Operational efficiency of decentralized Internet auction mechanisms

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Electronic Commerce Research and Applications 9 (2010) 111–125

Contents lists available at ScienceDirect

Electronic Commerce Research and Applications journal homepage: www.elsevier.com/locate/ecra

Operational efﬁciency of decentralized Internet auction mechanisms Roumen Vragov * Baruch College, CIS Department, 1 Bernard Baruch Way, New York, NY 10010, USA

a r t i c l e

i n f o

Article history: Received 16 November 2008 Received in revised form 6 April 2009 Accepted 7 April 2009 Available online 23 April 2009 Keywords: Internet auction mechanisms Electronic markets Operational efﬁciency Laboratory experiments Continuous double auction

a b s t r a c t The recent consumer-to-consumer (C2C) Internet auction boom at eBay, Yahoo, Amazon, and other sites has added new theoretical challenges to the science of auctions. This paper uses experiments with economically-motivated human subjects to measure the operational efﬁciency of decentralized Internet auction mechanisms as they compare to centralized double auction mechanisms. Subjects are recruited randomly from the undergraduate population of a large urban university to be buyers or sellers in a simulated trading environment. They are randomly assigned costs and values for 10 units of a virtual product. During the experiment subjects trade these units through computer terminals in auctions similar to those held on eBay and generate proﬁts, which subjects receive at the end of the experiment. The paper uses data from this experiment and previous laboratory experiments to compare operational efﬁciency and convergence pattern of prices to equilibrium levels in continuous double auctions versus online Internet auctions based on two variables: auction size and time. Experimental results suggest that, because of their decentralized nature, Internet auctions require a few more participants and more time to achieve operational efﬁciency levels than centralized markets which use continuous double auction mechanisms. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Over the last decade online consumer-to-consumer (C2C) auctions have had an enormous impact on business the world over. Yet we still know very little about how efﬁciently goods are being exchanged online and whether and how the efﬁciency of the online trading process could be improved. This is in parallel with the relative lack of studies that reliably measure efﬁciency even in traditional ofﬂine auctions. At the same time efﬁciency is often one of the major criteria when an agency is choosing between possible alternative mechanisms for selling various property rights or other products (e.g. see Cramton 1998; Cox et al. 2002). Tracking the efﬁciency of an auction mechanism has also important practical signiﬁcance for online auction managers (Gallien and Gupta 2007; Kauffman et al., in press; Caldentey and Vulcano 2007). On the web the major source of revenue for auction marketplaces is the commissions and listing fees. Commissions are usually a percentage of the transaction price. In order to maximize revenue, online auction managers should maximize transaction prices and transaction volume. However, if the process of raising prices also results in much lower buyer surplus, then many buyers would be turned away from the auction website to other alternatives. In order to improve proﬁtability without hurting buyers, online auction managers can implement policies that increase * Tel.: +1 646 312 3402; fax: +1 646 312 3351. E-mail addresses: [email protected], [email protected] 1567-4223/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.elerap.2009.04.008

transaction prices and auction efﬁciency at the same time and at least at approximately the same rate. This would guarantee that buyers are not hurt in the process of increasing auction website revenue. This is why auction managers should be concerned about efﬁciency when they make changes to auction rules that might inﬂuence auction prices and performance (Wenyan and Bolivar 2008). There are two different deﬁnitions of market efﬁciency that have been used to assess how well auctions in general and Internet auctions in particular perform. The ﬁrst type of market efﬁciency is known as operational (or allocative) efﬁciency. This efﬁciency is deﬁned as a percentage of the maximum possible surplus extracted by a market institution while demand and supply are being matched (see Parsons et al. 2006). This idea of efﬁciency works well for ﬁnal products – or products that have well-deﬁned production costs that the sellers incur and also have some intrinsic usually heterogeneous values to the buyers (see Milgrom and Weber 1982; also Krishna 2002, and Klemperer 2004). Both buyers and sellers need to perform only one transaction in order to enjoy gains from trade. The difference between the transaction price and the production and other costs is the seller surplus, and the difference between the buyer’s value and the transaction price is the buyer surplus. The sum of these two surpluses is the total surplus, and operational efﬁciency is the ratio between the total realized surplus and the total possible surplus. This idea of efﬁciency allows establishing efﬁciency baselines, ranking different auction mechanisms, and makes possible the estimation of the effect of a change in a

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certain market variable that is under a market designer’s control. This type of efﬁciency is hard to estimate using market data except in some limited circumstances (see Kang and Puller 2008; Hortacsu 2002; Gopal et al. 2007) because much of the information about real costs and values is never fully revealed by market participants. An easy way to see how operational efﬁciency is impacted by market variables is through laboratory experiments with economically-motivated human subjects (Smith 2002, 2003) in which values and costs are directly induced by the experimenter. The second idea of efﬁciency, which we call informational efﬁciency, exists when there is no potential for arbitrage in the market. This idea of efﬁciency is usually used to assess how well ﬁnancial markets perform (see Fama 1991). The idea is useful for ﬁnancial markets because ﬁnancial paper does not have intrinsic value, that is, in order to realize proﬁts, one has to buy a ﬁnancial product and then sell it later. Thus the value of a ﬁnancial product depends on the future expectations of all market participants. Market participants’ values for products similar to ﬁnancial paper are common or correlated. Informational efﬁciency is thus quite relevant in ﬁnancial and other markets where market participants are expected to re-trade an item before they can realize a proﬁt. Financial economists have developed methods to detect if a market is informationally efﬁcient by using past price data (see Davis 2008 for a review). There have already been several studies that have used this methodology to ﬁnd that current C2C auctions are not informationally efﬁcient (see Kauffman et al., in press). What are the factors that impact market efﬁciency? Classical economic theory suggests that one of the most important variables that can affect efﬁciency is the number of participants in a market mechanism (see MacKenzie et al. 2007). This is also termed market size. More recently modern auction theory has devoted much attention also to the importance of the market mechanism which is being used to match supply and demand (see Krishna 2002; Klemperer 2004; Smith 2003). We know the structure and rules of currently available Internet auction mechanisms. However, we do not know exactly how inefﬁcient the auctions are and how their efﬁciency is impacted by an increase in the number of auction participants. This paper is an initial attempt to ﬁll this gap in current research. In the new context of Internet auction mechanisms, this study asks the following research questions: How is the operational efﬁciency of online auctions inﬂuenced by auction size? How is the relationship between auction size and efﬁciency different in decentralized Internet auction mechanisms versus more centralized market mechanisms like continuous double auctions? How do prices converge over time to competitive levels in more decentralized mechanisms like Internet auction mechanisms versus centralized market mechanisms like continuous double auctions? To address these questions the paper uses an exploratory laboratory study with economically-motivated human subjects. The experiment presented here was conducted in the summer of 2001 and is among the ﬁrst laboratory experiments involving human subjects that tries to simulate the economic environment surrounding online auction mechanisms for ﬁnal goods. The main experimental ﬁnding reported here is that Internet auctions need more than seven buyer visits per auction in order for auction prices to reach competitive levels. It also turns out that Internet auction mechanisms require more time than centralized markets to achieve high efﬁciency levels. This paper makes several contributions to theory and practice. First, it shows that a basic principle from economic theory about the relationship between market size and market efﬁciency applies

to Internet auctions. Second, it extends previous experimental work in auctions to show that Internet auction mechanisms are different in their convergence properties from centralized double-auction mechanisms. Third, the paper can serve as a guideline to online auction designers as to how operational efﬁciency could be measured in the laboratory and describes a method to establish an efﬁciency baseline, change certain auction variables and estimate the effect of that change on the operational efﬁciency of the auction mechanism being tested. Lastly, the paper uses the reported research ﬁndings to suggest ways in which operational efﬁciency of online auctions could be improved. The article is organized in the following way: Section 2 provides an overview of previous research related to C2C Internet auctions and describes in detail the main differences between the centralized commodity markets experimentally tested by Smith and some of the most popular current C2C Internet auctions like eBay. Section 3 discusses the methodology and Section 4 describes the main features of the experimental design. Section 5 reports the experimental results, Section 6 discusses their implications. Section 7 provides a summary of the limitations and the conclusion.

