Comparative Multi-item Online Auctions: Evidence from the

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Comparative Analysis of Multi-item Online Auctions: Evidence from the Laboratory *

Ravi Bapna, Northeastern University Paulo Goes and Alok Gupta**, University of Connecticutϒϒϒϒ

Abstract The dynamics of customer relationship are being reshaped by price-setting processes

such as online auctions. This paper analyzes price setting process in business-to-

consumer online auctions. Typically, these auctions involve multiple identical units and

utilize a variant of the traditional English-auction mechanism. We describe an online

laboratory experiment that compares the efficiency of such a mechanism with a multi-

item version of Vickrey’s (1961) second-price auction with respect to both seller's

revenue and allocative efficiency. Our results reject the revenue equivalence principle

and indicate that English auctions may dominate the Vickrey auctions. However, we

observe that the allocative efficiency of Vickrey auctions is higher than the English

auctions.

Keywords: Online Auctions, Electronic Commerce, Laboratory Experimentation, CRM

(January 2001) Published in: Decision Support Systems, 32, 2001, 135-153.

* This research is supported in part by Treibick Electronic Commerce Initiative, Dept. of OPIM, University of Connecticut. The third author’s research is supported in part by NSF CAREER grant IIS-0092780. **Corresponding author, Dept. of Operations & Information Management, U-2041, School of Business Administration, University of Connecticut, Storrs, CT 06269-2041. Email: [email protected] ϒ Author names are in alphabetical order.

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1. Introduction

The emergence of widespread commercial activity over a ubiquitous Internet

Protocol based network of networks has brought about significant changes in the

relationships between businesses and consumers. Armed with increased access to

information and the absence of spatial and temporal constraints, consumers, who

previously were resigned to be mere price-takers, are now empowered to influence the

price-setting process [17]. This is best reflected in the growing popularity of online

auctions, and their emergence as a viable mercantile process in the electronic

marketspace, both from the point of view of consumers and businesses. Online auctions

have fueled the fire of dynamic pricing on the web and have given consumers an

alternative to the fixed posted price mechanism.

The issue of facilitating competitive price setting is an important but ignored part

of the discussion in the customer relationship management (CRM) literature. The primary

focus of CRM is to optimize customer interaction in all aspects of customer relationships

[24,27]. We contend that providing competitive pricing has to be one of the foundation

stone for CRM. Online auctions provide consumers intimacy with the price-setting

process, and above all, the possibility of a bargain. As a result they are now a critical

mechanism in the portfolio of mercantile processes of all major e-tailers, such as Amazon

and Yahoo. These auctions provide a sense of fairness and competitive thrill to the

consumers and help in building brand loyalty, which could then spill into cross channel

payoffs form increased posted price sales.

Businesses, on the other hand are looking towards auctions to liquidate excess

inventory, facilitate price-discovery for items that are otherwise difficult to price, and to

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enhance portions of the supply chain, such as procurement. Significantly, companies such

as Ebay are pioneering new secondary markets, and, in the process, raising consumer-to-

consumer competitive exchange to levels that were unimaginable just a few years ago.

While both consumer-to-consumer and business-to-business online auctions

promise to occupy a prominent place in the emerging electronic marketplace we focus

our analysis on the business-to-consumer category. Cambridge, MA, based Forrester

Research has predicted that business-to-consumer interactions would account for 66% of

a $19 billion consumer related online auction market by 2003, with the remaining 34%

belonging to the consumer-to-consumer category.

Van Heck and Vervest [31] called for an extensive examination of the pervasive

impact of advance electronic communication on the theory and practice of auctions.

Klein and O’Keefe [18] present an overview of the impact the Web is having on the

viability, operation and diffusion of the practice of auctions. Bapna, Goes and Gupta [4,5]

comprehensively summarize the online auction landscape and pay close attention to the

workings of auctions in the business-to-consumer (B2C) domain. They observe that the

majority of these B2C auctions involve multiple items, which incidentally is a much-

neglected area of research in auction theory. In contrast, most consumer-to-consumer

online auctions involve single items. This is primarily due to the special interest or

collectible nature of merchandise that is sold using this channel. There is a lack of

theoretical work in the area of multi-item auctions as stated by McAfee and McMillan

[21] and by Milgrom [25].

