A theoretical and empirical investigation of multi-item on-line auctions

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1 Information Technology and Management 1 (2000) A theoretical and empirical investigation of multi-item on-line auctions Ravi Bapna, Paulo Goes and Alok Gupta Department of Operations and Information Management, School of Business Administration, University of Connecticut, Storrs, CT 06269, USA {bapna;paulo;alok}@sba.uconn.edu In this paper we explore and analyze the structure of Internet auctions from an analytical and an empirical perspective. Such web-based auctions are rapidly emerging as a mercantile process of choice in the electronic marketplace. We observe current Internet auctions for one-time products, such as rapidly aging hardware, and analyze them within the framework of the existing auction theory. While traditional auction theory focuses on single-item auctions, we observe that a majority of on-line auctions are multi-item auctions. A significant contribution of this work is the theoretical derivation of the structure of the winning bids in multi-item progressive on-line auctions. Additionally, for comparative purposes, we explore the structural characteristics of alternative multi-item auction mechanisms proposed in the auction theory. We derive hypotheses based on our analytical results and compare two different types of auction mechanisms. We test the traditional auction theory assumption regarding the homogeneity of bidders and present the first ever empirically derived classification and performance-comparison of on-line bidders. We test our hypotheses using real-world empirical data obtained by tracking a premier web-based auction site. Statistical analysis of the data indicates that firms may gain by choosing alternative auction mechanisms. We also provide directions for further exploration of this emerging but important dimension of electronic commerce. Keywords: auction theory, on-line auctions, multi-item auctions, and electronic markets 1. Introduction Business organizations are increasingly relying on the electronic marketplace heralded by the Internet to gain new efficiencies, expand markets and lower costs. Simultaneously, a globally expanding consumer-base is demanding greater convenience, competitive prices and improved customer service. While immense strides have been taken in the technical development of the Internet, our understanding of its economic impact is still nascent. In this research, we conduct an in-depth analysis of traditional and emerging mercantile processes that support current business activity on public data networks such as the Internet. In contrast with the traditional posted-price based pricing mechanism we focus on on-line business auctions, an increasingly popular form of buying selling activity on the WWW. We answer Van Heck and Vervset s [11] Baltzer Science Publishers BV

2 2 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions recent call of examining the pervasive impact of advanced electronic communications on the well-established theory of auctions. The growing impact of on-line auctions is evident from examining the revenue predictions of Forrester Research, a Cambridge, Massachusetts based research firm. For 1998, the revenues derived from on-line auctions are estimated to be $8.7 billion in comparison to $2.5 billion for Among the biggest on-line auctioneers are Onsale.com, Surplusauction.com and ebay.com. These companies sell a wide range of goods such as computer hardware, consumer electronics, collectibles and perishables such as airline tickets and hotel rooms. All of them are attempting to capitalize on the Internet s primary advantage of a large and globally dispersed audience. While traditional auction theory has focussed on single-item auctions, we observe that the majority of on-line auctions are multi-item in nature. Rothkopf and Harstad [10] point out that single-item results do not carry over in multiple-item settings. Our work represents the first attempt at theoretically analyzing the bid structures of multi-item on-line auctions. The theoretical exposition of the bid-structures is utilized to reveal significant insights into the revenue generation process of such auctions. Importantly, this is done without making any distribution assumptions regarding the valuations of individuals. To begin with, we characterize on-line auctions from the perspective of expected revenues. Subsequently, we compare these revenues to those derived from a hypothetical, more efficient, auction mechanism. Furthermore, we utilize these theoretical characteristics to develop a series of hypotheses that are subsequently tested using real-world data obtained by monitoring auctions on the WWW. This empirical investigation gives us further insights into the theoretical aspects of our work. Specifically, it leads us to question the typical auction theory assumption regarding homogeneity of bidders. This assumption dictates that all individuals behave rationally with an objective of maximizing their net worth. In contrast, using our empirical data, we are able to identify at least three different types of on-line bidders. Another significant contribution of our work is the first ever comparison of performance among these different types of on-line bidders using real-world data. We utilize our theoretical exposition to devise two new metrics that allow us to compare: (a) auctioneer s expected revenue under observed and hypothetical types of auctions with empirically obtained data, and (b) the performance of the different types of bidders with respect to their consumer surplus. Another contribution of this work is the identification of the significant role played by the bid-increment in revenue generation. The results obtained from this paper give several insights into the theoretical implications of on-line auctions. Additionally, we also provide significant directions for carrying out future research in this important dimension of electronic commerce. In the next section we present some background information relevant to theoretical and empirical investigation of on-line auctions. In section 3 we present our theoretical results. In section 4 we detail our data collection process and the test hy-