2. Theory As stated by Kannan and Kopalle (2001), dynamic pricing on the Internet has become very popular over the last decade. Consumers and businesses are seemingly embracing various auction formats as legitimate ways to exchange goods and services online. This trend has been driven by the substantial decrease in search costs (Bakos 1997) and by the positive attitude of consumers towards using computers and technology to support C2C transactions (Stafford and Stern 2002). Electronic auctions of various kinds have also been used extensively in online B2B market settings as part of traditional supply chains and supply networks (Anandalingam et al. 2005; Pinker et al. 2003). So far efﬁciency and prices in online auctions have been explored with the help of two scientiﬁc methods: data analysis of naturally occurring Internet auctions, and data analysis of results from ﬁeld experiments. We next review the results from both of these approaches. 2.1. Analyzing price data from naturally occurring Internet auctions and from ﬁeld experiments Lucking-Reiley et al. (2007) and Ariely and Simonson (2003) are one of the ﬁrst studies to investigate the behavior of prices in online auctions using price data from eBay. The econometric models presented in these studies are useful because they show important relationship between various observable auction variables, however, they do not report results speciﬁcally related to the efﬁciency of the auction mechanisms being studied. We later use these models to establish similarity in behavior between the laboratory and the real world, and to illustrate the results of the paper. Roth and Ockenfels (2002) is an attempt to analyze an important phenomenon in online auctions with hard deadlines: sniping. Sniping occurs when buyers wait until the very end of the auction before they submit bids. They claim that sniping would decreases efﬁciency but they do not measure efﬁciency itself. This study is also useful because the theoretical model and econometric analysis presented there could serve again as way to establish similarity between subject behavior in the laboratory and buyer behavior online. Most of the studies based on price data do not investigate efﬁciency directly. The same observation pertains to studies that use data from ﬁeld experiments (e.g. Durham et al. 2004; Ba and Pavlou 2002; Lucking-Reiley 1999). Just recently Gopal et al. (2007) argue that the fundamental principles driving ﬁnancial markets and online markets are very

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similar. They claim ideas about arbitrage that have been widely used in the ﬁnance literature to estimate market efﬁciency could be useful in an online auction setting. They develop two basic arbitrage principles and use them to evaluate price behavior in temporally proximate auctions. They ﬁnd some evidence of inefﬁciencies using price data from current auctions on eBay. Another study in Oh (2002) uses naturally occurring price data to detect the presence of winner’s curse, which suggests that inefﬁciencies are present. Winner’s curse results from bidders having afﬁliated or common values, which suggests that informational efﬁciency rather than operational efﬁciency is at focus in that study (see Cox et al. 1999). Kauffman et al., (in press) in a similar fashion apply the widely accepted theory of market efﬁciency in ﬁnance to test if eBay coin and rare stamp auctions are efﬁcient. They perform unit root and variance ratio tests using price data from tens of thousand of auctions and conclude that there are clear indications of inefﬁciencies. They also ﬁnd an inverse relationship between market informational efﬁciency and liquidity. So far, however, not much is known about the relationship between operational efﬁciency and liquidity. 2.2. Internet auctions mechanisms versus centralized double auction mechanisms Efﬁciency of Internet auctions might be possible to measure relative to efﬁciency in other markets like centralized continuous double-auction mechanisms. Note, however, that Internet auction mechanisms are different from a centralized double auction mechanism in several important aspects according to previous literature. I next provide a list of differences together with the previous studies, in which these differences are mentioned. 2.2.1. Localization of demand and supply The existing supply and demand curves in Internet auctions are not as well ‘‘localized” as in a centralized setting. Buyers and sellers can participate only in a fraction of all available auctions. There is a very clear difference between single-unit and multiple-unit auctions in the theoretical and experimental literature to date (Bapna et al. 2000, 2001). Scientiﬁc investigation has focused separately on these two types. On the Internet one can have a multi-unit and a single-unit auction for the same items happening at the same time. Therefore the existing large market demand and supply curves are fragmented among different auctions at every point of time. This feature is expected to have a negative impact on efﬁciency and the speed of convergence of market prices to the equilibrium price. 2.2.2. Market information Market information in Internet auctions is not complete. Buyers and sellers can physically observe only a fraction of all different auctions going on at different times. That is because in Internet auctions there is no centrally occurring open outcry of bids and offers that everyone can observe at all times. That is why it is very hard for any one market participant to collect and process all market information already available. This feature is also expected to have a negative impact on efﬁciency and on the speed of convergence of market prices to the equilibrium price. 2.2.3. Time-related issues Because of their decentralized nature, many Internet auctions have temporal deadlines that affect strategies and behavior. Auctions on eBay can last from 3 to 11 days so time preferences on the part of market participants become important (Gallien and Gupta 2007). Auctions at Amazon and Yahoo are automatically extended if there is too much activity before the auction ends. Temporal deadlines provide incentives for bidders to wait until the very last moment before they submit a bid. This strategy is called snip-

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ing. It has been shown theoretically (Roth and Ockenfels 2002), empirically (Hayne et al. 2003) and experimentally (Ariely et al. 2005; Vragov, 2004/2005) that similar behavior might cause lower-than-equilibrium prices and lower efﬁciency levels. 2.2.4. Strategic symmetry of market participants Most current C2C auctions are isomorphic to the standard English auction. Prices in these auctions are always ascending and bids are open. Buyers and sellers are not symmetric in terms of their strategies. Sellers start an auction usually with a minimum required bid and a secret reservation price. For example, eBay has introduced a buy-it-now option which allows a buyer to win the auction before it starts. In that case the seller decides on and posts a buy-it-now price that any buyer can accept. See Mathews and Katzman (2006), Budish and Takeyama (2001), and Gallien and Gupta (2007). After the auction has started the sellers cannot participate in the bidding process. Buyers then take over. They become the only active participants on the market until the auction is over. As shown in Vragov (2005) and Lopomo et al. (2005), open ascending auctions are prone to bidder collusion, which causes lowerthan-equilibrium prices and lower efﬁciency levels. 2.2.5. Flexibility Internet auctions are much more ﬂexible in terms of auction rules than the centralized exchanges. On the Internet many similar items can be sold on the same auction web site using an auction with slightly different rules. Thus buyers and sellers can endogenously select among different auction types. The effect of this feature on efﬁciency levels is presently uncertain. A preliminary experimental attempt is reported in Vragov (2005). 2.2.6. Automation It is much easier to use robot traders on Internet auctions than on standard commodity or stock exchanges. eBay allows buyers to participate in auctions through proxy bidding (Ward and Clark 2002). It is also well known that buyers on eBay use sniping robots to submit bids in the very last second of an auction (Hayne et al. 2003). It is the hope of many practitioners that the use of simple automated strategies can close the expected efﬁciency gap between commodity and stock exchanges and Internet auctions (Bapna et al. 2004). 2.2.7. Identity issues Internet auctions are characterized by issues related to participants’ true identities and ability to pay. This has resulted in the invention of various reputation ratings and different ways to limit false identities. It is certain that all these features can have a major impact on human behavior and on the auctions prices and efﬁciency. Generally efﬁciency levels are expected to be lower if reputation scores are subject to easy manipulation (Standiﬁrd 2002) and if participants are dubious about the real identities of some buyers and sellers (Kauffman and Wood 2005). 2.2.8. Experience of market participants There is another practical difference between the centralized commodity exchanges and C2C Internet auctions. Most of the traders in the former have much experience, and participation in the market is usually their occupation. Most of the traders in the latter might not be very experienced and might engage in Internet transactions only occasionally. For example, Wilcox (2000) provides an extensive treatment of the topic and demonstrates that experience is important in Internet auctions using data analysis of results from real auctions. The experiment presented here uses a relatively unsophisticated traditional pool of undergraduate students as subjects similar to most behavioral laboratory experiments including the ones

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been tested and evaluated in the laboratory and none of them has emerged as a standard (see Parsons et al. (2006), for a nice review of theoretical, computational, and experimental results, also Friedman and Rust (1993) for discussion of most existing models). The general agreement is that the best guideline for the efﬁciency and price convergence properties of the continuous double auction mechanism is a large collection of controlled laboratory experiments performed under different economic environments and utilizing different subject pools (Smith 2003). This data show remarkable robustness of operational efﬁciency of continuous double auctions under many underlying economic environments. 2.4. Operational efﬁciency, market atomicity, and Smith’s market experiments

Fig. 1. Graphic comparisons of the price convergence process according to theory and according to experimental observation of centralized exchanges and C2C Internet auctions.

in Smith (1962, 1982). The experimental design presented here is different from Smith’s classic experimental design because it represents an attempt to mimic the ﬁrst four major differences between C2C Internet auctions and centralized exchanges from the ones mentioned above as closely to the naturally occurring circumstances as possible. The last four differences are excluded from the current design for the sake of simplicity and will be investigated in the future. The excluded features are the choice of different auction rules, the choice of automated proxies, the effects of buyers’ and sellers’ reputations, the ability of market participants to bid in an on-line auction under different names. Fig. 1 provides a visual comparison of the price-convergence process in a market. Note that so far the only generally accepted theory of price-formation is the classical economic paradigm as shown in the ﬁrst part of the ﬁgure. The convergence pattern in some centralized double auction settings as illustrated in the second part of the ﬁgure is taken from Smith (1962, 1982). The convergence pattern in a simulated online auction setting illustrated in the third part of Fig. 1 is based on experimental results reported in Vragov (2005). 2.3. Theories of efﬁciency and price-convergence in centralized doubleauction mechanisms Centralized continuous double auction mechanisms are truly dynamic and quite complex in nature. This has resulted in the relative lack of theoretical models that explain their efﬁciency and convergence properties. Moreover, every proposed model is based on many unrealistic assumptions about the behavior of market participants and only explains some observed properties of a continuous double auction but not others. Most of these models have