The utilization of multiple item auctions in the B2C domain makes sense if one

examines the kind of merchandise being sold. The majority of these auctions involve

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multiple units of identical goods such as rapidly aging computer hardware and consumer

electronics. The global reach of the Internet provides a critical mass of consumers who

are interested in these goods, which in turn makes the auctioning of multiple units of

items at a time feasible. This accelerates the process of clearing aging inventory, and

clears shelf space for current models that are likely to provide higher returns and could be

sold using the integrated, traditional posted-price storefront that accompanies most

prominent B2C auction sites1. Given the wide dispersion in consumers’ valuations across

the globe, firms are discovering that using auctions to dispose aging inventory is far more

attractive than extracting a small salvage value for these ‘obsolete’ items. After all, what

is obsolete in one part of the globe may yet be of significant value in another.

The key research question in this paper is how the current online auction

mechanisms used in the B2C domain compare with their theoretical or practical

counterparts. Given the wide variety of mercantile processes in the B2C space, such as

posted price, auctions, reverse auctions (reverseauction.com), and quantity discounts

(mobshop.com or mercata.com), what are the implications on consumers who have a

process choice to make and subsequently strategize on how much to bid. Some Recent

work by Mehta and Lee [23] compared posted price versus auctions for the sale same

goods from the point of view of the consumers’ welfare. Their preliminary analysis found

evidence of winner’s curse in that “non-expert” bidders paid 18.5% more than would be

considered the rational price.

Bapna, Goes and Gupta [4] observe that the majority of multi-item online

auctions involve indivisible goods and are open, ascending and pay-your-bid type of

auctions (termed MIPEA, for Multiple Item Progressive Electronic Auctions). Thus, they

1 Onsale and Egghead have now merged.

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resemble the English auction process, with the difference that most auctioneers

endogenously set a bid-increment and hence at any given instance, only a subset of the

current winning bidders is affected by an incoming higher bid. This discretizes the

commonly assumed continuous probability structure surrounding the auctioneer’s

revenue and leads to interesting strategic behavior among bidders. A secondary research

objective of this paper is to examine the impact of different bid-increment levels on the

revenue generation process of MIPEA.

Another variety of B2C auctions observed on the web is termed a Dutch auction

by sites such as Ebay.com and Amazon.com. However, unlike the traditional Dutch

auction that is descending in nature and most closely resembles the sealed-bid first price

auction (in the single-item case), the auction mechanism offered by Ebay is a multi-item,

progressively ascending, uniform price, lowest winning bid, open auction. For instance, if

five identical units were being auctioned, the five highest bidders would win and would

pay the same price that is equal to the lowest winning bid. The openness of Dutch

auctions, ironically negates the important incentive compatibility property that comes

along with the sealed-bid versions of such auctions [32]. In on-line Dutch auctions,

rational individuals do not have the incentive to reveal their true valuations. Instead, they

utilize the extra information they receive in the form of their competitors’ bids and derive

a new set of preferences that may or may not coincide with their true valuations.

Theoretically, this implies that the allocative efficiency of such mechanisms is dominated

by mechanisms that are incentive-compatible. Allocative efficiency is defined as the

ratio of auctioneer’s revenue plus consumers’ surplus allocated by the mechanism under

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consideration to the allocation if there were full demand revelation, i.e., consumers' bid

their true valuations [1,10].

While the rewards of observing real-world economic agents participate in

meaningful exchange are many, the one drawback is the lack of control that a researcher

can exert to isolate her variables of interest. It is here that controlled laboratory

experimentation methodology is a perfect fit. In such environments, all factors other than

the one being tested can be controlled and in the process can reinforce or refute empirical

and analytical findings.

In this paper we describe a controlled laboratory experiment to compare the

MIPEA mechanism with a sealed-bid, uniform price, highest-rejected bid multi-item

auction that is based on Vickrey's [32] original, incentive-compatible, second-price

auction. While not as widespread yet as the MIPEA, we would like to point out that

major financial institutions such as OpenIPO.com (a subusdiary of WR Hambrecht) are

in fact using the MVA auction2.