3 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions 3 potheses. In section 5 we present our empirical analysis. Finally, in section 6 we summarize our contributions and present directions for future research. 2. Background We establish the context of our work by first examining the various ways in which society pursues the allocation of economic resources. There are three primary types of economic resource allocation mechanisms: (i) capacity allocation mechanisms, (ii) posted price mechanisms, and (iii) auctions and negotiations. Capacity allocation mechanisms usually are the most efficient mechanisms if the type of individual customers (and thus their needs) can be identified by the controlling entity. In general, posted price mechanisms can be considered as the mathematical dual of capacity allocation mechanisms (Greenwood and McAfee [2]); under this mechanism the general distribution of customer types is known, however, individual customer types are not identifiable or, in other words, the demand curve is known. Even though some recent research has been devoted to developing posted price mechanisms that can dynamically compute the posted prices based on changing demand (Gupta, Stahl and Whinston [3]), these mechanisms are more suitable for ongoing allocation of the same resource over time. Posted prices typically have had the lowest transaction costs. However, this proposition is challenged with the advent of low cost on-line auctions. Typically, ignorance of what price to post is a reason for negotiating or holding an auction. Rothkopf and Harstad [9] provide a behavioral reason for holding auctions by asserting that one of the critical reasons for the use of bidding is that the formality of the auction process provides legitimacy in a way that the other economic means cannot. Wang [13] compares auctions with posted prices in a simplified setting under the assumptions of the independent private values model. Her central result is that auctions are preferable if the marginal revenue curve is steep. The global steepness of the marginal revenue curve is found to coincide with the dispersion around the mean for a number of standard distributions. This confirms the intuition that the more dispersed the value of an object or a service to the potential buyers, the more auctions are preferred. This increased dispersion can only be expected to grow as the audience addressed by electronic markets becomes truly global and non-homogenous. To further explore this general background in the specific context of electronic markets we next present a description of the current state of affairs of on-line mercantile processes Traditional versus emerging on-line mercantile processes Traditional business activity on the Internet has relied on the posted-price based electronic catalog process. In such systems firms design a systematic inventory of HTML pages, scripts, and applets to manage on-line assets and create applications that dynamically integrate the marketing, sales, order processing and customer-service functions. Increasingly, as firms look for new mercantile processes to gain efficiencies, auctions are becoming popular as an efficient and flexible channel. A growing set

4 4 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions of firms is looking towards using auctions to fit naturally fluid markets, clear aging inventory, or dynamically set prices based on real demand. The frenzied rate of technological innovation and consequent quick obsolescence of products and services increases the fluidity of markets. Thus, as the window of opportunity to adjust posted prices shrinks rapidly, business auctions provide a natural mercantile process to cope with these changes. A survey of the various auction sites on the Internet reveals that a majority of sites sell one-time products such as collectibles, specific hardware such as computer systems, and perishable products such as excess telephone capacity (for example, London based Band-X at These auctions are typically for multiple units of the same product and are sold to multiple buyers. While traditional auctions can evoke images of covert brokers and middlemen utilizing ad-hoc processes that hide margins, on-line auctions provide the kind of transparency that was once the preserve of business-school simulations. These auctions are more open and have sellers and bidders linked to the auction via Web browsers bypassing the network of brokers. Everyone has equal visibility into lot descriptions, asking price, last offer, and time remaining, while still retaining his/her anonymity. From a researcher s perspective such changes provide interesting opportunities to re-visit the existing theories and examine whether or not the traditional results and assumptions hold. There is a lack of theoretical work in the area of multi-item auctions as stated by McAfee and McMillan [5] and by Milgrom [6]. However, there have been attempts to compare the efficiency of different auction mechanisms both theoretically and empirically. The focus has been on comparing single-item sealed-bid competitive auctions with sealed-bid discriminatory auctions. In the former mechanism, the highest bidder wins, however, the price paid is the second highest bid; whereas in the latter the highest bidder wins with the price being the highest bid. Competitive auctions were first suggested by Vickrey [12] in his seminal article; the special property of this mechanism is that all the bidders have incentive to bid their true valuation. Plot and Smith [8] were among the first to design a controlled laboratory experiment to compare competitive auctions with discriminatory auctions. Actual bidding data has also been analyzed by various researchers such as Baker [1]. The key results of these empirical investigations have been inconclusive with respect to sellers revenue. Harris and Raviv [4] compare the efficiency and expected revenue of the uniform price (Vickrey-like) auction mechanism with that of the discriminating (first price sealed-bid) mechanism when a fixed quantity of divisible goods is to be sold to many buyers. There results indicate that the sellers revenue under a specific mechanism depends on the risk characteristics of the bidders. To the best of our knowledge, our work represents the first analysis and comparison of expected revenue between a discriminatory open ascending auction and a competitive (Vickrey) sealed-bid auction with multiple units of indivisible goods and multiple buyers. Additionally, we do not make any assumptions regarding the risk characteristics and the distribution of bidder valuations for our results. Instead, we

