Optimal reserve prices in sealed-bid auctions with reference effects

The reference effect and loss aversion are incorporated into the buyer’s utility in the symmetric independent private value models of sealed-bid auctions. The buyer’s equilibrium bidding strategy and the seller’s optimal reserve price are derived for the first-price and second-price sealed-bid auctions. In both auction mechanisms, the seller’s optimal reserve price and expected revenue are increasing in the reference point. We compare the seller’s expected revenues as well as the optimal reserve prices in the two auctions. The results show that the seller will set a higher optimal reserve price but obtain lower optimal expected revenue in the second-price auction compared to the first-price auction. Further, we extend the model to the gain-seeking case, and endogenize the reference point as the ex-ante expected price of the item in equilibrium. In contrast to the loss-averse case, the seller will set a lower optimal reserve price but obtain higher optimal expected revenue in the second-price auction compared to the first-price auction if the buyers are gain-seeking. With an endogenous reference point, similar results are obtained in terms of revenue comparison between the two auctions.     

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 quantity externalities and endogenous supply

This paper studies the design of license auctions when the number of licenses allocated in the auction determines structure of the post-auction market. I first show that a sequence of conditional reserve prices that specify minimum acceptable bid at each supply level can be used to determine supply endogenously. Then I construct a static auction called multi-dimensional uniform-price auction and a dynamic auction called Walrasian clock auction that allow the auctioneer to condition reserve price on supply and allow bidders to condition bids on supply. I show that both proposed auctions can implement the efficient market structure that maximizes total surplus in the post-auction market in a dominant strategy equilibrium. I next characterize the optimal auction and show that the two proposed auctions can yield the optimal revenue under a sequence of optimal reserve prices.     

Optimal choice of a reserve price under uncertainty

The revenue function for a standard auction is typically asymmetric around the revenue maximizing reserve price. Thus, choosing a reserve price that is smaller than the revenue maximizing reserve price can result in a substantially different loss than choosing one that is larger by the same amount. Therefore, when the revenue function is unknown, it is important to consider uncertainty around the revenue function and its asymmetric structure. For this purpose, I propose a Bayesian decision rule and illustrate its typical revenue gains. I then apply the rule to the bid data from the U.S. timber sales.     

Secret reserve prices in first-price auctions

This article offers a theoretical explanation for the use of secret reserve prices in auctions. I study first-price auctions with and without secret reserve price in an independent private values environment with risk-neutral buyers and a seller who cares at least minimally about risk. The seller can fix the auction rules either before or after she learns her reservation value. Fixing the rules early and keeping the right to set a secret reserve price can be strictly optimal. Moreover, I describe the relation of using a secret reserve price to phantom bidding and non-commitment to sell.     

How to Set Minimum Acceptable Bids, with an Application to Real Estate Auctions

In a general auction model with affiliated signals, common components to valuations and endogenous entry, we compute the equilibrium bidding strategies and outcomes, and derive a lower bound on the optimal reserve price. This lower bound can be computed using data on past auctions combined with information about the subsequent sales prices of unsold goods. We illustrate how to compute the lower bound using data from real estate auctions.     

THE EFFECT OF AUCTION FORMAT ON EFFICIENCY AND REVENUE IN DIVISIBLE GOODS AUCTIONS: A TEST USING KOREAN TREASURY AUCTIONS*

This paper measures the efficiency and revenue properties of the two most popular formats for divisible goods auctions: the uniform‐price and discriminatory auction. We analyze bids into the Korean Treasury auctions which have used both formats. We find that the discriminatory auction yields statistically higher revenue. Unlike previous work that uses data from only one format, we are able to compare the efficiency properties of the two formats. We find that the discriminatory auction better allocates treasury bills to the highest value financial institutions. However, the differences in revenue and efficiency are not large because the auctions are very competitive.     