We also discuss the implication of our results in the context of Ebay’s ‘Dutch’

auction that possesses some of the features of the Vickrey auction without the incentive

compatibility property. We are able to derive results that compare the auction

mechanisms in terms of the revenue generated and the allocative efficiency

2 “Based on an auction system designed by Nobel Prize-winning economist William Vickrey, our OpenIPO auction uses a mathematical model to treat all qualifying bids in an even-handed and impartial way. It is similar to the model used to auction U.S. Treasury bills, notes and bonds.just like a typical auction, the highest bidders win in an OpenIPO auction. But there are important differences. In our OpenIPO auction, the entire auction is private, and winning bidders all pay the same price per share the public offering price.” http://www.openipo.com/offerings/auctions/openipo/faq.html

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In the next section we present the prior research in this area. In Section 3 we

describe the experimental design, which is based on the induced values theory. In Section

4 we present our test hypothesis and results, and in Section 5 we discuss directions for

future research.

2. Prior Research

Most researchers attempting to test the predictions of auction theory have been

forced to rely on the experimental laboratory to simulate real-world behavior. Empirical

research has been rare due the lack of meaningful data sets, which in turn could be

attributed to the lack of mainstream appeal of auctions. The best data set available prior

to the arrival of the web-based auctions covers US Forest Service sales of contracts for

harvesting timber in the Pacific Northwest during 1977. Hansen [14] uses this data set to

provide evidence in favor of revenue equivalence between a sealed-bid and an open

auction under a common-values setting. This is in contrast to earlier work by Mead, et al.

[22] which reported a roughly 10% higher price with sealed-bid auctions. Early lack of

empirical and/or realistic experimental test environments is increasingly disappearing

with the technological advancements in online auction technology. The widespread

popularity of online auctions, coupled with the open computing paradigm upon which the

Internet applications are built, together present a golden opportunity for researchers to

revisit the various branches of auction theory in a setting that is more realistic and has

higher inductive value.

Lucking-Reiley [20] acknowledges the difficulty in obtaining field data that

allows for testing of equivalences between the basic auction. His field experiments that

auction collectible magic cards to real world subjects involve real monetary payoffs and

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utilize a natural web based interface that is familiar to consumers interested in his wares.

While testing the revenue equivalence of single-item auction formats, Lucking-Reiley

[20] finds that Dutch auctions yield 30% higher revenues than the first-price auction

formats and that the English and second-price formats produce roughly equivalent

revenues. This contradicts the theoretical predictions of revenue equivalence.

Of late there is evidence of research spawning in multi-item auctions. List and

Lucking-Reiley [19] examine the case when consumers are allowed to bid for more than

one item under two different types of two-unit, two-person sealed bid auctions. When

consumers are allowed to bid for more than one-item in an m-item auction, Vickrey’s

original proposition -- full demand revelation occurs in a sealed-bid auction -- does not

hold [2]. Instead, the rule has to be modified such that for an m-item Vickrey auction

bidders can submit as many individual unit bids as they like. Further, the top m bids are

declared winners and for the jth unit won by a bidder, she pays an amount equal to the jth

highest of the rejected bids submitted by others [9,13]. Hence this revised mechanism

offers discriminating prices in contrast to the original mechanisms’ uniform pricing.

Appendix A provides an example that differentiates these two mechanisms.

In the two-item case, List and Lucking-Reiley [19] indicate that there is evidence

of demand reduction, i.e. lowering of the second bid below the true valuation, when the

uniform pricing rule is applied. This is a cause for concern and leads to lower allocative

efficiency. In the case of real-world B2C online multi-item auctions consumers are

allowed to bid for more than one-item but these bids cannot be discriminating, i.e. they

all have to be of the same amount. For instance, a given individual can bid for 3 items at

$100 each but cannot bid for 2 items at $110 and 1 item for $80. Whether this constraint

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is designed to prevent demand reduction in auctions that sell multiple (far greater than 2

units) is an open and interesting research question.