5 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions 5 rely solely on the assumption that each on-line bidder myopically makes his decision with the knowledge of historical observable bids. In the next section we outline our research methodology and present our theoretical results. 3. Research methodology In this section we explore the on-line auctions from an analytical perspective. Specifically, our objective is to develop theoretical propositions that characterize and contrast auctions conducted on the Internet and theoretically compare them with other auction mechanisms 3.1. Theoretical results First, we examine the characteristics of on-line auctions. The majority of auction sites surveyed conducted a variant of the open, first-price English auctions for multiple items. In these auctions, several consumers vying for a pre-determined lot can bid the same dollar amount until there are as many bids equal to or greater than the current asking bid as the lot-size. The current asking bid is the minimum bid required to enter the winners list. This can be done either by displacing an existing winner or entering at a juncture where the lot-size is greater than the current number of winners. We call these auctions Multiple Item Progressive Electronic Auctions (hereafter, MIPEA). Figure 1 provides a snapshot of a typical Internet auction. Figure 1 contains a graphic of the product being auctioned, the opening and closing times of the auction, the current minimum asking bid, the bid increment and the current list of high bidders. Next, we contrast current Internet MIPEA auctions with other theoretical auctions that use the direct revelation mechanism. In such mechanisms, bidders are asked to announce their valuation directly. The seller, on the other hand, commits to using pre-specified rules for allocating the goods and for charging the buyers. These rules ensure: (a) the buyers willingness to participate, and (b) that each buyer will find it in his interest to announce his true valuation. Nobel laureate William Vickrey [12] proposed one such mechanism. In his seminal work he noted that when a sealed bid second-price auction is used that is, the high bidder wins but pays only the price of the second highest bidder each bidder has a dominant strategy of bidding his true valuation. In our setting of multiple, say N, item auctions, we extend this definition to include the N highest bidders as winners and the bid of the (N + 1)th highest bidder as the uniform price. We call such auctions Multiple-item Vickrey Auctions (hereafter, MVA). We now introduce some basic notation followed by some initial propositions and observations. Let there be N items to be auctioned and let there be I bidders, each with a value Vi for the product. Let Bi denote the current bid of consumer i. For MIPEA, as observed on the Internet, let there be a minimum bid increment denoted by k.

6 6 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions Figure 1. Snapshot of an on-line auction.

7 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions 7 Consumers are not allowed to place bids in between the bid increments, as noted on the website of all prominent On-line auctioneers. They state, All bids are subject to a minimum bid and bid increment, as posted with each item. If you place a bid that is between bid increments, we will round your bid down to the nearest increment. We introduce the marginal consumer as the person who has the (N +1)th highest value for the item being auctioned. Let the value of the marginal consumer be denoted by V.LetB m be the highest bid that does not win the auction. In general, there can be several bidders who bid B m, but fail to win the auction. We define the marginal consumer as the first person to bid B m, and who failed to win the auction. Without loss of generality, it should be pointed out that while there can be an arbitrary number of consumers who participate in any auction, the process will reach a state where only N + 1 of these consumers play a role in the winning bid sequence. We will show later the significant role played by the marginal consumer in the structure of the winning bids. As is traditionally assumed in auction theory, we assume that individuals participate in the auction process with an objective of maximizing their net worth. Since their valuation V i is fixed, the only quantity that affects their net worth is the surplus they can extract. If x is the amount they pay for obtaining an item then the surplus is the difference between how much they value the item and what they pay for it, that is V i x and their net worth is ([V i x] + V i ) MVA as a price-setting mechanism The first theoretical result that can easily be obtained regarding the multiple items Vickrey auction (MVA) is that the incentive compatibility property of singleitem Vickrey auctions is retained by MVA. Theorem 1 formally presents this result. Theorem 1. MVA is incentive compatible, i.e., bidders will bid their true valuations. Sketch of proof. The proof of theorem 1 is straightforward along the lines of Vickrey s original proof. The complete proof can be easily sketched from the following two observations: (i) There is no incentive to bid higher than the true valuation since the bidder might be the last person to receive the item at a price higher than her true valuations if someone else bids lower than her bid but higher than her true valuation. (ii) There is no incentive to bid lower than the true valuations since the bidder might be the first person not to receive the item and someone might bid higher than her but lower than her true valuation. In this case, bidding the true value would have provided a positive surplus. Next we present the result regarding the revenue generated by the MVA. Proposition 1. The total revenue for the seller selling N goods using MVA is N V.