Opportunity cost of spectrum for mobile communications: Evaluation of spectrum prices in Bangladesh

The purpose of this study is to focus attention on the choice of the reserve price made by the telecom regulator to explain the under-performance of spectrum auctions in Bangladesh. The overestimation of the reserve prices for several auctions in Bangladesh including the auction of the 3G – 2100 MHz band in 2013, the 2G - 1800 MHz band in 2015, and the 4G – 1800 and 2100 MHz bands in 2018 is established by comparing the reserve prices to the economic value of spectrum, determined by using the engineering valuation and production function approaches. Possible reasons for the inflation of the reserve price are discussed.     

The Role of Undisclosed Reserves in English Open Outcry Auctions

This study considers the role that reserve prices may play in residential property auctions. In comparison to much of the previous empirical work, this study has access to undisclosed reserve prices from English auctions. Consistent with theoretical arguments in the auction literature, the results obtained illustrate that while higher reserve prices increase the revenue obtained for the seller, they also reduce the probability of sale. The findings also highlight the importance of auction participation, with the number of individual bidders and the number of bids significant in most specifications.     

The effect of competition on eBay

I examine the effect of competition on eBay Motors. I specify a simple model of auction choice and show that the expected transaction price falls with an increase in the number of competitors. I then test for this effect using data from 5,500 auctions for Chevrolet Corvettes. To address potential endogeneity of the level of competition, I introduce an instrument which takes advantage of the unique features of eBay. Results indicate that an additional competitor leads to a 6% reduction in the final transacted price ($960 for the average car). Further, I provide evidence that this effect is due to the thinning of the bidder market rather than dynamic bidding.     

On Strategic Quantity Bidding in Multiple Unit Auctions

Standard studies of multiple unit auctions generally overlook the strategic role of bidders' quantity decisions. Using a simple equilibrium model of bidding I analyze bidders' incentives to choose quantities in discriminatory and competitive auctions. The main result is that bidders have a stronger strategic incentive to bid for fewer units in competitive auctions. Since under competition a bidder pays the lowest accepted price for each unit she gets, she may benefit from dropping her quantity to let lower-valuing bidders enter the set of winners. This prediction is consistent with empirical observations from foreign currency and spectrum auctions.     

PENNIES FROM EBAY: THE DETERMINANTS OF PRICE IN ONLINE AUCTIONS*

This paper presents an exploratory analysis of the determinants of prices in online auctions for collectible United States one‐cent coins at the eBay web site. Starting with an initial data set of 20,000 auctions, we perform regression analysis on a restricted sample of 461 coins for which we obtained estimates of book value. We have three major findings. First, a seller's feedback ratings, reported by other eBay users, have a measurable effect on her auction prices. Negative feedback ratings have a much greater effect than positive feedback ratings do. Second, minimum bids and reserve prices have positive effects on the final auction price. In particular, minimum bids appear only to have a significant effect when they are binding on a single bidder, as predicted by theory. Third, when a seller chooses to have her auction last for a longer period of days, this significantly increases the auction price on average.     

The impact of auction choice on revenue in treasury bill auctions – An empirical evaluation

I evaluate whether uniform price or discriminatory auctions are revenue-superior for selling Treasury bills. To this end, I apply two structural econometric models, Hortaçsu and McAdams (2010) and Fevrier et al. (2002), to a dataset on Polish zero-coupon bonds. My secondary aim is to analyze mutual inconsistencies in prediction from these models. I find that both agree on the revenue-superiority of discriminatory auctions, by between 0.01% and 1.5%; the models’ predictions are contradictory in only 7% of auctions. The large-scale agreement of two vastly different models gives confidence that the conclusions on Polish data are robust to varying many of the underlying economic and econometric assumptions, and not likely just a modeling artifact.     