Bapna, Goes and Gupta [4] raise the revenue comparison question for multi-item

online auctions while analyzing the revenue structure of MIPEA. Because of the lack of

real-world data from auction mechanisms other than the MIPEA they rely on estimating

the revenues of alternative mechanisms by extrapolating the behavior of bidders under

MIPEA to other mechanisms. They assume that net-worth maximizing rational bidders

under MIPEA would shave their valuations by at least one bid-increment and utilize this

to estimate revenue from a multi-item extension of Vickrey’s original single-item

uniform highest-rejected-bid auction (termed MVA, for Multiple Vickrey Auction). Thus,

the conjecture was that assuming that the MVA is incentive-compatible an individual

bidding $x would be willing to bid $(x + k) under MIPEA where k represents the bid-

increment.

Another interesting analytical and empirical finding of Bapna, Goes and Gupta [4]

was that the hitherto undescribed discrete and sequential nature of MIPEA, caused by the

presence of the bid increment, had a significant impact on the revenue realization

process. Thus we extend our experimental objective to test whether for the same item,

can different choices in the bid-increment yield different revenues.

There have been other 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.

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Competitive auctions were first suggested by Vickrey [32] 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 [26] were among the first to design a controlled laboratory

experiment to compare competitive auctions with discriminatory auctions. Actual

bidding data have also been analyzed by various researchers such as Baker [3]. The key

results of these empirical investigations have been inconclusive with respect to sellers'

revenue. Harris and Raviv [15] 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 are to be sold to

many buyers. Their results indicate that the sellers' revenue under a specific mechanism

depend 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.

In this paper we revisit the revenue equivalence question through the controlled

environment of a laboratory experiment. Much like Lucking-Reiley's work we exploit the

online auction technology to create an environment that closely resembles its real-world

counterpart. The only methodological difference between our laboratory environment and

that of Lucking-Reiley's field experiment is that whereas his subjects are drawn from the

real world we choose to control within-subject variation by utilizing undergraduate

student subjects. The commodity being auctioned is picked from the list of goods that are

commonly sold in the real-world online B2C auction domain and our web interface

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closely resembles real auctions conducted on the web. Both approaches utilize salient

monetary incentives.

In summary, the objectives for our controlled laboratory experiment are as

follows. First, keeping everything else constant we compare the auctioneer's revenue

from the typical B2C online auctions with that from the MVA. Second, keeping

everything else constant we assess the impact of the bid increment on the auctioneers'

revenues. Finally, we investigate the allocative efficiency of these mechanisms with

respect to the aforementioned treatments.

3. Experimental Design

To answer the above-mentioned research questions we created an online auction

environment utilizing state-of-the-art interactive web development technologies

(Javascript and dynamic HTML for the front end, and an IDC/HTX connection to an

ODBC data source for the back end) that closely resembles its real-world counterpart.

Student subjects are typical Internet users and we deal with real goods that are sold in

similar real-world online auctions. Importantly, the web based auction environment is

identical to its real-world counterpart and allows us to isolate the impact of our treatment

variables. In the next subsection we set the stage for our experiment by elaborating on the

incentive structures that we designed for the different economic agents involved. As with

any laboratory experimentation, the key concern was that the results obtained from the

laboratory should have real-world implications.

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3.1 Inductive Value and Incentive Mechanism

The question of inductive value of our exercise is a key one. An economic experiment

consists of agents (e.g. buyers and sellers) and market institutions (e.g. different types of

auctions). For an experiment that takes place in a controlled economic environment of a

laboratory to have general theoretical implications one cannot rely on deductive logic.

Instead we have to rely on the general principle of induction which maintains that

behavioral regularities will persist in new situations as long as the relevant underlying

conditions remain substantially unchanged. An important underlying condition for the

successful design of a controlled economic experiment is the ability to control agents'

characteristics. We rely on Vernon Smith's [29] induced-value theory that identifies

sufficient conditions for experimental control. The key idea is that proper use of a reward

mechanism allows an experimenter to induce pre-specified characteristics in

experimental subjects. Proper use is further defined to comprise of a monotonic non-

satiable utility for the reward and that the incremental reward a person receives depends

on her actions (and those of other agents) as defined by the institutional rules that she

understands. The use of real currency is known to satisfy these important conditions.

Jamal and Sunder [16] find that use of above described salient rewards tend to increase

the reliability of results. Smith and Walker [30] provide a summary of evidence that

further supports the use of real monetary rewards in experimental economics.