8 8 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions Proof. The MVA is a closed, uniform price asset re-allocation mechanism where the highest N bidders are assigned the items at the price equal to the bid of the marginal consumer. Since MVA is incentive compatible, the marginal customer will bid her true value V. Thus the total revenue for the seller selling N goods using MVA is N V MIPEA as a price-setting mechanism We construct our arguments assuming that the bidders satisfy the individual rationality assumption. In other words, we assume that bidders are myopic and do not bid higher than the minimum required bid at any stage of MIPEA. This argument directly follows from the assumption that individuals are maximizing their net worth. At any stage bidding higher than the minimum required bid would imply that the bidder is willing to surrender excess surplus. Later, when we present and discuss our experimental results we will look into the empirical validity of this assumption. We begin with some observations. Observation 1. At any stage of MIPEA, a person will not bid her true valuation V i. This is true since bidding V i gives a surplus of zero to the bidder, or in other words, they are equally well off without bidding. In fact, if we consider the transaction costs of making another bid, they might get negative returns. Note that, since k is usually much smaller than V i, this observation means that highest bid placed by a person having a value V i is approximately V i k. We make no distributional assumptions regarding the private information of the bidders, other than the fact that their need for the product is independent. However, as mentioned earlier we do assume that consumers participating in the auction maximize their net worth. This implies that, under MIPEA, a consumer with value V i will not bid V i, which would lead to a surplus of zero with certainty. In the case of the MVA however, the consumer will have a favorable stochastic mass of deriving the surplus by revealing his true valuation V i because there is a fair chance of the uniform winning price i.e., the first losing bid being V i or lower. Observation 2. A bidder i will bid the minimum asking bid V c, if and only if (V k) V c. Since V c (B i + k), where B i was person i s last bid, a bidder i will bid higher only if his true value is higher than the current asking bid and there are N bids higher than his last bid. At this juncture it is convenient to define two sets of bidders who will be involved in the final bidding sequences. Let L be the set of consumers who were able to bid at the level B m but failed to win the auction. Also, let the cardinality of the set L be M, that is L = M. LetW be the set of auction winners. By construction, W = N. Based on observations 1 and 2 we propose the following propositions: Proposition 2. If the marginal consumer is the jth person to bid at the level B m, j = 1,..., N, the winning bids under the MIPEA have the following structure: Bm 1, B2 m,... Bj 1 m,(b m + k) 1,(B m + k) 2,...,(B m + k) N (j 1).

9 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions 9 Proof. Let the marginal consumer be the jth person to bid B m. Then, there were (j 1) bidders from the set W who bid at the level B m before the marginal consumer. By definition of the set L, thereare(m 1) other bidders who bid their highest possible bid B m. Note that by construction M N (j 1). This implies that, an additional (N j) (M 1) bidders from set W bid at the level B m. However, this leaves N [N j M j 1] = M consumers from set W, who cannot bid at the level B m. These consumers will bid at the level (B m + k). Consider the first consumer who bids at the level (B m + k). He will displace either a consumer from the set L, or from (N j) (M 1) consumers from the set W whowereabletobidb m. If the consumer displaced from the winners list at the level B m was from the set W, then note that there will still be M consumers from the set W that have to bid at the level (B m + k) to enter the winners list. However, if the consumer displaced was from set L, then the remaining consumerswhohavetobid(b m + k) go down by one to M 1. This process will be repeated at every bid at level (B m +k). Note that since all the consumers from the set L have to be displaced, there will be M +(N j) (M 1) = N (j 1) bids at the level (B m + k). Thus, there will be (j 1) bids at the level B m and N (j 1) bids at the level (B m + k) in the winning bid structure 1. Thus, the superscript j corresponds to the temporal position of the marginal consumer s bid. Along with B m it plays a significant role in the revenue generation process which we explain below by means of an example. Example 1. Consider an auction of 3 goods, with k = 5, and seven bidders with the following distribution of valuations. Consumer A B C D E (marginal F G consumer) V i k Consider the bid pattern presented in figure 2 with time on x-axis and bid levels on y-axis: 1 From an operational point of view it should be mentioned that while most on-line auctioneers do announce a specific closing time for their auctions, the actual closing happens when no new bids are received for a pre-determined time interval after the closing time. This implies that marginal consumer has the opportunity to place her final bid, and consumers in general have the opportunity to bid all the way to V i k, if necessary.

10 10 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions Figure 2. Bidding progression over time. The set L = {E, C} where E is the marginal consumer, the first consumer to bid B m = $15. The set W = {F, G, B} comprises of the individuals who have the three highest valuations. Observe that the position at which the marginal consumer bids B m, i.e., j = 1. Observe that the cardinality of the set L, i.e., M = 2, satisfies the inequality M N (j 1) where N = 3. Also, there are j 1 = 0 bidders from the set W who bid earlier than marginal consumer and there are (N j) (M 1) = (3 1) (2 1) = 1 bidder (B) from the set W at the level B m = $15. This leaves N [N j M j 1] = M = 2 bidders from set W (consumers F, G), who cannot bid at $15. These consumers will bid at the level (B m + k) = $20. When consumer F bids $20 then he displaces consumer B from the winners list at the level B m. Note that there will still be M = 2 consumers from the set W that have to bid at the level (B m + k) = $15 to enter the winners list. However, when consumer G bids $20 he displaces consumer C from set L. Then the remaining consumers who have to bid (B m + k) go down by one to M 1 = 1. The process is completed when consumer B enters the set W by bidding $20. Proposition 3. The lower bound on the revenue of a seller selling multiple units under MIPEA is N (V k). Proof. The lower bound occurs when none of the bidders in set L has the opportunity to bid (V k). This implies that all N people from the set W are in the winners list at the level (V k) before any bidder from the set L had the opportunity to bid at the level (V k). Thus, for the marginal consumer to get back into the list he would have to bid higher than (V k), which, as per observation 1, he would be unwilling to do since it implies the same net worth as he currently has. Therefore, the lower bound under MIPEA is N (V k). Proposition 4. The upper bound on the revenue of a seller selling multiple units under MIPEA is N V.