Abschätzung des Erlöspotentials aus der Leistungsvorhaltung am Schweizer Tertiärregelmarkt

The analysis attempts to estimate the revenue potential from the provision of tertiary reserve capacity in the Swiss electricity control area based on publicly available data on historic tenders (June 2010–December 2013). A series of bidding strategies is defined for this purpose and backtested over the available time frame. We compare deterministic strategies derived from the observed price distribution of the previous day or week on the one hand with a model-based strategy on the other hand. The latter is implemented as a random forest regression model that takes into account, amongst other factors, the fill level of reservoir lakes in Switzerland. The results suggest that the model-based strategy be favoured over the deterministic strategies as it captures a higher amount of potential revenues and, most importantly, as it is more efficient. With the simplifying assumption that only a relatively small reserve capacity is offered and thus the results of the historic tenders are not affected, we get an average revenue potential of between 6 and 8 CHF/MW/h for negative tertiary reserve capacity and between 3 and 4 CHF/MW/h for positive tertiary reserve capacity.     

The value of 1800 MHz and 2100 MHz spectrums in India and implications for auction design

The sequence of events leading up to the upcoming auction of 1800 MHz spectrum in India has led to the auctions acquiring an extraordinary significance for the future of the Indian mobile industry. A key feature of the auction design proposed by the regulator TRAI is the benchmarking of the reserve price of 1800 MHz to the price of 2100 – 3G spectrum revealed in the 2010 auction. In the context of the low number of LTE devices available and the fragmentation in the 1800 MHz band, this paper proposes reducing the duration of spectrum holding to ten years (from the current level of twenty years), and calibrating the reserve price of 1800 MHz with its value with GSM deployment. An economic model is used to compute the value of startup and incremental 1800 MHz spectrum. The estimated values are shown to differ from the value of 2100 MHz spectrum at a pan-India level and also in their distribution across circles. A new set of reserve prices are computed based on the estimation. The estimated values are also shown to be close to the AGR-adjusted price revealed in the 2001 auction. A reserve price based on the 2001 auction is also provided. Concomitant features of the auction are suggested to give coherence to the auction design.     

Bid Coordination in Sponsored Search Auctions: Detection Methodology and Empirical Analysis*

Bid delegation to specialized intermediaries is common in internet ad auctions. When the same intermediary bids for competing advertisers, its incentive to coordinate client bids might alter the functioning of the auctions. This study develops a methodology to detect bid coordination and presents a strategy to estimate a bound on the search engine revenue losses imposed by bid coordination. When the method is applied to data from auctions held on a major search engine, coordination is detected in 55% of the cases of delegated bidding and the search engine's revenue loss ranges between 5.3% and 10.4%.     

Auction versus Negotiated Sale: Evidence from Real Estate Sales

We offer a theoretical and empirical comparison of auctions and negotiated sales. We first build a simple model to show that auctions generate a higher relative price than negotiated sales when demand for the asset is strong, when the asset is more homogeneous and when the asset attracts buyers with higher valuations. Using data from property sales in Singapore, we find support for our theoretical predictions. In addition, we find that auctions do not necessarily generate a higher price premium for foreclosed properties than for nonforeclosed properties.     

Do Auctions and Forced Divestitures Increase Competition? Evidence for Retail Gasoline Markets

To foster competition, governments can intervene by auctioning licenses to operate, or by imposing divestitures. The Dutch government has done exactly that, organizing auctions to redistribute tenancy rights for highway gasoline stations and imposing divestitures of such stations on the four major companies. We evaluate this policy experiment and find that the auctioning of licenses without an obligation to divest has no discernible effect on prices. An obligation to divest lowers prices by 1.3–2.3% at divested sites. Moreover, prices decrease by 0.9–1.2% at sites nearby. This suggests that the observed price decreases are at least partly due to competitive spillovers.     

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.     

Penny auctions

This paper studies penny auctions, a novel auction format in which every bid increases the price by a small amount, but placing a bid is costly. Outcomes of real-life penny auctions are often surprising. Even when selling cash, the seller may obtain revenue that is much higher or lower than its nominal value, and losers in an auction sometimes pay much more than the winner. This paper characterizes all symmetric Markov-perfect equilibria of penny auctions and studies penny auctions’ properties. The results show that a high variance of outcomes is a natural property of the penny auction format and high revenues are inconsistent with rational risk-neutral participants.