Based on the above theory we designed our experiment to consist of agents

(student buyers) who participate in online auctions of consumer goods like computer

hardware and receive a real monetary reward that is a direct function of their

performance. While, drawing parallels between behavior exhibited by naïve students and

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experienced auction participants may be a far stretch for traditional auctions dealing with

high value goods, the case of online auctions points to the contrary. In fact, university

students represent a significant portion of all Internet users, which gives credence to the

inductive value of our proposed exercise.

The final compensation scheme, detailed in the next sub-section, ensures that the

expected payoff for the students was $7 for 45 minutes of their time, which is 50% above

the comparable hourly wage of $6. The idea being that participating in the auction is

worth their while. Freidman and Sunder [11] state that most economists believe this to be

the appropriate reward level to generate interest among participants.

3.2 The Environmental Variables

We constructed an experimental design that ensures a sufficient sample size, and reliable

data. The auction item was a set of 5 floppy diskettes. Students require these for a variety

of tasks in the School of Business Administration for example to submit assignments,

projects and taking computer lab work from the school to their residences. The number of

batches for sale (lotsize) was fixed at 5 per auction. The desired number of participants

for each auction was 10. In all we had four treatment levels, namely the two types of

auction mechanisms and two levels of the bid increment. However, since the bid

increment is only applicable to the MIPEA we were able to economize our design by

exploiting this commonality to have three distinct treatment levels. Thus the total number

of distinct student subjects required was around 300.

By utilizing distinct subjects from the same pool of undergraduate students we

ensured that the treatment comparison is made within a homogenous pool of subjects and

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at the same time there are no learning effects from earlier treatments. This could have

occurred if we had chosen a pure crossover design and not restricted subjects from

repeating experiments.

The subjects were recruited from the 350 students enrolled in the junior level

courses at the School of Business Administration. To account for no-shows we actually

allowed up to 12 students to sign up for any give auction. Eventually, the number of

participants for each experiment ranged from 8 - 12 with an average value of 9.2.

Each subject was promised an up-front sum of $5 for participation. Freidman and

Sunder [11] recommend this practice for three reasons: (a) to reduce tardiness, (b) to

establish ex ante credibility with the subjects that the rewards being promised to them

will be paid to them promptly, and (c) to provide an initial cushion of wealth they can

afford to lose in the actual experiment without dipping into their own wallets.

To create uncertainty regarding the exact price (value) of diskettes, in each

experiment, we randomly drew the value of a set of 5 diskettes from a uniform

distribution, with intervals ranging from $3 to $7, after the winners of a particular auction

were determined. The final payoff of a winner was calculated based on the price they

paid and the (randomly drawn) value. For example, suppose the randomly drawn value is

$5 and a participant bids $6 and wins the auction, then he/she will get the diskettes + $4

($5 - $1 for overbidding and loss of surplus). If he/she bids $3 and wins, then they get

diskettes + $7 ($5 + $2 gain of surplus). Example 1 illustrates this process in detail for

the MIPEA.

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Example 1

Suppose there are 10 participants competing for 5 units of the commodity being

auctioned. Let the randomly determined true market value be $4. Table 1 shows the

bidders' list after the close of the market and the corresponding payoffs. The bids are

ordered by bid amount and by time within bid amount. Hence, the first 5 bids (shaded)

are the winning bids and the last 5 bids are the losing bids.

Case Jane Smith (Winner):

Final Bid = $6. Since the true market value was determined (randomly) to be $4, Jane in

effect over bid by an amount equal to $6-$4 = $2. Since Jane is among the top 5 bidders

she will receive the set of 5 floppy disks. However, the amount she overbid by, that is $2,

will be subtracted from her participation money of $5. Hence Jane Smith's net payoff will

be the Set of 5 floppy diskettes + [$5(participation money) + $4 (true market value) -

$6 (Jane's bid) = $3].

Case John Doe (Loser):

Final Bid = $3. John is not among the top 5 bidders hence he shall not receive the floppy

diskettes. Hence John Doe's net payoff will be the $5(participation money).

Case Ram Singh (Winner):

Final Bid = $3.75. Since the true market value was determined (randomly) to be $4, Ram

in effect under bid by an amount equal to $4-$3.75 = $0.25. Since ram is among the top 5

bidders he will receive the set of 5 floppy disks. Additionally, the amount he underbid by,

that is $0.25, will be added to his participation money of $5. Hence Ram Singh's net

payoff will be the Set of 5 floppy diskettes + [$5(participation money) + $4 (true

market value) - $3.75 (Ram's bid) = $5.25].