11 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions 11 Proof. Based on the winning bid structure of proposition 2 we observe that the lower bound occurs if B m = (V k) andj = 1. This implies that the marginal customer is the first one to bid (V k). Using proposition 2, recall that this implies that all N consumers from the set W have bid at level V. Hence, the upper bound under MIPEA is N V. Proposition 5. MVA dominates the MIPEA. Proof. Based on propositions 1, 3, and 4 we observe that irrespective of the probability distribution of the winning values and the corresponding bid-structure generated under MIPEA, its expected revenue is never greater than the one under MVA, i.e., N V. We illustrate the mechanics of these propositions with the following numerical example. Example 2. Consider the following hypothetical scenario. Let N = 3 and k = 1. Let there be four bidders, say A, B, C, D with true valuations of 51, 52, 53, 54, respectively. Let A be the marginal customer. The MVA revenue is 51 3 = 153. The MIPEA lower bound occurs if we observe the following sequence of progressive bids: D(48) C(48) B(48) A(49[V 2k]) B(49) C(49) D(50) C(50) B(50) STOP because A will have to, and will not, as per observation 1, bid 51 to get in now. Revenue = 150. The MIPEA upper bound occurs if we observe the following sequence of progressive bids: A(50[V k]) C(49) D(49) B(50) D(50) B(51) C(51) D(51) STOP because A will have to, and will not, as per observation 1, bid 51 to get in now. Revenue = 153. The theoretical propositions indicate that MVA may be a better mechanism from the revenue perspective. Also, the costs involved with implementation, administration, and management of MIPEA are much larger as compared with MVA since the auctioneer has to monitor the bids and maintain the lists of high bidders. In the next section we describe our empirical investigation aimed at testing the above-described theoretical results. 4. Empirical investigation Utilizing our theoretical understanding of the structural characteristics of the revenue generation process under MIPEA and MVA, we design a set of hypotheses to test the validity of the theoretical results presented in the previous section. First, we compare the expected revenue under the two auction mechanisms. Additionally, given the intrinsic diversity of the electronic marketplace, we test the validity of the homoge-

12 12 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions nous rational bidders assumption. To begin with we describe our sophisticated data collection methodology that ensures a sufficient sample size and reliable data Data collection Initially, a survey was carried out of various Internet auction sites to identify a sub-set that could be polled on a regular basis. Sites examined ranged from large public corporations such as onsale.com that attract thousands of bidders to rarely visited auction sites such as artrock auction. We selected on-line retailer Egghead Corporation s surplusauction.com based on the following criteria: the company profile of an innovative on-line retailer with an expanding repertoire of mercantile processes ranging from posted-price based catalogs to MIPEA, the significant volume of merchandise being auctioned every day and the significant consumer interest, as measured by web-traffic, in these auctions. Data collection was carried out by an automatic agent that was programmed to download at frequent intervals of 5 to 15 minutes the html document containing a particular auction s product description, minimum required bid, lot size and current high bidders. A typical auction lasts 24 hours and we monitored auctions each day. Subsequently, the series of html files were parsed to condense all the information pertinent to a single auction, including all the submitted bids, into a single spreadsheet. The data collection lasted about a month resulting in a total of 120 tracked auctions. This sample was further screened for sufficient participation, and occasional server break-downs resulting in a total of 105 auctions for analysis purposes. These auctions were carefully selected with respect to the important parameters of lot-size and bid increment so as to ensure a statistically sound sample Hypotheses tests Our first hypothesis attempts to compare the auctioneer s expected revenue under the MIPEA as compared to the theoretical MVA. To the best of our knowledge this exercise is the first attempt at examining the well-known revenue equivalence theorem in an on-line setting. Revenue equivalence results are known not to be robust with respect to the slightest deviation from the restrictive assumptions of the independent private values model (Myerson [7]). Clearly, the globally dispersed Internet audience, that on one hand gives on-line auctions the critical mass necessary for their viability, presents on the other hand interesting challenges to the traditional theory of auctions. This leads us to our first hypothesis: Null Hypothesis 1a There is no significant difference between the revenue obtained from the MVA and the MIPEA. This null hypothesis will be tested against the: Alternate Hypothesis 1b MVA dominates the MIPEA.

