Auction Revenue Research Articles

A Game Theoretical Approach for Solving Winner Determination Problems

Determining the winners in combinatorial auctions to maximize the auctioneer's revenue is an NP-complete problem. Computing an optimal solution requires huge computation time in some instances. In this paper, we apply three concepts of the game theory to design an approximation algorithm: the stability of the Nash equilibrium, the self-learning of the evolutionary game, and the mistake making of the trembling hand assumption. According to our simulation results, the proposed algorithm produces near-optimal solutions in terms of the auctioneer's revenue. Moreover, reasonable computation time is another advantage of applying the proposed algorithm to the real-world services.

Designing Truthful Spectrum Double Auctions with Local Markets

Market-driven spectrum auctions offer an efficient way to improve spectrum utilization by transferring unused or underused spectrum from its primary license holder to spectrum-deficient secondary users. Such a spectrum market exhibits strong locality in two aspects: 1) that spectrum is a local resource and can only be traded to users within the license area, and 2) that holders can partition the entire license areas and sell any pieces in the market. We design a spectrum double auction that incorporates such locality in spectrum markets, while keeping the auction economically robust and computationally efficient. Our designs are tailored to cases with and without the knowledge of bid distributions. Complementary simulation studies show that spectrum utilization can be significantly improved when distribution information is available. Therefore, an auctioneer can start from one design without any a priori information, and then switch to the other alternative after accumulating sufficient distribution knowledge. With minor modifications, our designs are also effective for a profit-driven auctioneer aiming to maximize the auction revenue.

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

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

Theoretical and experimental investigations of the performance of keyword auction mechanisms

AbstractTwo keyword auction mechanisms, the Generalized Second‐Price auction (GSP) and the Vickrey‐Clarke‐Groves mechanism (VCG), were compared theoretically and experimentally. The former is widely used in practice; the latter is not, but it has a dominant strategy equilibrium where all participants bid their true values. In the theoretical investigation, by applying the “locally envy‐free Nash equilibrium” to the VCG, we found that the allocations are efficient and that upper and lower bounds of the auctioneer's revenue coincide in the two mechanisms. A laboratory experiment, in which the revenues and efficiencies were similar in both mechanisms, supported this result.

Spectrum Auction Design: Simple Auctions for Complex Sales

Following the successful PCS Auction conducted by the FCC in 1994, auctions have replaced traditional ways of allocating valuable radio spectrum. Spectrum auctions have raised hundreds of billion dollars worldwide and have become a role model for market-based approaches in the public and private sectors. The PCS spectrum was sold via a simultaneous multi-round auction, which forces bidders to compete for licenses individually even though they typically value certain combinations. This exposes bidders to risk when they bid aggressively for a desired combination but end up winning an inferior subset. Foreseeing this possibility, bidders may act cautiously with adverse effects for revenue and efficiency. Combinatorial auctions allow for bids on combinations of licenses and thus hold the promise of improved performance. Recently, a number of countries have switched to the combinatorial clock auction to sell spectrum. However, the number of possible packages grows exponentially with the number of licenses, which adds complexity to the auction. We analyze the impact of two main design choices: simple compact'' bid languages versus complex fully expressive'' bid languages and simple pay-as-bid'' payment rules versus complex bidder-optimal core-selecting'' payment rules. We consider these design choices both for ascending and sealed-bid formats. We find that simplicity of the bid language has a substantial positive impact on the auction's efficiency and simplicity of the payment rule has as a substantial positive impact on the auction's revenue. The currently popular combinatorial clock auction, which uses a complex bid language and payment rule, scores worst on both dimensions.

Revenue and Efficiency in Multi-Unit Uniform-Price Auctions

I show that in a private value multi-unit uniform-price auction, the reservation price increases both the efficiency and revenue. In equilibrium the difference between the true value of a unit and the submitted bid (shading) is different for each unit; therefore, the seller cannot allocate units efficiently, i.e., to those who value them the most. When the seller increases the reservation price, the bidders increase their bids on the units with greater shading. Then more often the units are allocated among those who have higher values for them, that is, efficient, although some bidders with a low value do not participate in the auction. In contrast to some other auction formats, for a low range of reservation prices, the higher the reservation price, the higher is both the expected efficiency and revenue.

Revenue and efficiency in multi-unit uniform-price auctions

This paper analyzes efficiency in a uniform-price multi-unit auction with a positive reservation price. I demonstrate that the reservation price is an important policy tool that may increase efficiency (or welfare) in multi-unit uniform-price auctions. I show that the higher the reservation price is, the higher is the sellerʼs revenue and the higher is the efficiency of a final allocation of units that could be attained in a multi-unit uniform-price auction. The reservation price increases the bidderʼs equilibrium strategy in a specific way that is inherent to the uniform-price auction. Thus the reservation price effect on efficiency is in contrast to other auction formats; e.g., the reservation price decreases efficiency in the Vickrey auction and single-unit auctions with symmetric bidders. Therefore the main result can be added to the list of results from mechanism design and auction theory that fail to extend the single-unit/single-dimensional context to the multi-unit/multi-dimensional one.