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Insert Table 1 Here.

Because of the relative unfamiliarity of Vickrey like uniform pricing auctions, the

instructions for the MVA (Appendix C) contained some extra examples for the benefit of

the subjects' understanding. In particular, three examples were used to represent the cases

when the overall bid values were a) around the expected value of $5, b) extremely low,

and c) extremely high, respectively. These three examples provided the subjects with a

comprehensive overview of the range of expected revenue and incentive structures that

could arise due to the MVA. Example 2 presents the first of the three examples utilized.

Example 2

Suppose there are 10 participants competing for 5 units of the commodity being

auctioned. Let the randomly determined true market value be $3.25. The following

table shows the bidders' list after the close of the market and the corresponding payoffs.

The bids are ordered by bid amount and by time within bid amount. Hence, the first 5

bids (shaded) are the winning bids and the last 5 bids are the losing bids. Observe, that

ZZ (the 6th highest bidder) is the marginal consumer at a level of $3.5. Hence the

auction price for all 5 winners will be equal to ZZ's bid, that is $3.5.


Final Bid = $6. Since the true market value was determined (randomly) to be $3.25, and

the auction price (ZZ the marginal consumer's bid) is $3.5, Jane in effect over bid by an

amount equal to $3.5-$3.25 = $0.25. Since Jane is among the top 5 bidders she will

receive the set of 5 floppy disks. However, the amount she overbid by, that is $0.25, will

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be subtracted from her participation money of $5. Hence Jane Smith's net payoff will be

the Set of 5 floppy diskettes + [$5(participation money) + $3.25 (true market value) -

$3.5 (uniform auction price) = $4.75].





Final Bid = $3.75. Since this a uniform-pricing auction the price for Ram will be the

same as the price for Jane Smith. Hence Ram Singh's net payoff will be the Set of 5

floppy diskettes + [$5(participation money) + $3.25 (true market value) - $3.5

(uniform auction price) = $4.75].


Each online auction was designed to last for about 45 minutes. It commenced with

an instructional and familiarization session (see Appendix B for MIPEA and Appendix C

for MVA) that was supplemented by using visual aids, which was followed by a trading

session. The instructions of Appendix B or C were read out aloud to students and they

were given the opportunity to clarify any doubts prior to the commencement of the

trading. Just like in real online auctions student subjects were asked to register by

providing their name, social security number and a user-id that would protect their real

identity during the course of the auction. Figure 1 contains a snapshot of the login screen.

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Care was taken in designing the laboratory online auction interface, depicted below in

Figure 2 for MIPEA, so that it closely resembles its real world counterpart.

Insert Figure 1 Here.


Additionally, an interactive console was designed as shown in figure 3. This

console allowed the auctioneer to control the various parameter for each auction. Two

pilot runs were carried out with the dual objective of training the facilitator and,

identifying and correcting any bugs in the online auction system. It should be noted that

no special expertise or knowledge was required from the students in order to participate

in the bidding process. Unlike other types of behavioral experiments, this was not a case

where performance in the experiments was tied to previous expertise in the domain of the

experiment.


4. Theoretical Basis, Test Hypothesis and Results

4.1 Auction Mechanism as Treatment Variable, MIPEA v. MVA

We first provide the theoretical basis for the development of our hypothesis of interest,

which compares the revenues from the two auction mechanisms. Let V be the marginal

consumer's valuation, and δ be a segment of the bid increment k that measures the

distance between the marginal consumer's valuation V and the nearest lower feasible bid.

Then the lower bound and the upper bound on the revenue of a seller selling multiple

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units under MIPEA are respectively N(V-δ) and N(V-δ+k), where N is the lot size and k is

the bid increment [6]. Since the MVA is expected to be incentive compatible [32] the

total revenue for the seller selling N goods using MVA is N* V. Which leads us to the

following hypothesis:

H1: There is no significant difference in the auctioneer's revenues under MIPEA

and under MVA.