13 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions 13 Aggregate data analysis indicated a divergence between the theoretical results of proposition 5 and the empirical results. To investigate the possible causes for such divergence we closely examined the bidding patterns of individuals. Data analysis indicated that the usual assumption of homogeneity among the auction participants is significantly violated. While traditional auctions have appealed to a certain profile of individuals, e.g., Sotheby s conducts them by invitation, on-line auctions open up this sphere of economic activity to a wider heterogeneous group of people. A significant contribution of this research has been the identification of at least three different types of bidders. We classify them as: 1. Evaluators these are early one time high bidders who have a clear idea of their valuation. They, typically, execute a single bid, often during the early phases of the auctions. Their bids are, usually, significantly greater than the minimum required bid at that time. Surely, such bidders would be rare in traditional auction settings, where the cost of physically getting to an auction site to make just a single bid would be a significant deterrent. Significantly, the existence of evaluators violates the assumption of rational behavior described in section Participators these consumers derive some utility from the process of participating in the auction itself. They typically make a low initial bid equal to the minimum required bid and progressively monitor the progress of the auction and make ascending bids. 3. Opportunists consumers who by nature are looking out for bargains and buy when they see one. They typically place minimum required bids just before the auction closes. Given the above classification a natural question of interest would be the relative performance of the different types of bidders. We devise a metric for such a comparison based on the consumer surplus that the different bidder types are able to retain. The revenue maximizing auctioneer attempts to extract as much as possible of this surplus and it is interesting to observe how the nature of this tussle varies with bidder types. Let B l denote the lowest winning bid under the MIPEA. We formulate our propositions using the concept of loss of surplus which is defined as the difference between an individual s bid and the minimum winning bid, i.e., (B i B l ). Proposition 6 presents a theoretical result that deals with the consumer surplus of opportunists. Proposition 6. Opportunists will at most lose a surplus of $k. Proof. Let B denote the minimum bid amongst a set of winning bids received by the auctioneer at a given time. An opportunist can always force his way through by bidding B + k, at the expense of the last person to bid B. Thus, the maximum loss of surplus is k, since the best price he could have received the item is B. While proposition 6 presents an interesting result that opportunists do not do too badly and suffer minimal transaction costs, observe that at any stage of the bidding

14 14 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions process a bidder has only two bids that form the consideration set. These bids are B c and (B c + k), where B c represents the current minimum required bid. Based on proposition 6 we observe that even opportunists can always enter the winning list by bidding (B+k). This implies that as long as there is a non-zero likelihood that level B c will be a winning bid then any active bidder will not have the incentive to bid higher than the current minimum required bid since the only potential benefit of participating is to obtain the item at minimum possible price. Bidding B c minimizes the expected cost for the consumer and would likely be the preferred bid. A rational consumer may try to bid an amount higher than B c during the early stages of the auction with a view of entering the winners list at an earlier stage at a given bid level. However, these early stages do not adequately characterize the structure of the MIPEA mechanism, therefore we have concentrated on the penultimate stages of the bidding process and all our results should be viewed in the context of near equilibrium behavior of bidders. In fact, consumers who enter early at higher bid level, say B o, outside the above mentioned consideration set reduce their chances of winning at the next bid increment (B o + k). This is because they are the last ones to be ousted from the winners list at B o and therefore will be the last ones to enter in at (B o + k) since auction rules do not allow bidders to place multiple bids. In summary any action other than bidding from the consideration set of B c and (B c + k) will not minimize the expected cost for a rational net-worth maximizing consumer. Next we examine the surplus loss of different types of consumers via the following pair-wise hypothesis tests. Hypothesis 2a There is no significant difference in loss of surplus between opportunists and evaluators. This null hypothesis will be tested against the: Alternate Hypothesis 2b Evaluators lose more surplus than the opportunists. The reasoning behind the alternate hypothesis is that while the loss of surplus for opportunists is expected to be bound by proposition 6, the same cannot be said of evaluators. They choose to place a single bid that may well be significantly higher than the minimum required bid and hence will have a higher likelihood of losing more surplus. Hypothesis 3a There is no significant difference in loss of surplus between opportunists and participators. Alternate Hypothesis 3b Opportunists lose more surplus than participators. Participators, by virtue of keeping a close eye on the progression of the MIPEA tend to make maximum utilization of the information available and hence can be expected to time their bids better so as to win at lower prices. They do however incur a higher time cost of acquiring and processing the information in order to keep more of their surplus. In contrast, the time cost for evaluators and opportunists is insignificant.