Economists have long held that one of the most important requirements for markets to be efﬁcient is their atomicity. Atomicity is the presence on the market of a large number of market participants. Since operational efﬁciency cannot be directly observed in naturally occurring circumstances, experiments were required to test this hypothesis. The assumption of large size was shattered in the 1960s and 1970s by laboratory experiments conducted by Smith (1962, 1982). He established that most of the time one needs a small number of symmetric market participants (usually about ﬁve buyers and ﬁve sellers) to ensure a competitive and therefore efﬁcient market if the market institution used to match supply and demand is a version of the continuous double auction (Smith 1962). He also found that, after several rounds of a market laboratory experiment, prices converged quickly to the competitive equilibrium level. Smith tested market efﬁciency in centralized laboratory environments. The study was designed to simulate on a modest scale the multi-lateral auction trading process in well-organized commodity exchanges. In his laboratory studies buyers and sellers were assigned values and costs for a ﬁctitious product and were allowed to submit bids and asks orally (or using an electronic system in Smith et al. 1982) and transact publicly. The experiments consisted of several trading ‘‘days”, each 5–10 min long, with the demand and supply conditions kept constant. Results showed that markets do not need the presence of an inﬁnite number of traders in order for prices to converge to competitive equilibrium. The experimental electronic market needed about ﬁve symmetric buyers and sellers and one or two trading ‘‘days” for prices to converge to competitive levels. Since then the impact of change in size on the operational efﬁciency of market mechanisms has not been explored. 2.5. Laboratory experiments related to online auctions There is one laboratory experimental study that has compared the operational efﬁciency of the hard and soft closing rules in online auction mechanisms (see Ariely et al. 2005). This study measures the efﬁciency of four different auction mechanisms in the laboratory and concludes that hard deadlines decrease operational efﬁciency. The authors use a methodology very similar to the one presented in this paper. Their focus of investigation is different, so they do not use the centralized double auction as one of the mechanism for comparison. One of the problems with the study, however, is that the experimenters did not model any costs related to time or the length of auction participation, which is an important consideration in online auctions. The study presented here includes transaction costs related to time that provide an incentive for buyers and sellers to complete a transaction as soon as possible. Smith’s experimental results mentioned in Section 2.4 can be used to provide a benchmark for the operational efﬁciency of a continuous double auction mechanism and the variables that are related to it (auction size and time). These experimental results

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can be compared to results from experimental environments similar to online auction mechanisms currently in use. 3. Methodology The use of laboratory experiments in E-business research has been already discussed in Kauffman and Wood (2008) in the context of Runkel and McGrath’s ‘three horned dilemma’ for research methodologies. Under this methodological framework, laboratory experiments allow scientists to study relevant phenomena with complicating environmental context-related conditions removed. Such experiments allow precise measurements of relevant effects while sacriﬁcing some generality and realism. In the context of the research questions posed in this paper, we can see that, while data from naturally occurring Internet auctions and from ﬁeld experiments are useful to compare relative revenue performance of different electronic markets or auction formats, only laboratory experiments can pinpoint with accuracy the distance between market prices and the theoretical equilibrium price as well as the exact absolute and relative departures from efﬁciency (Porter and Vragov 2006). For example, in the context of the scientiﬁc investigation described here, results from empirical studies and ﬁeld experiments can only show that increasing the size of a market increases or decreases auction prices. Data from naturally occurring auctions and ﬁeld experiments cannot be used to compare the occurring auction prices with the theoretical equilibrium price because values and costs are unobservable and the theoretical equilibrium price is not known. Only a laboratory experiment can demonstrate how market prices are changing with respect to the theoretical equilibrium price and how much total surplus is generated in the market. A simple example can illustrate this clearly. Suppose we have a market with three sellers selling one unit of the same product and three buyers each wishing to buy one unit of the product. Suppose that two units are exchanged under each of three different auction mechanisms. The observable transaction prices in Mechanism 1 are $120 and $105, the observable transaction prices in Mechanism 2 are $65 and $85, and the observable transaction prices in Mechanism 3 are the same as in Mechanism 1, namely $120 and $105. This information is not sufﬁcient to reliably compare the operational efﬁciency of these three mechanisms because we do not know the unobservable preferences of the buyers and sellers who participated in these transactions. Let us suppose that in all of the above mechanisms buyers’ private values are $125 for Buyer 1, $110 for Buyer 2, and $63 for Buyer 3, and sellers’ private costs are $45 for Seller 1, $60 for Seller 2, and $95 for Seller 3 (see Fig. 2). Suppose that under the ﬁrst and the second mechanism Buyer 1 and Seller 1 exchanged a unit in the ﬁrst transaction and Buyer 2 and Seller 2 exchanged a unit in the second transaction, and under

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the third mechanism Buyer 1 and Seller 1 exchanged a unit in the ﬁrst transaction and Buyer 2 and Seller 3 exchanged a unit in the second transaction. Now we are in a position to compare the operational efﬁciency of these mechanisms as deﬁned in the introduction. The efﬁciency of Mechanism 1 is (125 120 + 120 45 + 110 105 + 105 – 60)/(125 + 110 45 60) = 125/125 = 100%, the efﬁciency of Mechanism 2 is (125 65 + 65 45 + 110 85 + 85 – 60)/(125 + 110 45 60) = 125/125 = 100%, and the efﬁciency of Mechanism 3 is (125 – 120 + 120 – 45 + 110 – 105 + 105 – 95)/(125 + 110 45 60) = 95/125 = 76%. We see that Mechanisms 1 and 2 have very different prices but the same efﬁciency, and Mechanisms 1 and 3 have exactly the same prices but very different efﬁciencies. The theoretical equilibrium price range for all three institutions is [63, 95] and, in this speciﬁc example, this price range is too wide and not helpful in detecting how efﬁcient these mechanisms are. However, if there are more participants in the market mechanism or more units with heterogeneous values to be traded, demand and supply are closer to being continuous and the theoretical equilibrium price range usually shrinks. Then the theoretical equilibrium price range can be used as a proxy to compare the operational efﬁciency of various market mechanisms. This is because situations where transaction prices are out of the equilibrium price range but the market is still 100% efﬁcient happen extremely rarely, especially towards the end of a trading period. Generally, an exchange mechanism will be more efﬁcient if more transaction prices fall within the equilibrium price range (see Parsons et al. 2006). In view of the above example, we see that in order to measure operating efﬁciency directly, we need to know the private values of all market participants. This is easily achievable through the use of experiments with human subjects in which monetary performance-based incentives are utilized to induce the values which are otherwise unobservable in real life (Smith 2002). Fortunately, baseline studies measuring efﬁciency in centralized double-auction mechanisms are readily available (Smith et al. 1982). The experimental procedure in Smith (1962, 1982) includes accepted methods and rules for recruiting subjects, presenting instructions to subjects, establishing the length of an experiment, inducing subject values, and paying subjects. In order to see the effect of size on operational efﬁciency and on the speed of convergence of market prices to the equilibrium price in online auction mechanisms as compared to centralized continuous double-auction mechanisms we can use the same experimental procedure as in Smith et al. (1982) but create an experimental environment that closely resembles these newly emerging decentralized on-line auction mechanisms. Then we can compare efﬁciencies and price convergence. We use this speciﬁc study as a baseline because (1) it is the most comprehensive experimental study of the continuous double auction mechanism, (2) it is the study that established clear experimental measures for price convergence, (3) we know well how to replicate all of the study’s experimental procedures.

4. Experimental design

Fig. 2. Demand, supply, transaction prices and operational efﬁciency in each of the three mechanisms for the example in Section 3.

There are 26 subjects in the experiment (13 buyers and 13 sellers). The number of buyers and sellers is equal in order to keep the market symmetric as in the baseline experiments mentioned above. The upper limit on the number of subjects was only constrained by laboratory space. At the moment when the experiment was conducted the laboratory had 28 functioning computers, two of which were prepared to be used as a back-up in case of a computer malfunction. In principle, the experimental software could handle a larger subject pool. I next describe how the demand and supply curves are designed with the help of induced value theory (see Smith 1976).

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Table 1 The independent private values and monitoring costs for all buyers in the experiment. All values are shown in experimental dollars. Values are used in the following way: if Buyer 1 buys one unit for 4.00, his proﬁt would be 8.00 – 4.00 = 4.00. If Buyer 1 buys three units for $4.00 each, then his proﬁt is 8.00 + 7.41 + 6.22 – 3 4.00 = 9.63. Monitoring costs are subtracted every minute from the total proﬁt. Unit Buyer Buyer Buyer Buyer Buyer Buyer Buyer Buyer Buyer Buyer Buyer Buyer Buyer

1 2 3 4 5 6 7 8 9 10 11 12 13

1

2

3

4

5

6

7

8

9

10

Mon. cost

8.00 8.00 7.25 7.87 8.00 8.00 8.00 8.00 7.50 8.00 7.78 8.00 8.00

7.41 7.00 7.24 7.58 7.30 8.00 7.83 7.23 6.90 6.78 7.60 7.50 8.00

6.22 6.80 7.20 7.04 7.20 7.13 5.70 7.00 6.63 6.51 6.90 7.49 8.00

6.15 6.54 7.00 7.00 7.00 7.00 5.68 6.79 6.35 6.47 6.80 6.70 7.71

5.74 6.34 6.97 6.12 5.67 5.97 5.66 6.54 6.27 6.25 6.00 6.65 7.00

5.69 5.80 5.74 5.00 5.30 5.32 5.49 5.50 6.02 5.97 5.00 5.20 4.84

5.58 5.50 5.22 4.77 5.00 5.03 5.27 5.13 5.14 4.77 5.00 5.17 4.79

5.05 4.80 4.17 4.33 4.84 4.33 5.08 4.01 4.94 4.60 4.47 4.89 4.21

4.40 4.70 4.11 4.22 4.08 4.16 5.00 4.00 4.63 4.50 4.45 4.09 4.03

4.02 4.00 4.00 4.20 4.00 4.00 4.83 4.00 4.35 4.41 4.00 4.00 4.00

0.11 0.12 0.08 0.02 0.10 0.09 0.02 0.03 0.05 0.06 0.06 0.07 0.11

Table 2 The independent private unit costs, monitoring cost, and inventory cost of all sellers in the experiment. All costs are shown in experimental dollars. Costs are used in the following way: if Seller 1 sells one unit at 4.00, his proﬁt would be 4.00 – 1.58 = 2.42. If Seller 1 sells three units at $5.00, his proﬁt would be 3 5.00 – 1.58 – 1.59 – 1.95 = 11.88. Monitoring costs are subtracted every minute from the total proﬁt. Inventory costs are multiplied by the units unsold every minute and are also subtracted from the total proﬁt. Subject