For the MVA, the incentive mechanism and the objects being auctioned were kept

the same as above. The subjects were reminded that MVA was a sealed bid auction and

that they got only one, irreversible chance at bidding. Figure 4 below depicts the online

screen that was designed for the MVA auction.


Table 3 below displays the results of the test hypothesis H1. It is very clear that

the MIPEA dominates MVA in our controlled laboratory setting, and the results are

indeed statistically significant. This is in contrast to the implied empirical evidence of

Bapna, Goes and Gupta [4] where the MIPEA empirical data was used to infer MVA

revenues. The results there indicted that there was little to choose between the two

mechanisms' revenues.


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At the same time, it should be emphasized that the relatively high revenues obtained from

MIPEA are neither unreasonable nor unexpected. In fact, given the a priori knowledge of

the valuation of the object being auctioned (a set of 5 floppy diskettes) it is not surprising

that the equilibrium points reached were towards the maximum expected revenue from

such auctions as described by Bapna, et al. [4]. Additionally, it should be borne in mind

that no online auctioneer is actually conducting the MVA and thus the empirical estimate

utilized in that study was the observable behavior of the marginal consumer under

MIPEA that was adjusted for the MVA.

4.2 Bid Increment as Treatment Variable

Given that all B2C online auctions set a discrete bid increment we next examine the

impact the choice of the bid increment has on the auctioneers' revenue. It should be

mentioned that there has been very little research done on the impact of discrete bid

levels in auctions. In contrast the standard auction theory assumption is to model the

amount bid as a continuous variable. Yamey [33] and Rothkopf and Harstad [28] are the

only researchers who have dealt with the somewhat related issue of analyzing auctions

from a more decision theoretic perspective rather than a game theoretic perspective.

However, their analysis deals with single item auctions. Thus based on the gap in the

literature and our empirical evidence we chose the bid increment as a treatment variable,

leading to our hypothesis of interest:

H2: There is no significant difference between the B2C online auction revenues with

different values of the bid increment.

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Keeping everything else constant we manipulated the bid increment k and

observed the effect on the auctioneer's revenue. Two levels of the treatment variables

where chosen as k = $0.10 and k = $0.25 (corresponding to a dime and a quarter

respectively) and 10 auctions were conducted at each level. Table 4 below shows the

results obtained from this experiment. As can be seen, both levels of the treatment

variables yielded approximately the same average revenue and the large variance lead to

the t-statistic having a low and insignificant value. In essence the results show that the

step size did not make a difference in MIPEA revenue. While, this result might seem

surprising, we believe that this result is influenced by relative closeness of absolute value

of increments and students were not much affected by the range of bid increment when

purchasing commodities that are relatively inexpensive.


4.3 Experimental Validity and Robustness

In order to test the validity of our experimental design we examined our data to determine

whether the incentive structure that was induced on the market did indeed control the

subjects’ characteristics. Recall that the subjects were told that the true value of the

objects being auctioned would be randomly drawn from a distribution [$3, $7].

Interestingly, we found that the median value of all the bids that were placed in the 30

trials to be exactly $5 which coincides with the expected value of any symmetric

distribution between the interval [$3, $7].

In addition, to examine the robustness of the design we tested the three treatments

for equality of variance. Table 5 displays the F statistic for the pair-wise tests for equality

of variance. The values clearly indicate that there is no significant difference in the

22

variances between the treatments indicating that subjects behaved similarly over the

course of the trials.


4.4 Allocative Efficiency

The allocative efficiency measure used in this study to compare the allocations of our

various treatments is the percentage of the maximum possible gains that are realized by

the allocation process. Our metric for allocative efficiency is based on Becker's [7]

realization that basic features of an economic mechanism can be measured by market

level consequences. It is difficult to control the market agents' behavior exactly [12],

however the market level consequences remain more robust.

Let S be the consumer surplus for each bidder in the auctions. It is calculated as S

= (Randomly Drawn Value – Actual Bid). Note that the quantity S can be either negative

or positive. The overall allocative efficiency η for a given auction is computed as:

revelation demand full assuming revenueBenchmark surplus)consumer Total revenueauction (Total +=η (1)

The above metric provides the ratio of:

• The sum of the auctioneer’s revenue and the consumer surplus resulting from the

allocation process, and

• The sum of the auctioneer’s revenue and the consumer surplus which would be

realized if there were full demand revelation.