15 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions 15 Lastly, we compare the performance of evaluators with that of participators with the expectation that evaluators will lose more surplus than the participators based on the reasoning above. Hypothesis 4a There is no significant difference in loss of surplus between evaluators and participators. Alternate Hypothesis 3b Evaluators lose more surplus than participators. In the next section we present results that test the above mentioned hypothesis using the empirical data collected from the Net. 5. Data analysis and results We first examine the sample data in order to determine the various sources of variation and perform any pre-processing in order to reduce noise and obtain a statistically sound sample. Our first test hypothesis dictates that for each auction we need some measure of revenue under the MIPEA and the MVA. Additionally, we also need to segregate the winning bidders into the three categories and estimate the average loss of surplus for each category. The data collected varied in three important parameters. They are bid increment k, number of items N, and lastly the magnitude of the dollar value of the auction represented by the ordered pair of the lowest and highest winning bids, denoted as (B l, B H ). While the first two serve as control factors, the magnitude of the values B l and B H represent noise that could significantly interfere in the process of revenue and consumer surplus comparison. For example consider the situation wherein we had to compare an auction for a CD-ROM drive whose winning bids range from $ with another auction of, say a computer system, whose winning bids may range from $ To overcome the above mentioned noise factor we introduce an offsetting mechanism that essentially levels the playing field for all auctions that have the same bid increment k. The offsetting mechanism works on the principle of shifting each winning bid to the left by an amount equal to B l, the lowest winning bid for that auction. Since all our theoretical results are dependent on bid increment k, foragivenk the offsetting mechanism should provide equivalent revenue for aggregation across different auctions with different magnitudes. For each auction we offset the individual revenue contribution by the minimumwinning bid and then compute the average revenue per winner for each auction. Finally, the mean MIPEA revenue is computed by aggregating across all the auctions with the same bid increment level k. To compute the estimated revenue if MVA was used, we rely on observation 1. Recall that observation 1 states that maximum bid a person having a value V i is going to make is V i k. If we take the marginal consumer (the person who was the last person to be removed from the list of high bidders) then her true value V can be estimated by adding k to her last bid. Then the revenue for MVA can be estimated as N (B m + k), where B m is the marginal consumer s last bid.

16 16 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions Table 1 Auction number 80512A-PT Canon BJC-4550 (W95) CD RFB Auction Lot #: 80512A-PT Opening Bid: $ Bid Increment: $5.00 Quantity Available: 8 Auction Opens: Mon., 05/11/ :13 AM PDT Auction Closes: at or after Tue., 05/12/ :00 AM PDT Table 2 Categorized winning bids for auction number 80512A-PT Type Min Max Type Type Participator Evaluator 174 Opportunist 154 Evaluator 169 Opportunist 154 Evaluator 159 Evaluator 159 Evaluator 149 We explain the entire process of bidder categorization and subsequent offsetting by demonstrating it for an actual auction. Example 3. Consider auction number 80512A-PT described in table 1. Figure 3 presents the sequence of bids that arrive during this auction. The last eight bids represent the winning bids and the bidding pattern of the winners is tracked for categorization purposes to form table 2. Using B L the lowest winning bid of $149, the individual losses of surplus are calculated for each winner and averaged out per category. Also a weighted average is used to compute the MIPEA offset revenue for this auction which turns out to be $ In this particular auction the MIPEA dominates the MVA whose offset revenue is simply equal to the first losing bid ($149), plus the bid increment, less the offset amount. That is $[( ) 149] [n/n] = $5. A cursory look reveals that this auction was dominated by evaluators who bid significantly higher than needed to obtain the item resulting in higher revenues for MIPEA than the theoretical prediction. Also notable is the resulting high value of the ($13) evaluators average loss of surplus as compared to 5 for opportunists and 10 for participators. Our first test hypothesis is concerned with the issue of revenue comparison between the two auction types, and is repeated here for the benefit of the reader. Null Hypothesis 1a There is no significant difference between the revenue obtained from the MVA and the MIPEA. This null hypothesis will be tested against the: Alternate Hypothesis 1b MVA dominates the MIPEA.

17 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions 17 Figure 3. Entire collection of bids for auction number 80512A-PT

18 18 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions Figure 3. (Continued.)

19 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions 19 Table 3 Offset revenues for auction number 80512A-PT Offset revenues by $149 Participators Evaluators Opportunists = MIPEA Total offset revenue Bidder count Average offset revenue Table 4 Ho: Revenue MIPEA Revenue MVA; Ha: Revenue MIPEA < Revenue MVA. Bid increment # of auctions df Auction size t-statistic Small (<10 items) Large (>= 10 items) Small Large Large Small Large Significant at the 5% level. Significant at the 10% level. Table 4 presents the results of the t-tests with unequal variances that were carried out using the average offset MIPEA and MVA revenues obtained from the various auctions. The two control factors described earlier namely k and N are used to further partition the data. An overall median N value of 10 was used to create the partition between what are termed as large and small auctions. The results indicate that MVA tends to dominate MIPEA only in large auctions as can be observed in the significant t-statistics in row 2 and row 7. Interestingly, in both these cases the average offset MVA revenue was exactly equal to the respective bid increments of 5 and 20, respectively. This seems to suggest that there was sufficient participation in these auctions, which resulted in the ubiquitous equivalence of the lowest winning bid and the highest losing bid. In other words there were enough bidders at the marginal level, such that the creation of a bi-partition of losers and winners at that level was feasible. In smaller auctions the different type of users (that theoretical results do not account for) induce enough variance in behavior so that the revenue equivalence cannot be rejected.