1

2

3

4

5

6

7

8

9

10

Mon. cost

Inv. cost

Seller Seller Seller Seller Seller Seller Seller Seller Seller Seller Seller Seller Seller

1.58 0.20 0.13 0.10 0.33 0.03 0.14 0.65 0.34 0.10 0.48 0.01 0.10

1.59 1.25 1.34 1.20 0.34 0.27 0.43 0.72 0.54 1.20 0.96 0.05 0.20

1.95 1.28 1.96 1.30 1.00 0.99 1.04 1.00 0.74 1.36 1.25 0.23 0.30

1.96 1.38 1.98 1.40 1.00 1.20 1.13 1.05 1.94 1.50 1.54 1.02 0.40

1.99 2.00 2.64 1.71 1.01 2.37 2.00 2.14 2.00 2.08 1.71 2.32 0.50

2.01 2.40 2.65 1.93 1.56 2.59 2.44 2.70 2.88 2.46 1.96 3.00 2.00

2.02 2.62 2.66 2.16 3.00 2.77 2.76 2.90 2.93 2.74 2.01 3.20 3.00

2.03 3.23 2.72 2.31 3.00 2.88 2.89 3.07 3.34 2.75 3.20 3.38 4.00

2.86 3.59 2.77 3.10 3.35 3.00 2.93 3.60 3.63 2.76 3.40 4.00 4.00

4.00 3.80 3.91 3.86 3.61 4.00 3.01 3.90 3.61 3.90 3.48 4.00 4.00

0.01 0.00 0.04 0.07 0.08 0.05 0.00 0.03 0.09 0.10 0.01 0.01 0.12

0.00 0.01 0.03 0.01 0.03 0.03 0.02 0.00 0.00 0.02 0.04 0.00 0.02

1 2 3 4 5 6 7 8 9 10 11 12 13

Each buyer has demand for 10 units of a homogeneous product and each seller has costs for 10 units of a homogeneous product (see Tables 1 and 2, Fig. 3, and Appendix). If all sellers start auctions for all of their items, the buyers can participate in as many as 130 auctions. Sellers’ costs are independently drawn from a uniform distribution with support ($0.00, $4.00); buyers’ values are drawn independently from a uniform distribution with support ($4.00, $8.00). This guarantees that all units present on the market can be exchanged without loss if time costs (described later) are disregarded.

Fig. 3. Induced demand and supply schedules at the beginning of the experiment obtained by plotting the values and costs from Tables 1 and 2 with the exception of monitoring and inventory costs.

Buyers can buy up to 10 items. Buying more than 10 items does not add value to a buyer. Sellers can start up to 10 auctions and can sell only up to 10 items. Since we can have only 13 buyers and 13 sellers because of the laboratory limitations mentioned in the previous paragraph, we endow buyers and sellers with multiple values/costs in order to achieve smoother demand/supply curves. This increases the amount of transactions that can happen during an experimental session and also makes the theoretical competitive equilibrium price at the beginning of each experimental session unique at $4.00. Convergence of prices to the theoretical equilibrium price is thus much easier to trace. One might argue that buyers in C2C Internet auctions are usually interested in one speciﬁc item at a time. However, having single-unit demand or supply in this design will severely limit the amount of data gathered from the experiment and will limit our ability to trace convergence. As mentioned in Section 2, preferences related to time are important in online auctions much more than in traditional auctions. Because of this time-related costs are introduced as a type of transaction costs in this experimental design. Every minute during the experiment subjects incur two types of charges related to time. The ﬁrst charge is a monitoring cost (mi) that depends on the time that buyers or sellers need to buy/sell 10 units. For example if it takes s minutes for subject i to complete 10 transactions, then subject i’s total monitoring cost is s mi, where mi is randomly chosen from the following set {0.00, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12}. Once the charge is picked for each subject, it remains ﬁxed for the entire session. This is done so that subjects are not confused by frequent changes in their parameters. You can see the actual mi draws for all buyers

R. Vragov / Electronic Commerce Research and Applications 9 (2010) 111–125

and sellers in Tables 1 and 2. The monitoring cost represents the effort necessary to observe and participate in the market. The second charge is an inventory cost (rj) per unsold item from the initial allocation. This cost is applied only to the sellers. For example if during the ﬁrst s minutes of the experimental session seller j has not sold any items, then seller j’s inventory cost will be 10srj where rj is randomly chosen from the following set {0.00, 0.01, 0.02, 0.03}. Once this per second and per unit inventory charge is chosen for each seller at the beginning of the experiment, it is kept constant. During the course of the experiment a buyer could incur time costs somewhere between $0.00 and $2.40, which is approximately between 0% and 13% of the possible attainable individual proﬁt. The sellers’ monitoring cost is in the same range as the buyers, but sellers also have inventory costs. They can be between $0.00 and $6.00, or approximately between 0% and 33% of the possible attainable individual proﬁt per seller. The maximum cost of $6.00 is incurred only in the special case when a seller has not been able to sell anything throughout the duration of an experimental session. This cost represents the cost of storage and handling of unsold inventory. The experiment consists of three sessions, and each session is terminated at a pre-speciﬁed time (20 min after start). Sellers can choose to sell an item at any time during the 20 min, and buyers can choose to participate in any of the active auctions. The cost and value parameters are the same for all sessions. All subjects go through a training session that explains the rules of the auction and gives the subjects the chance to participate in preliminary trial session. Normally, the more sessions can be conducted, the more data is obtained. Subjects start getting tired quickly about 2 h within an experiment. Because of this constraint only one practice and three real experimental sessions could be conducted (see Fig. 4). The induced demand and supply curves at the beginning of each experimental session cross at $4.00. This price is the competitive equilibrium price at the beginning of each session. The equilibrium quantity at the beginning is 130, and the total surplus is $481.22. However, as the session goes on, buyers and sellers start incurring time costs. Since sellers’ time costs are higher than the buyers’ the supply curve starts shifting up faster than the demand curve shifting down. The equilibrium quantity should then be less than 130 and the equilibrium price around $4.12 (This is calculated by adding the average inventory cost per unit for 20 min – $0.32 – to the supply curve and ﬁnding the new point of intersection between the updated demand and supply curves). As mentioned earlier sellers can sell their items on an auction web site very similar to eBay. The rules of this auction are described next (see Appendix for subject instructions). The seller has to specify a reserve price, and a length for the auction. There are only four possible lengths that are predetermined – so the seller has to choose one of these four options. Each auction is opened to everyone who wishes to participate. Bidders can start submitting bids, with the only requirement that every new bid has to sat-

Subjects walk in lab

Read instructions

Participate in one practice session

about 45 min Participate in Session 1 of experiment

Participate in Session 2 of experiment

Participate in Session 3 of experiment

Receive Pay

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isfy a minimum increment rule. Buyers are not told the reserve price, but they are informed if they are below or above it. When the end is reached and the highest bid is greater than or equal to the reserve price, the auction is successful. The seller receives the price and the buyer receives the value of the item. The auction lengths are 5, 8, 11, and 14 min. These lengths were chosen to imitate the four different options that sellers face on eBay. They are equally spaced and the largest possible length is made shorter than the timing of each session. In this experimental design the cost and value information is readily available to the experimenter, and efﬁciency and losses can be measured directly. In this design we will measure the effect of the size of an auction on efﬁciency. We will record the number of different buyers that visit an auction and chart the effect of this number on the auction price. We expect the price to be more consistently over $4.00 with the increase in the number of bidders who visit the auction. Tracing the price with the ﬂow of time will give us an idea about the pattern and speed of convergence of the auction price to the equilibrium price. When trying to elicit the effect of market size on the auction price it was not initially certain what variable to count. Because of the decentralized nature of Internet auctions, there are three possible candidates: bidders per auction, visitors per auction, and bids per auction. Visitors per auction is chosen to be the best possible proxy for market size because every bidder who visits an auction has the potential to participate in it even though eventually he or she might decide not to bid. In centralized markets everyone observes the movement of price and all bids and offers and therefore has the potential to buy or sell an item at all times. This experimental design contains a dilemma that is very hard to overcome. The main purpose is to look at the effect of the number of visitors per auction on efﬁciency but the design does not provide a control mechanism for ensuring enough variation in the number of bidders per auction. Subjects were given the chance to decide for themselves in which auction to participate. There is no limit on the number of visitors or on the number of bidders in any of the experimental auctions. Subjects individually decided whether to log into an auction and participate in it. They could not observe the auction size unless they logged into the speciﬁc auction. It was possible for the experimenter to pre-determine the size of each auction in its beginning by limiting the number of bidders or number of visitors. This, however, was considered too much of an interference in subject individual choices and, in addition, such a feature is not present on any of the discussed C2C auction web sites. In this case I decided that it is better to not directly control for auction size in other to preserve the likeness of the experimental environment to an on-line auction environment. In this dilemma realism won over control. It is possible for a subject to complete the experiment with negative proﬁt. This happens when a subject could not buy or sell at least a unit of his or her inventory. Fortunately for the experimental designer there were no negative proﬁts at the end of the experiment although there were two subjects with slightly negative proﬁts in the ﬁrst session. Negative proﬁts pose a problem. Institutional Review Board (IRB) approval for this research required that subjects were guaranteed a minimum payment for their participation in the experiment. The possibility of some participants not receiving compensation because they took losses in certain rounds is considered ethically unacceptable, although it may be preferable from a market-design perspective.

