

We study multi-object auctions in the presence of post-auction trade opportunities among bidders who have either single- or multi-object demand. We focus on two formats: Vickrey auctions where package bidding is possible and simultaneous second-price auctions. We show that, under complementarities, the Vickrey format has an equilibrium where the objects are allocated efficiently at the auction stage whether resale markets are present or not. The simultaneous second-price, on the other hand, leads to inefficiency with or without resale possibility. Our experimental findings show that the possibility of resale in second-price auctions decreases the efficiency rate at the auction stage compared to the no resale case. However, after resale, the efficiency rate in second-price is as high as that of Vickrey auction without resale outcomes in the experiment. Preventing resale neither benefits nor hurts auction revenues in a second-price format.

Optimal Revenue Maximizing Mechanisms in Common-Value Position Auctions

We study the optimal mechanism in position auctions in a common-value setting where only ordinal information about the advertisers is posted and auctioneer revenue depends on consumer belief about ad qualities. We show that when bidder valuations are correlated, existence of a simple non-ironed optimal mechanism requires a stronger condition that the usual increasing virtual valuation assumption. With fixed number of positions, the corresponding optimal decision rule (among all mixed and pure strategies) is to allocate the ad positions to advertisers in decreasing order of quality. More importantly, when the search engine also chooses the number of ads to post, ignoring the consumer belief endogeneity will lead to posting too many ads compared to what maximizes the search engine revenue. We also show that when only one ad position is available, the optimal allocation rule uses a reserve price which is higher than what is implied by Myerson 1981 seminal work. Finally, we characterize the optimal mechanism when cardinal information about advertiser quality is posted, and we provide results on how search engine revenue compares under the two regimes.

In the Race Towards High-Speed Mobile Broadband Spectrum Allocation is Not Only a Matter of Auction Revenue

Inspired by the Colombian mobile telecommunications market, this paper reviews the process by which a government’s spectrum agency decides on the allocation of new spectrum bands to the mobile communications markets, including 4G and mobile broadband. It discusses the elements the spectrum agency needs to consider in order to build an analytical framework that helps assess the most important issues that may have a potential impact on the efficient allocation of spectrum and, consequently, on future market development.

From English to First-Price Sealed Bid: An Empirical Assessment of the Change in Auction Type on Experienced Bidders

Abstract This paper estimate the differential impact of first-price sealed-bid (first-price) auctions relative to English auctions on auction revenue. While there is a theoretical literature on the potential outcomes of first-price relative to English auction, there is a paucity of articles that empirically estimate this relationship. The answer to this question is important not only to economists but also those designing auction for practical application. Using a unique dataset from tax lien auctions in Illinois, I empirically test the effect of a switch in auction type from English to first-price. I find auction revenue is greatly increased, by as much as 22 percent, under the first-price auction. The results are supported by a within county difference-in-difference model specification and are robust when restricting the sample across various specifications

Asymmetry and revenue in second-price auctions: a majorization approach

Bidder asymmetries are common in certain auctions where heterogeneous bidders coexist. In this paper, we employ the tool of majorization to study the effect of bidder asymmetry on revenue in second-price auctions. As a preorder on vectors of real components, the majorization is used to rank the asymmetry of bid distributions from different auctions. Our analysis indicates that bidders’ asymmetries may raise revenue under certain classes of value distributions (e.g., proportional reversed hazard rate models) and may not in others (e.g., proportional hazard rate models). These results are further validated through supportive evidence that is based on simulated three-bidder auctions. The use of majorization allows us to extend and strengthen the results obtained in the existing literature under more general conditions. This study adds to the literature a useful analytical technique for future research on asymmetric auctions.

Hierarchical modeling and prediction of spectrum auction revenue by a posteriori clusters

The electromagnetic spectrum is a crucial asset for wireless technology innovation and for the industry's economy. We examine spectrum auction-related databases, construct a hierarchical data matrix, and propose an optimal auction revenue model. The model incorporates statistically derived deterministic and stochastic variables to develop a spectrum valuation methodology for its primary market. Our study reveals that the underlying regulations, bidding behavior, and spectrum demands due to wireless technology advancement are effectively elucidated by the selected explanatory variables and are highly correlated with auction revenues. This paper is the first to introduce a hierarchical modeling technique that incorporates a multilevel data matrix culminated from 3995 licenses of 15 Federal Communications Commission spectrum auctions to enable economic valuation for future spectrum auctions. Furthermore, the results of this study can be applied to evaluate the significance of sunk costs, winner's curses, and associated cost synergies, which are economic implications of spectrum auctions. Our research contributions are twofold. First, the hierarchical auction model can maximize spectrum valuation methodologies, thereby assisting spectrum regulators and the wireless industry. Second, we compare the reproducibility of hierarchical and ordinary least squares modeling techniques to support adequate validation and their extensive utilization in academic disciplines.