Will Bidder Exclusions Increase Auction Revenue? A Review of the Arguments

In this PERSPECTIVE, I will review the arguments made to exclude AT&T and Verizon from the spectrum Incentive Auction scheduled in 2015. These argument is that the exclusion of the larger provides will increase auction revenues. My analysis seeks to determine whether or not economics support their “revenue enhancement by exclusion” hypothesis. It does not. As I explain, exclusion advocates are playing fast-and-loose with economic theory. Upon inspection, the research used to support the revenue enhancement hypothesis show that excluding the two larger carriers will, in fact, reduce auction revenues. Additionally, the research cited the exclusion advocates consistently and fervently warns about the dangers of such exclusions.

A lower bound on seller revenue in single buyer monopoly auctions

We consider a monopoly seller who optimally auctions a single object to a single potential buyer, with a known distribution of valuations. We show that a tight lower bound on the seller’s expected revenue is 1/e times the geometric expectation of the buyer’s valuation, and that this bound is uniquely achieved for the equal revenue distribution. We show also that when the valuation’s expectation and geometric expectation are close, then the seller’s expected revenue is close to the expected valuation.

Ranking asymmetric auctions

We compare the expected revenue in first- and second-price auctions with asymmetric bidders. We consider “close to uniform” distributions with identical supports and show that in the case of identical supports the expected revenue in second-price auctions may exceed that in first-price auctions. We also show that asymmetry over lower valuations has a stronger negative impact on the expected revenue in first-price auctions than in second-price auctions. However, asymmetry over high valuations always increases the revenue in first-price auctions.

Valuation structure in first-price and least-revenue auctions: an experimental investigation

In many auctions the valuation structure involves both private and common value elements. Existing experimental evidence (e.g. Goeree and Offerman in Am. Econ. Rev. 92(3):625–643, 2002) demonstrates that first-price auctions with this valuation structure tend to be inefficient, and inexperienced subjects tend to bid above the break-even bidding threshold. In this paper, we compare first-price auctions with an alternative auction mechanism: the least-revenue auction. This auction mechanism shifts the risk regarding the common value of the good to the auctioneer. Such a shift is desirable when ex post negative payoffs for the winning bidder results in unfulfilled contracts, as is often the case in infrastructure concessions contracts. We directly compare these two auction formats within two valuation structures: (1) pure common value and (2) common value with a private cost. We find that, relative to first-price auctions, bidding above the break-even bidding threshold is significantly less prevalent in least-revenue auctions regardless of valuation structure. As a result, revenue in first-price auctions is higher than in least-revenue auctions, contrary to theory. Further, when there are private and common value components, least-revenue auctions are significantly more efficient than first-price auctions.

The Economic Implications of Restricting Spectrum Purchases in the Incentive Auctions

This paper contains two chapters on the economic impact of proposed FCC restrictions on participation in the 2015 spectrum auction, which would limit access to additional spectrum by large incumbent Internet Service providers (ISPs). The first chapter by Holtz-Eakin and Bazelon reports that such restrictions could reduce FCC auction revenues by as much as $12 billion or 40 percent, which in turn could mean that the FCC would be unable to purchase the full amount of spectrum being made available by broadcasters. They further report that this large shortfall could lead to a series of declining revenues and fewer frequencies allocated, and jeopardize funding for the new national network, FirstNet, planned for the exclusive use of public safety personnel. The second chapter by Shapiro reports that restricting auction participation by large, relatively-efficient incumbent ISPs would shift spectrum resources towards less efficient mobile carriers. This shift also would force the large incumbent carriers to deploy more costly responses to fast-rising consumer and business demand for bandwidth, raising prices and thereby slowing the transition to 4G technologies. Further, the slower transition to 4G would dampen the employment growth that should otherwise follow from the adoption of more advanced Internet technologies. Shapiro estimates that those effects could more than 118,000 jobs by 2017.

Empirical Evidence on the Impact of Reserve Prices in English Auctions

We study the impact of reserve prices on the revenue of English auctions using a unique hand‐collected database of virtual football players from the online football management game Hattrick. As theoretically predicted, setting a reserve price entails a trade‐off between the cost of setting it too high and having the good go unsold, and the benefit associated with a higher revenue should the reserve price successfully extract surplus from the highest bidder. Overall, we find the net benefit of setting a higher reserve price to be negative, regardless of the value of the reserve price. This is a novel result insofar as previous literature has generally found an insignificant or positive effect of the reserve price on unconditional auction revenue.

Auctions with contingent payments — An overview

I survey a literature on auctions with contingent payments, that is auctions in which payments are allowed to depend on an ex-post verifiable variable, such as revenues in oil lease auctions. Based on DeMarzo et al. (2005), I describe a partial ranking of auction revenues for auctions that differ in terms of contract forms, pricing rules and seller commitment and why the revenue equivalence theorem does not apply even in an independent private values setup. I discuss models that incorporate adverse selection, moral hazard, competition between auctioneers, common values and the sale of multiple units.