20 20 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions Table 5 Ho: Loss of surplus participator Loss of surplus oppurtunist; Ha: Loss of surplus participator < Loss of surplus oppurtunist. Bid increment # of auctions df Auction size t-statistic Small (<10 items) Large (>= 10 items) Small Large Large Small Large Significant at the 5% level. Significant at the 10% level. The dominance of the MVA for large N is an interesting issue that needs further exploration with a larger and more selective data sample, and is the subject of future research. We next present results that test hypotheses 2 4 to compare the loss of consumer surplus. Table 5 presents the comparison of loss of surplus between the opportunists and the participators. It should be noted that statistically significant results are obtained in the majority of the rows leading to significant conformance between the theoretical proposition of participators doing well in comparison with opportunists and empirical evidence. Since loss in surplus seemed to be greater for opportunists, these results indicate that participators indeed benefit from participating in the auctions and monitoring the auctions closely. Table 6 presents the comparison of loss of surplus between the opportunists and the evaluators. There does not seem to be a conclusive evidence in this case. While in three out of seven cases the null hypothesis of equivalence can be rejected, two of them favor opportunists and one favors evaluators. Therefore, while in general it seems that opportunists do better than evaluators, the results are not conclusive. Table 7 presents the comparison of loss of surplus between the evaluators and the participators. The negative value of the t-statistic indicates that in every case the participators performed better than the evaluators with statistical significance evident in three out of seven cases. A significant contribution of this research is the empirically derived identification of non-homogeneity amongst on-line bidders. Empirical evidence suggests that participators tend to perform better than opportunists who in turn perform better than evaluators. In summary, while the complex issue of revenue comparison between the two types of auctions requires further investigation with a larger and perhaps more refined data sample, the present research provides significant indication that there is a likeli-

21 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions 21 Table 6 Ho: Loss of surplus oppurtunist Loss of surplus evaluators; Ha: Loss of surplus oppurtunist < Loss of surplus evaluators. Bid increment # of Auctions df Auction size t-statistic Small (<10 items) Large (>= 10 items) Small Large Large Small Large Significant at the 5% level. Significant at the 10% level. This is significant in other direction (at 0.01 level of significance) indicating loss of surplus for opportunists being greater than that of evaluators. Table 7 Ho: Loss of surplus participator Loss of surplus evaluators; Ha: Loss of surplus participator < Loss of surplus evaluators. Bid increment # of auctions df Auction size t-statistic Small (<10 items) Large (>= 10 items) Small Large Large Small Large Significant at the 5% level. Significant at the 10% level. hood of the MVA dominating in case of large N. Important conditions under which the MVA dominates, namely the requirement of significant participation in the auction so as to have the lowest winning bid equal the highest losing bid, are characterized theoretically and supported empirically. 6. Conclusion As the electronic marketplace defined by the Internet matures into a significant player in the global economy, the need for re-examining traditional mercantile processes has never been more urgent. Consumers demands regarding lower prices and better service coupled with firms need to capture newer markets and remain com-

22 22 R. Bapna et al. / A theoretical and empirical investigation of on-line auctions petitive, call for newer mercantile processes to gain efficiencies. This research examines on-line mercantile processes based on the theory of auctions to suit the needs of current product oriented electronic markets. The joint theoretical and empirical considerations of the properties of various online auctions reveals that traditional theoretical assumptions regarding the homogeneity of bidders are violated in electronic markets. We present the first empirically derived classification of individuals bidding patterns in on-line environments. Additionally, important insights are obtained regarding future research to investigate the complex issue of revenue comparison of various types of auctions. Specifically, this research identified the need for categorizing multi-item auctions into groups according to number of items for sale. The theoretical properties seem to be supported in large auctions as opposed to smaller auctions. In addition, the theoretical results for MIPEA suggest that bid increment plays a major role in revenue generation. All the theoretical properties of these auctions are dependent on the amount of minimum bid increment. An important contribution of this research is to identify a consistent adjustment factor that can be used within and across auctions to compare and predict revenues empirically. In future research we will closely examine both the smaller auctions and larger auctions in more detail. Specifically, we will look at the issues regarding the choice of minimum bid increment. For example, is it better to have smaller bid increments and not let bidders bid the same amount as others and require that each new bid is higher than all previous bids? Further, what are the specific characteristics of smaller auctions that make them deviate from theoretical results and can we improve the theoretical models and/or empirically categorize the choice factors to make better predictions? We also want to improve the estimation of empirical revenue for MVA. Note that MVA forces all the bidders to act as evaluators. In future research we will develop econometric procedures to estimate MVA revenues based on observed bids by evaluators and final bids of participators that do not win the auction. We will also experimentally validate our results via laboratory testing of our hypotheses. We will conduct both MIPEA and MVA auctions to validate our theoretical as well as empirical findings. In summary, on-line auctions are not completely understood or examined. These auctions show different characteristics than traditional single-item auctions because of the heterogeneity of participators and the fluidity of the products that are sold using these auctions. Our theoretical and empirical investigation suggests that there might be a more cost-effective and efficient auction mechanism, namely the MVA, that at least provides as much revenue as the current MIPEA auctions held on the Internet. References [1] C. Baker, Auctioning coupon-bearing securities: A review of treasury experience, in: Bidding and Auctioning for Procurement and Allocation, ed. Y. Amihud (NYU Press, New York, 1976) pp