5. Experimental results about 70 min Fig. 4. Experimental timeline.

Data descriptions of the three main variables observed can be found in Table 4. The parameters representing product values

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Table 3 T-statistics of the comparisons between mean number of last minute bids. Last minute bids are bids submitted within the last ﬁfth of the auction length. Mean of last minute bids (St. dev)

Versus session 1 mean

Session 1: 1.77 (1.93) Session 2: 2.03 (1.81) Session 3: 2.24 (1.90)

Versus session 2 mean

Versus session 3 mean

0.73 (df = 116) –

1.36 (df = 133) 0.71 (df = 157) –

Table 4 Descriptive statistics of the observed regression variables. Variable

Mean

Min

Max

St. dev.

Number of observations

Price Number_Of_Visiting_Bidders Auction_Number

3.80 4.40 103

1.00 1 1

5.50 10 206

0.7931 2.3168 59.6112

206 206 206

and costs were chosen to simulate a symmetric demand and supply environment. The heterogeneous monitoring and inventory costs were chosen to create a reasonable feeling of urgency in some buyers and sellers. Generally, a well-established theory about the correct levels of these parameters does not exist, and reasonability is a matter of interpretation. For this reason before reporting results of this experimental study we have to establish that market participant behavior matches patterns noticed by previous researchers. This is usually accomplished in three different ways. These are listed and explained below. Experimental results are compared to results from previous experiments that are very similar in design and procedure. The closest experimental study in design and procedure is the one reported in Ariely et al. (2005). That study investigates the effect of sniping on efﬁciency. We will use it to form and test hypotheses about sniping. Experimental behavioral patterns are compared to patterns in data from naturally occurring Internet auctions. Useful analysis of data from naturally occurring auctions that is related to our design is provided in Roth and Ockenfels (2002), Ariely and Simonson (2003), Lucking-Reiley et al. (2007), and Wenyan and Bolivar (2008). We use these studies to form and test hypotheses about sniping and some relationships between observed variables. Experimental behavioral patterns are compared to predictions based on theoretical models. Currently, the theoretical model that is most closely related to our experimental design is the one presented in Roth and Ockenfels (2002), although as mentioned earlier, this one focuses solely on sniping and does not explain other observed behaviors in online auctions.

Fig. 5. Number of bids per time category. Every auction is divided in ﬁve intervals of equal length and then bids are counted in each interval.

Hypothesis 1 (The Bid Sniping Hypothesis). The number of bids submitted in the last 20% of the time of the auction is larger than the number of bids submitted during any other ﬁfth. There is plenty of evidence for ‘sniping.’ To conﬁrm the Bid Sniping Hypothesis (H1) we can ﬁrst take as H0 that there is equal probability for every bid to be in any of the ﬁve possible parts of the time interval (see Fig. 5). Then, it is easy to show that under the null hypothesis the probability of having 88 bids in the ﬁrst and 186 in the ﬁfth interval is small (less than 0.8 109). Similar results pertain for the pair-wise comparison between 85 and 186, 79 and 186, and 154 and 186 bids from the other three parts of the time interval. This statistical procedure conﬁrms that the probability that a bid will be submitted in the last ﬁfth of the time interval is considerably greater than 0.20. Hypothesis 2 (The Winning Bid Timing Hypothesis). The winning bid in each auction in half of the cases is submitted in less than 10 s before the end. The Winning Bid Timing Hypothesis can be afﬁrmed by a nonparametric test for the median of the resulting experimental time distribution of the bids. To test the hypothesis, we assume that the distribution median is less than 10 s, then we calculate the probability that the experimental observations were generated by a distribution that has 10 s or less as its median. The p-value is 0.54, so our hypothesis holds at the 5% conﬁdence level (see Fig. 6). The Last Minute Bid Learning Hypothesis below also follows from the discussion in Roth and Ockenfels (2002). If ‘sniping’ is a part of an equilibrium strategy, then we might expect to see more ‘sniping’ as the participants gain experience.

5.1. Establishing similarity of experimental data to data from naturally occurring auctions Sniping is the most pervading phenomenon in online auctions with deadlines. Roth and Ockenfels (2002) offer a theoretical model of sniping in which sniping is part of a rational equilibrium strategy. They explain that sniping might be optimal because there is a non-zero probability that some of the last bids might not reach the system – thus buyers avoid expensive price wars. The phenomenon of sniping has been observed in experimental settings (Ariely et al. 2005) and in naturally occurring auctions (Roth and Ockenfels 2002; Ariely and Simonson 2003; Wenyan and Bolivar 2008). Based on these studies we formulate and test the following four hypotheses using our experimental data to show that subject behavior in the laboratory is quite similar to that observed in naturally occurring circumstances:

Fig. 6. The probability and cumulative densities of the timing of last (winning) bids in the eBay treatment.

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Hypothesis 3 (The Last Minute Bid Learning Hypothesis). The number of last minute bids will increase from session 1 to session 3. The Last Minute Bid Learning Hypothesis can be tested by a ttest of the difference in mean number of bids submitted in the last ﬁfth interval between the ﬁrst, second, and third session. The t-statistics of the pair-wise testing between the three sessions is shown in Table 3. The tendency of increasing number of bids with experience is there, but differences are insigniﬁcant. The next hypothesis is based on observations reported by Lucking-Reiley et al. (2007) and Ariely and Simonson (2003). Hypothesis 4 (The Bidder Participation – Auction Price Level Hypothesis). The number of bidders in an auction is positively correlated with the auction price. We can establish this with a simple non-parametric test of correlation between the two observed variables. The Spearman correlation coefﬁcient is 0.590, which suggests a relatively strong positive correlation. The coefﬁcient is signiﬁcant with a pvalue < 0.001. Fig. 7 displays two other variables that we can use to compare the data from this experiment and data from naturally occurring eBay auctions. We can see that the percentage of auctions with 0 bids and the percentage of auctions in which the reserve price was not reached in the experiment are close to observed means in naturally occurring auctions. 5.2. Main results The purpose of the experimental design is to answer the three exploratory questions that we asked in the introduction of this paper. Because of the way the experiment was designed, we know the theoretical equilibrium price range. This allows us to use the market equilibrium price as a benchmark to measure the relationship between market efﬁciency and other variables. As mentioned earlier, the closer the market price is to the equilibrium price, the higher the efﬁciency level of the market is. That is why we plan to estimate how the market price is affected by market size and time and then compare the market price to the theoretical equilibrium price. We note that widely acceptable theories of the mechanism by which market prices converge to equilibrium as a function of time or number of market participants are not currently available. To explore the relationship between market prices, market size, and time we consider a simple linear regression model as a good place to start. We analyze the data in the experiment using the following linear Price Regression Model (see Table 4 for descriptive statistics of the regression variables):

where the price in auction k is the dependent variable and the number of visiting bidders, and the auction number are the independent variables. The ﬁrst variable we chose is the Number_Of_Visiting_Bidders. The auctions in the experiment are numbered in sequence depending on the time that they ended during the experimental session. This means that Auction 2 ﬁnished before Auction 3 and so on. Thus the Auction_Number variable captures the effect of time on the market price. Individual and other effects are assumed to be expressed by the error term – they are normally distributed with a mean of 0. Because of the way the experimental design described in the previous section is set up, we control for the following variables and therefore remove any effects that they could have on prices: any characteristic or feature speciﬁc to the product traded, any variable related to buyer or seller feedback, any variable related to a daily, weakly or seasonal pattern. The results of the Price Regression Model are presented in Table 5. The regression includes all 206 successful auctions and R2 = 0.25. Coefﬁcient b1 is positive and signiﬁcantly different from 0, so we know that an increase in the number of visiting bidders results in an increase in the transaction price. Coefﬁcient b2 is also significant, which means that auction prices generally increased throughout the duration of the experiment. The R2 is low, which means that data are relatively noisy and convergence is weak. You can see scatter diagrams of the relationship between price and number of visiting bidders as well as price and auction number in Figs. 8 and 9. We next analyze the relationships between the variables above as compared to the theoretical equilibrium price. Result 1. An auction needs more than seven visits to achieve a high efﬁciency level. To better see the relationship between efﬁciency and the number of bidders visiting an auction let us look at Fig. 10 and Table 6, keeping in mind that the equilibrium price in the experiment is $4.00 at the beginning, then increases with the ﬂow of time and should be around $4.12 towards the end of the auction. If all transactions happen in the range between these two prices, the highest possible surplus will most likely be attained. The table and ﬁgure contain data about all auctions that were visited by a bidder at

Table 5 Results of the Price Regression Model. Effects

Coefﬁcients

Standard error

t Stat

P-value

a

2.9178 0.1353 0.0028

0.1171 0.0222 0.0008

24.92 6.12 3.25

<0.001 <0.001 0.001

b1 b2

Pricek ¼ ak þ b1 Number Of Visiting Biddersk þ b2 Auction Numberk þ ek

ð1Þ

Fig. 7. Comparing the percentage of auctions with 0 bids and the percentage of auctions in which the reserve price was not reached in this experimental study with the data gathered by Lucking-Reiley et al. (2007) during a period of a month.