Do core-selecting Combinatorial Clock Auctions always lead to high efficiency? An experimental analysis of spectrum auction designs

For many years the Simultaneous Multi-Round Auction (SMRA) has been the primary auction design for spectrum sales worldwide. Recently, the core-selecting Combinatorial Clock Auction (CCA) has been used as an alternative to the SMRA in a number of countries promising strong incentives for truthful bidding and high efficiency as a result. We analyze the efficiency and auctioneer revenue of the CCA in comparison to SMRA and examine bidding behavior in both formats. The experiments are based on two value models, which resemble single- and multiband spectrum sales in the field. Such applications often allow for thousands of possible bundles. Bidders in the CCA submitted bids for only a fraction of all bundles with a positive valuation. Bundles were selected based on synergies and payoff after the primary bid rounds. As a consequence, we found efficiency of the CCA to be significantly lower than that of SMRA in the multi-band value model and auctioneer revenue of the CCA to be lower in both value models. In addition, we characterize several properties of the auction format, which result from the two-stage design and the payment and activity rules.

Second chance offers in auctions

This paper examines situations in which a seller might make a second chance (take-it-or-leave-it) offer to a non-winning bidder at a price equal to their bid at auction. This study is motivated by the take-it-or-leave-it second chance offer rules used by eBay and a number of state procurement agencies. Equilibrium bidder behavior is determined for IPV sealed bid first price, second price, English, and Vickrey auctions when a second chance offer will be made with an exogenous probability \(p\). In all but the Vickrey auction (which elicits the dominant strategy of bidding one’s value) equilibrium bids are lower than if there were no possibility of a second chance offer and higher than if a second chance offer will be made for certain. Further, the possibility of a second chance offer erodes the strategic equivalence between second price bids and English auction drop out levels. If bidders are risk averse (with CRRA preferences), this difference leads to expected revenue dominance of the second price over the English auction, both of which dominate the Vickrey auction. The first price auction is also shown to revenue dominate the Vickrey auction, and moreover, numerical results and intuition from existing literature suggest that the first price auction revenue dominates the second price auction.

Comparing the Ability of Different Auction Mechanisms to Efficiently Designate Spectrum between Licensed and Unlicensed Use

This paper employs analytical methods to evaluate the ability of three different auction mechanisms to determine the efficient designation of spectrum between licensed and unlicensed use. The two regimes explored are 'licensed' spectrum, in which a licensee maintains exclusive rights to use the spectrum, subject to a set of service rules, and 'unlicensed' spectrum, in which multiple users are able to share spectrum on an open access basis. For each auction, we examine bidder incentives and provide detailed reports on both auction revenue and bidder surplus in a set of Nash equilibrium outcomes. Theoretical results are consistent with the conclusions of Bykowsky, Olson, Sharkey (2010), that a market can be used to allocate spectrum between licensed and unlicensed use. Results also show that a first-price and Clarke-Groves mechanisms are more likely to lead to the efficient designation of spectrum than a second-price auction.

Bayes–Nash equilibria of the generalized second-price auction

We develop a Bayes–Nash analysis of the generalized second-price (GSP) auction, the multi-unit auction used by search engines to sell sponsored advertising positions. Our main result characterizes the efficient Bayes–Nash equilibrium of the GSP and provides a necessary and sufficient condition that guarantees existence of such an equilibrium. With only two positions, this condition requires that the click–through rate of the second position is sufficiently smaller than that of the first. When an efficient equilibrium exists, we provide a necessary and sufficient condition for the auction revenue to decrease as click–through rates increase. Interestingly, under optimal reserve prices, revenue increases with the click–through rates of all positions. Further, we prove that no inefficient equilibrium of the GSP can be symmetric. Our results are in sharp contrast with the previous literature that studied the GSP under complete information.

A NOTE ON THE EFFECT OF ASYMMETRY ON REVENUE IN SECOND-PRICE AUCTIONS

We compare the seller's expected revenue in asymmetric second-price auctions with the benchmark case where all bidders have the average distribution. We show that with two bidders, asymmetry has a negative effect on revenue. However, for n > 2 bidders there is no clear observation we can make. We prove that in the case of weak asymmetry, sellers prefer asymmetry over low valuations and symmetry over high valuations. In addition, we show that a good approximation for the expected revenue in the case of weak asymmetry can be obtained by calculating the revenue of the symmetric auction with identical distributions equal to the geometric or arithmetic average.

Risk optimal single-object auctions

We analyze the preferences of a risk-averse auctioneer over several auction mechanisms with risk-neutral and symmetric bidders. We obtain the value at risk (VaR) for auctioneer revenue in auction mechanisms belonging to a parametric family which includes two classic mechanisms, the first-price auction and second-price auction. By calculating the VaR for revenue an auctioneer can estimate the amount that will be lost within a given confidence level, depending on the number of bidders and the auction mechanism chosen. The contribution of this paper is the calculation of the VaR for auctioneer revenue in some common auction mechanisms that yield the same expected revenue, including first-price auction and second-price auction and the following mechanisms: Santa Claus auction, sad-loser auction and all-pay auction. We describe how to quantify the maximum loss for an auctioneer at a given probability. We study the value at risk of the auctioneer as a criterion to determine which auctions would best suit the auctioneer's interests.