Fig. 8. Scatter diagram of the relationship between price and number of visiting bidders.

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Fig. 9. Scatter diagram of the relationship between auction number and price.

Fig. 10. The darker line shows the relationship between average price and number of visiting bidders, the lighter line shows the relationship between average price and number of bidders. The two lines with dashes show the equilibrium prices at the beginning and end of each session.

least once. These include auctions that were not successful because the reservation price was too high. The convergence of price to more competitive levels depending on the number of visits is apparent. Using the information in Table 6 and assuming normal distribution for the prices in the market we can ﬁnd out the minimum number of visits for which the average price is greater than or equal to $4.06 (which is midway between $4.00 to $4.12) with at least 95% probability. It turns out that auctions need more than seven visiting bidders to pass the $4.06 mark. If we perform the same test using the number of bids we ﬁnd that four actual bids in an auction might be enough to drive up the price to more competitive levels. Unfortunately, not enough experimental observations for the inﬂuence of the number of above ﬁve bids was generated in the experiment. Result 2. Auction prices tend to converge to the equilibrium price with the passage of time but much more slowly than under centralized market structures.

This result is obtained by comparing the coefﬁcients of convergence between the prices in the current experiment and prices observed in the centralized exchange market experiments by Smith. The coefﬁcient of convergence (Smith 1962) is the ratio of the standard deviation of exchange prices to the predicted equilibrium price. The ratio is expressed as a percentage. In this experimental design the coefﬁcient of convergence for sessions 1, 2, and 3 is respectively 23%, 16.9%, 15%. The fact that the percentages decrease is a good indication of convergence. Nevertheless the corresponding coefﬁcients from the centralized exchange experiments are close to 6% only after 10–15 min of trading. This clearly demonstrates that prices converge faster when markets are centralized and both sides of the market (buyers and sellers) participate together in the bid-offer process. Result 3. Auction prices converge to the competitive equilibrium price range from below. Fig. 11 illustrates this result. Convergence from below serves as an indication of the asymmetric strategic nature of open-bid ascending auctions. Buyers have the upper hand in these auctions. When they bid in such auctions, they use a variety of signaling strategies in an effort to get better deals at lower prices. Jump-bidding, sniping, and bid-withholding are three types of strategies that are suspected to be widely used by bidders in this regard. These types of behavior have been shown to cause lower revenues for the sellers even in symmetric demand-supply environments (Vragov 2005). Compare Fig. 11 to Fig. 2. One can see very clearly the relationship between prices and efﬁciency in Fig. 11. Observe that when prices stay for too long outside of the equilibrium price range as it happened during Session 1 of the experiment, the resulting efﬁciency level is quite low (57%). Also note that the efﬁciency

Fig. 11. The time convergence of average prices toward the competitive equilibrium price interval and realized efﬁciency levels. The two lines with dashes show the equilibrium price at the beginning ($4.00) and the approximate equilibrium price at the end of each session ($4.12).

Table 6 Average price by number of visiting bidders on the left and by number of bids on the right. Number of visiting bidders

Average price

St. dev.

Number of auctions

Number of bids

Average price

St. dev.

Number of auctions

1 2 3 4 5 6 7 8 9 10

$2.10 $2.60 $3.08 $3.58 $3.68 $3.75 $4.14 $4.24 $4.43 $4.54

1.460872 1.524454 1.312301 1.071506 0.971332 1.074815 0.794605 0.962872 0.492443 0.549811

62 56 60 45 41 28 23 22 4 4

1 2 3 4 5 6 7 8

$2.55 $3.48 $3.88 $4.21 $4.56 $4.13 $5.08 $4.50

1.264084 1.104333 0.735841 0.556509 0.530618 0.53033 0.860717 N/A

114 95 73 32 10 2 3 1

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levels in all three sessions of this experiment are lower than the 99% efﬁciency level observed in many continuous double-auction experiments only after 10–15 min of trading.

6. Discussion The experimental ﬁndings have several broad implications for academics and practitioners. The results from testing all four hypotheses reafﬁrm the claim that laboratory experiments are a cheap and reliable method to duplicate online auction behavior. This adds legitimacy to and conﬁrms the relevance of results from previous laboratory studies reported in Ariely et al. (2005) and Vragov (2004, 2005). If we can duplicate successfully online behavior in the laboratory, we can reliably trace causal relationships between market variables by manipulating experimental parameters. We can also establish baselines and test a wide range of design options before we implement them in practice. In addition, the ﬁrst two main results of this study suggest that decentralized online auction mechanisms need a larger number of participants and more time to achieve high efﬁciency levels as compared to centralized auction mechanisms like the continuous double auction, whereas the third main result suggests that buyers and sellers are not strategically symmetric under the rules of current online auction mechanisms. Auction designers do not have control over the number of participants visiting an auction or the timing of auction closings but they do have control over auction rules. The main results from this exploratory study hint that Internet auction mechanisms can be improved if their rules are made more similar to these of the continuous double auction mechanism. The more similar the rules, the more likely it will be that online auctions will achieve operational efﬁciency levels comparable to these of continuous double auctions. There are many different ways to do that but we can mention three of them here. The ﬁrst possible change is already used by eBay and other auction sites – it is the so-called buy-it-now (BIN) option. This option makes the auction more symmetric from a strategic point of view and takes away some of the strategic advantages that buyers possess in most online auction. There already have been some studies showing that the introduction of BIN options increase auction efﬁciency (see Zhang et al. 2007; Yoo et al. 2006; Wang et al. 2006; Onur and Tomak 2003; Durham et al. 2004). The second possible change is related to the way market information is presented to market participants. Market information is aggregated and exchanged in a centralized manner under a CDA mechanism. The current best bid and ask are displayed to everyone interested. If a buyer or a seller submits a competitive offer, then everyone in the market for that product can see that offer and react to it immediately. In contrast, if a bidder is interested in many single-unit eBay auctions that happen simultaneously she has to click many times through many screens in order to know what the current competitive bid is each auction. She can bid in any one of these auctions but she would never know if she won until the very end of each auction because the majority of bidders snipe. One way to make this process easier for buyers is to introduce an exclusive ‘‘Or” option. If a bidder is interested in buying only one item from many simultaneous auctions, she should be able to link them together for easy supervision and then bid only once. The auction web site should make sure that her bid is submitted conditionally in all auctions that she chose to combine. This would not only result in an improved service for the buyer but also in reduced costs for the sellers. This option is now partially available on eBay under the name of ‘‘Bid Assistant”. Continuous double auctions also feature strategic and informational symmetry. All buyers and sellers have to follow the same

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rules: they have access to the same set of strategies, and they have access to the same message space. From a strategic point of view, eBay’s rules for buyers and sellers are very different. Sellers are stuck with decisions that they made in the beginning of the auction and cannot change them even if the economic environment changes. However, buyers can change their strategy and bids as often as they want throughout the whole duration of an auction. eBay can make its auction environment more symmetric and probably more efﬁcient by helping sellers adjust their buy-it-now prices throughout the duration of an auction or allow buyers to submit sell-it-now bids that the seller can accept any time during the duration of the auction (see Wenyan and Bolivar 2008; Vragov et al. 2008).

7. Conclusions This paper compares the operational efﬁciency of Internet consumer-to-consumer (C2C) auctions to the operational efﬁciency of the continuous double auction (CDA), a market institution whose efﬁciency properties have been studied extensively in the laboratory. The author chose the experimental method to explore this comparison because this is the only method which allows direct observation of operational efﬁciencies and exact deviation from equilibrium prices. The results of the study demonstrate because of four basic features of C2C auctions that continuous double auctions do not possess, C2C auctions achieve lower market operational efﬁciency levels than the continuous double auction under similar economic environments. These four features are: the distributed localization of demand and supply, the incompleteness of market information, the increased importance of time-related cost, and the asymmetric strategic relationship between buyers and sellers. The experiment reported here also explores the relationship between operational efﬁciency, market size and time in Internet auctions. The experimental results are compared to naturally occurring auction data to establish similarity and then to earlier experiments that look at similar relationships in continuous double auctions with open outcry of bids and offers. The experimental results conﬁrm that Smith’s ﬁndings pertaining to centralized institutions of exchange do not apply with the same strength to decentralized C2C auctions on the Internet. Generally prices converge much more slowly to the equilibrium level in Internet auctions. There is some downward stickiness in prices that might be erased with the presence of more bidders. It appears that an Internet auction needs to be visited by at least seven bidders and needs to have at least four bids from different bidders in order for the prices to reach competitive levels and for operational efﬁciency to move closer to 100%. From an auction design perspective the experimental results reafﬁrm the claim that laboratory experiments are a cheap and reliable method to duplicate online auction behavior. The study shows that one can reliably trace causal relationships between market variables by manipulating experimental parameters, establishing efﬁciency baselines, and testing a wide range of design options before an auction is implemented. The results also help us suggest changes in online auction design that have the potential to improve the operational efﬁciency of online auctions. The experimental design outlined above does not simulate all practical aspects of Internet auction mechanisms. For example, all auctions in the experiment happen within the span of an hour while auctions on eBay take at least 3 days unless the buy-itnow option is exercised. Roth and Ockenfels (2002) suggest that this limitation might not be that restrictive because the relationship between bid timing and auction length is fractal and thus the graph of bid timing has a similar shape irrespective of the

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auction length. The same relationship might be true for the bidprices in C2C Internet auctions and future research in this direction will throw more light on this yet unexplored property of the time/ bid-price relationship. The experiment also could not probe Internet auction environments with more potential visits and bids per auction in order to discover the auction size required to erase the collusive pressures on the price. Other necessary additions to this experimental design that we omitted include ﬂexibility of auction rules, reputation, shill bidding, and agent usage. Testing the effect of these additional features on prices and efﬁciency should be performed to get a complete picture. An interesting exercise would be to investigate the relationship between informational and operational efﬁciency in environments that represent a mix of ﬁnancial markets and markets for ﬁnal products. Another possible concern is the level of experience of subjects in the laboratory as compared to bidders in Internet auctions. Obviously participants in online auctions are a very diverse group of people and might act differently than undergraduate subjects. This study, however, is comparative in nature. Efﬁciencies of two different mechanisms are measured while the experience of the experimental subjects is the same. Subjects in both the experiment reported here and these reported in Smith (1962, 1982) were undergraduate students from a large public university in the US. Another limitation of this laboratory study was the size of the laboratory. As explained earlier, only 26 computers were available for experimental subjects. Because of this limitation alternative ways to measure auction size were not viable. Clearly a better picture of the relationship between the several important variables investigated here could be obtained by a larger study. In addition the study does not model the winner’s curse – a phenomenon that has been detected in online auctions. Subjects’ values and costs in this experiment are independent and private. Winner’s curse happens when market participant’s values are afﬁliated or common. Since independent private value environments are simpler from a market participant’s and an experimenter’s viewpoint than afﬁliated or common value environments, they are a good starting point for this experimental study. Later experiments could model afﬁliated or common values in addition to private values. Given the results of our study, a plausible expectation is that online auction mechanisms would perform worse than continuous double auction mechanisms in more complex environments as well but this is something that is still to be tested in the laboratory.

to 20 min after the start will cost you a certain amount of cents. This amount is shown to you in your balance sheet under the label monitoring cost. Thus, your total experimental proﬁt will be: Total proﬁt = sum of the values of the items that you bought – sum of the prices of items that you bought – monitoring cost Today’s exchange rate between experimental dollars and US dollars is 4–1. That is 4 experimental dollars = 1 US dollar. Below you see an example of a buyer’s balance sheet at the beginning of a session.

In this case, $8.00 is the value to you of the ﬁrst purchased unit and $7.78 is the value to you of the second purchased unit. Your monitoring cost is $0.06 per minute of the experiment. Your login name ‘‘krum” is shown at the bottom of the screen. If you buy an item, you will see the ID of the auction in which you bought the item in the column labeled ‘‘Auction” to the right. If you buy more than 10 items in a round, you have to pay for them but you do not get value for them. This is the BEAuctions.com web site.

Acknowledgements The author would like to thank Robert Kauffman, Charles Wood, Claudia Loebbecke, David Porter, Marc Olson, Vernon Smith, Bart Wilson, and Stephen Rassenti for their helpful comments and suggestions. This work was partially funded by the International Foundation for Research in Experimental Economics. Appendix. Experimental auction instructions Experiment instructions for buyers In this experiment you will participate in several Internet auctions as a buyer. There are four rounds. In each round buyers are given values for a ﬁctitious good. As a buyer, your proﬁt per unit is equal to your value for that unit minus the price paid. Your proﬁt/unit = value for that unit price for that unit Thus if you are a buyer, your total proﬁt will be: Total proﬁt = sum of the values of the items that you bought sum of the prices of items that you bought Remember that all values and costs in this experiment are between $0.00 and $8.00 per unit. In this experiment, you will also have a monitoring cost. Every minute in the experiment up

To log in, enter your password in the box in the upper right corner and press the ‘‘Log-in” button. You will see a list of active auctions to the left. If you want to bid in an auction, you have to select

R. Vragov / Electronic Commerce Research and Applications 9 (2010) 111–125

one of the auctions on the list with your mouse and press the ‘‘Join” button. You will see the following screen:

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shown on your balance sheet. You will also incur an inventory cost for each minute per every unsold item. Your inventory cost per minute per unsold item in also shown on your balance sheet. Your total experiment proﬁt will be: Total proﬁt = the sum of the prices of the items that you sold the sum of the costs of the items that you sold monitoring cost inventory cost Below you see an example of a seller’s balance sheet.

Every auction has a certain length chosen by the seller. You can see the time left in each auction in the top left corner of the screen. On the left side you see the owner of the item for sale. On the right side you see a list of all buyers who have submitted a bid in the auction together with their bids. To enter a bid in the auction: 1. Press bid. Two boxes will appear for you to enter the dollars and cents (your bid price). Your bid has to be greater than or equal to the minimum bid shown on the screen. 2. Press send and then yes to conﬁrm your bid. Your bid is visible to the other participants. You can submit many bids per auction as long as they are greater than the minimum bid and there is still time left. 3. If the seller’s reserve price is reached during the auction a green upper case R will show up in the middle of the screen. The auction is over when there is no time left. You do not have to wait for the auction result. You will be informed if you are the winner. The winner is the person who submitted the highest bid. If you win the auction, in which you participate, you have to pay your bid. Your proﬁt from the auction is equal to: Your value for the item the price of the item, which is equal to your bid Summary

In this case, $0.13 is the cost to you of the ﬁrst unit sold and $1.34 is the cost to you of the second unit sold. Your monitoring cost is $0.04 per minute. Your inventory cost is $0.03 per minute per unsold item. Your login name ‘‘boril” is shown at the bottom of the screen. If you sell an item, you will see the ID of the auction in which you sold the item in the column labeled ‘‘Auction” to the right. This is the BEAuctions.com web site.

1. You have values for 10 items. 2. You can buy items by bidding on the BEAuctions.com web site. 3. Your proﬁt is equal to:the sum of the values of all items that you bought the sum of the prices of all items that you bought monitoring cost 4. Four experimental dollars = 1 US dollar 5. The experiment is composed of one practice session and three real sessions, with 20 min in each session. Experiment instructions for sellers In this experiment you will participate in several Internet auctions as a seller. Sellers have costs for selling a ﬁctitious good. As a seller, your proﬁt per unit is equal to the price received for that unit minus its cost. Your proﬁt/unit = price of that unit cost for that unit Your total proﬁt will be: Total proﬁt = the sum of the prices of the items that you sold the sum of the costs of the items that you sold Remember that all costs and values in this experiment are between $0.00 and $8.00 per unit. In this experiment you are also going to have two other types of cost. You will incur a monitoring cost for each minute in the experiment. Your monitoring cost is

To login, enter your password in the box in the upper right corner and press the ‘‘Log-in” button. You will see a list of active auction to the left. If you want to start an auction, press the ‘‘Start” button. Enter the minimum price at which you are willing to sell your item under the label ‘‘Reserve Price”. Note that you have to enter the dollars and cents separately. You have to choose the length of your auction. There are four options available: 5, 8, 11, and 14 min. Press ‘‘Send” and then ‘‘Yes” to start your auction. You will see an auction ID with your login name after it appear

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in the list of active auctions. Press ‘‘Join” to look at your auction. You will see the following screen.

You will see the time left in the auction in the upper left corner of the screen. On the left side you will see your login name as the owner of the item for sale. On the right side you see a list of all buyers who have submitted a bid in the auction, and their bids. The winner of the auction will be the person who has submitted the highest bid by the end of the auction. The highest bid has to be greater than or equal to your reserve price. The highest bid will be the amount of money that you will receive for your item. If the item sold successfully, you will be informed about the winner and the price that he paid. Your proﬁt form the auction is equal to: The price of the item sold, which is the highest bid the cost of the item to you Summary: 1. You can only start 10 auctions in each round. 2. Your proﬁt is equal to: The sum of the prices of the items that you sold the sum of the costs of the items that you sold monitoring cost inventory cost 3. Four experimental dollars = 1 US dollar. 4. The experiment is composed of one practice session and three real sessions, with 20 min in each session.

Table of deﬁnitions. Operational/ allocative efﬁciency Informational efﬁciency Continuous double auction (CDA) Final products Market/auction size Market atomicity Sniping Winner’s curse

The ratio between total attainable surplus and total realized surplus in a market All relevant information is perfectly reﬂected into the market prices, so arbitrage is not possible An auction mechanism in which both buyers and sellers submit open orders and exchange products in real time Products whose values to individuals are independent and private The number of market/auction participants The presence of an inﬁnite number of buyers and sellers in a market Bidding at the very end of an auction An auction winner ends up with a negative proﬁt after winning an auction

References Anandalingam, G., Day, R., Raghavan, S. The landscape of electronic market design. Management Science, 51, 3, March 2005, 316–327. Ariely, D., Simonson, I. Buying, bidding, playing, or competing: value assessment and decision dynamics in online auctions. Journal of Consumer Psychology, 13, 1 and 2, 2003, 113–123. Ariely, D., Ockenfels, A., Roth, A. An experimental analysis of ending rules in online auctions. Rand Journal of Economics, 36, 4, Winter 2005, 890–907. Ba, S., Pavlou, P. Evidence of the effect of trust building technology in electronic markets: price premiums and buyer behavior. MIS Quarterly, 26, 3, September 2002, 243–268. Bakos, J. Y. Reducing buyer search costs: implications for electronic marketplaces. Management Science, 43, 12, December 1997, 1676–1679. Bapna, R., Goes, P., Gupta, A. A theoretical and empirical investigation of multi-item on-line auctions. Information Technology and Management, 1, 1, 2000, 1–23. Bapna, R., Goes, P., Gupta, A. On-line auctions: insights and analysis. Communications of the ACM, 44, 11, November 2001, 42–50. Bapna, R., Goes, P., Gupta, A., Jin, Y. User heterogeneity and its impact on electronic auction market design: an empirical exploration. MIS Quarterly, 28, 1, March 2004, 21–43. Budish, E. B., Takeyama, L. Buy prices in online auctions: irrationality on the internet? Economics Letters, 72, 3, September 2001, 325–333. Caldentey, R., Vulcano, G. On-line auction and list price revenue management. Management Science, 53, 5, May 2007, 795–813. Cox, J., Dinkin, Samuel H., Smith, Vernon L. The winner’s curse and public information in Coomon-value auctions: Comment. American Economic Review, 89, 1, March 1999, 319–324. Cox, J., Offerman, T., Olson, M., Schram, A. Competition for vs. on the rails: a laboratory experiment. International Economic Review, 43, 3, August 2002, 709–736. Cramton, P. The efﬁciency of the FCC spectrum auctions. Journal of Law and Economics, Part 2, 41, 2, October 1998, 727–736. Davis, J. The informational efﬁciency of stock prices: a review. Dimensional white paper, accessed Dec. 12, 2008 at . Durham, Y., Roelofs, M., Standiﬁrd, S. eBay’s buy-it-now function: who, when and how? Topics in Economic Policy and Analysis, 4, 2004, article 28. Fama, Eugene F. Efﬁcient capital markets: II. Journal of Finance, 46, 5, December 1991, 1575–1617. Friedman, D., Rust, J., (Eds.). The Double Auction Market: Institutions, Theories and Evidence. Santa Fe Institute Studies in the Sciences of Complexity, Perseus Publishing, Cambridge, MA, 1993. Gallien, J., Gupta S. Temporary and permanent buyout prices in online auctions. Management Science, 53, 5, May 2007, 814–833. Gopal, R. D., Tung, Y. A., Whinston, A. B. Efﬁciency considerations in online auction markets. Journal of Organizational Computing and Electronic Commerce, 17, 4, October 2007, 311–328. Hayne, S., Smith, C., Vijayasarathy, R. Who wins on eBay: an analysis of bidders and their bid behaviors. Electronic Markets, 13, 4, May 2003, 262–293. Hortacsu, A. Bidding Behavior in Divisible Good Auctions: Theory and Evidence from the Turkish Treasury Auction Market. Mimeo, University of Chicago, 2002. Kang, T., Puller, S. The effect of auction format on efﬁciency and revenue in divisible good auctions: a test using Korean treasury auctions. Journal of Industrial Economics, 56, 2, June 2008, 290–332. Kannan, P. K., Kopalle, P. K. Dynamic pricing on the internet: importance and implications for consumer behavior. International Journal of Electronic Commerce, 5, 3, Spring 2001, 63–83. Kauffman, R., Spaulding, T., Wood, Ch. Are online markets efﬁcient? an empirical study of market liquidity and abnormal returns in online auctions. Decision Support Systems, in press. Kauffman, R., Wood, C. The effect of shilling on ﬁnal bid prices in on-line auctions. Electronic Commerce Research and Applications, 4, 1, March 2005, 18–29. Kauffman, R., Wood, C. Research strategies for e-business: a philosophy of science view in the age of the internet. In R. Kauffman, P. Tallon (Eds.), Economics, Information Systems, and Electronic Commerce: Empirical Research, ME Sharp Inc., 2008 September 30. Klemperer, P. Auctions: Theory and Practice. Princeton University Press, Princeton, NJ, 2004. Krishna, V. Auction Theory. Academic Press, San Diego, CA, 2002. Lopomo, G., Marshall, Robert C., Marx, L. M. Inefﬁciency of collusion in English auctions. Journals in Theoretical Economics: Contributions to Theoretical Economics, 5, 1, 2005, 1–26. Lucking-Reiley, D. Using ﬁeld experiments to test equivalence between auction formats: magic on the internet. American Economic Review, 89, 5, December 1999, 1063–1080. Lucking-Reiley, D., Bryan, D., Prasad, N., Reeves, D. Pennies from eBay: the determinants of price in online auctions. Journal of Industrial Economics, 55, 2, June 2007, 223–33. MacKenzie, D., Muniesa, F., and Siu, L. Do Economists Make Markets: On the Performativity of Economics. Princeton University Press, 2007. Mathews, T., Katzman, C. The role of varying risk attitudes in an auction with a buyout option. Economic Theory, 27, 3, April 2006, 597–612. Milgrom, P., Weber, R. A theory of auctions and competitive bidding. Econometrica, 50, 5, September 1982, 1089–1122.

R. Vragov / Electronic Commerce Research and Applications 9 (2010) 111–125 Oh, Wonseok, C2C vs. B2C: a comparison of the winner’s curse in two types of electronic auctions. International Journal of Electronic Commerce, 6, 4, Summer 2002, 115–138. Onur, I., Tomak, K. Buy-it-now or snipe on eBay? Proceedings of the Twenty-Fourth International Conference on Information Systems (ICIS-03), Seattle, WA, IEEE Computer Society Press, December 2003, 841–845. Parsons, S., Marcinkiewicz, M., Niu, J., Phelps, S. Everything you wanted to know about double-auctions, but were afraid to (bid or) ask. Working paper, Brooklyn College, CUNY, University of Liverpool, August 18, 2006. Pinker, E., Seifmann, A., Vakrat, Y. Managing online auctions: current business and research issues. Management Science, 49, 11, November 2003, 1457–1484. Porter, David, Vragov, R. An experimental examination of demand reduction in multi-unit versions of sealed bid and English auctions. Managerial and Decision Economics, 27, 6, September 2006, 445–458. Roth, Alvin, Ockenfels, Axel. Last-minute bidding and the rules for ending secondprice auctions; evidence from eBay and Amazon auctions on the internet. American Economic Review, 92, 4, September 2002, 1093–1103. Smith, V. L. An experimental study of competitive market behavior. The Journal of Political Economy, 20, 2, June 1962, 111–137. Smith, V. L. Experimental economics: induced value theory. In American Economic Review, 66, 2, Papers and Proceedings of the Eighty-eighth Annual Meeting of the American Economic Association, May 1976, 274–279. Smith, V. L. Method in experiment: rhetoric and reality. Experimental Economics, 5, 2, October 2002, 91–110. Smith, V. L. Constructivist and ecological rationality in economics. American Economic Review, 93, 3, June 2003, 465–508. Smith, V. L., Williams, A. W., Bratton, W., Vannoni, M. G. Competitive market institutions: double-auctions vs. sealed-bid offer auctions. American Economic Review, 72, 1, March 1982, 58–78.

125

Stafford, M. R., Stern, B. Consumer bidding behavior on internet auction sites. International Journal of Electronic Commerce, 7, 1, Fall 2002, 135–150. Standiﬁrd, S. Online auctions and the importance of reputation type. Electronic Markets, 12, 1, January 2002, 58. Vragov, R. Why is eBay the King of Internet Auctions? An Institutional Analysis Perspective. eService, 3, 3, Summer 2004/2005, 5–28. Vragov, R. Implicit consumer collusion in auctions on the internet. In Proceedings of 35th Hawaii International Conference on Systems Sciences, Kona, Hawaii, January 2005. Vragov, R., Shang, D., Lang, K. Should online auctions employ dynamic buyout pricing models. In Proceedings of 38th Hawaii International Conference on Systems Sciences, Hawaii, January 2008. Wang, Sh., Jank, W., Shmueli, G., Smith, P. Modeling Price Dynamics in eBay Auctions Using Principal Differential Analysis. Robert H. Smith School Research Paper No. RHS-06-052, December 8, 2006. Ward, S. G., Clark, J. M. Bidding behavior in on-line auctions: an examination of the eBay Pokemon card market. International Journal of Electronic Commerce, 6, 4, Summer 2002, 139–155. Wenyan, H., and Bolivar, A. Online auction efﬁciency: A survey of eBay auctions. In: Proceedings of WWW 2008 Conference, Beijing, China, April 21–26, 2008, 925– 934. Wilcox, R. The role of experience in internet auctions. Marketing Letters, 11, 4, November 2000, 363–340. Yoo, B., Ho, K., Tam, K. The impact of information in electronic auctions: Ab analysis of buy-it-now auctions. In Proceedings of 36th Hawaii International Conference on Systems Sciences, Hawaii, January 2006. Zhang, H., Yin, F., Hsu, V. The impact of the buy-it-now option on online auctions: An empirical investigation. In Proceedings of the 6th International Workshop on EBusiness (Web 2007), Montreal, Canada, December 9th, 2007.

Operational efficiency of decentralized Internet auction mechanisms

Operational efficiency of decentralized Internet auction mechanisms

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