To compute this we first need to estimate the benchmark revenue that would have

accrued had there been full demand revelation. We utilize the experimental data obtained

from the MVA (since it is incentive compatible for consumers) to compute the median

bids at each of the top 5 winning positions and take the sum of the medians, across

23

auctions, to obtain our benchmark revenue (denominator). Note that the bids are

consumers’ true valuations and not the price they pay and thus include both the price

they paid and the surplus they keep.

The allocative efficiency for the MVA turns out to be 96%, the efficiency of the

MIPEA with bid increment of $0.10 is 84.8% and that with bid increment of $0.25 is

85.7%. Thus, we observe that while the MIPEA yields significantly higher revenue for

the auctioneer, from a social welfare perspective it is dominated by the MVA since it has

a high allocative efficiency of 96%. The result implies that the MVA should be the

mechanism of choice in the design of auctions where social welfare maximization is the

objective. This is the case of the auction of bandwidth for public data networks, which

are considered public goods.

5. Directions for Future Research

At present the spirited and tenacious entrepreneurs of the networked economy are

carrying out bold, but at times direction-less experimentation with regards to adopting

new mercantile processes. There exists an unique opportunity for researchers who can

anticipate these future trends and present a priori evidence for or against a given

mechanism in a given domain. We demonstrated one such approach when we compared

the revenue from the MVA with that of the MIPEA. Our research clearly suggests that

the question regarding the choice of the optimal auction mechanism for multi-item B2C

online auctions is still an unanswered one. Online auction laboratory environments such

as ours can provide a low-risk high inductive value environment for testing the efficacy

of alternative mechanisms before they are implemented in the real world.

An immediate question that needs to be answered deals with the comparison of

the two mechanisms described above and the so-called ‘Dutch’ auction conducted by

24

sites like Ebay and Amazon. From a theoretical perspective the open uniform pricing

‘Dutch’ auctions conducted by sites like Ebay and Amazon do not offer the necessary

incentives for consumers to reveal their true valuations. This leads us to hypothesize that

their allocative efficiency will be dominated by both MIPEA and the MVA. Testing this

hypothesis in an empirical setting would require auctions of the same items using the

same lot size under the three different mechanisms, an event that is unlikely to happen.

Instead, researchers can rely on a laboratory setting like ours and test this hypothesis

under a controlled environment.

There is immense potential in the extension of this approach to other domains. In

the domain of consumer-to-consumer online auction that primarily deals with collectibles

it would be interesting to see whether individuals’ valuations are correlated and whether a

true descending Dutch auction can be utilized to yield higher revenues in the presence of

risk-averse bidders. In the domain of business-to-business online auction, where sealed

bids for contracts and procurement fulfillment are de rigueur, can a stock market like

Walraisan bid-ask market mechanism be designed that could increase the efficiency of

the procurement process.

As the networked economy makes auction-based dynamic pricing increasingly

prevalent and expands its reach to a wide variety of goods and services, the challenges to

the academic community are many. No longer can these online mercantile processes be

analyzed in a vacuum, out of context of the markets in which they take place. Another

interesting area of research where the laboratory experiments will be valuable is in

examining the complimentarities and interactions between the posted price based

electronic catalog method of selling on the web and the emerging auction based dynamic

25

pricing mechanism. The problem can be viewed from both the sellers' and the buyers'

perspective. In what situations and under what criteria should sellers switch from one

mechanism to the other. From the consumers' point of view the two models increase

selection and coexist very nicely. Consumers do not wake up in the morning and say, "I

want to buy something using the auction mechanism." Presumably, they know what they

are looking for and have to determine where they can find it. Whether they ultimately get

it via a fixed price or auction mechanism will be a function of their variables of interest,

which need to be further understood.

In the future we anticipate further enrichment of the portfolio of mercantile

processes. There will be different horses for different courses and many different kinds

of negotiating mechanisms will co-exist on the web. An interesting research question is

determining the correct mapping between a given mechanism and a target domain in the

online environment. For instance, can we establish that an MVA type uniform pricing

mechanism will always be preferable to an equivalent discriminatory mechanism in

situations where the maximum valuations of the objects being auctioned are well known?

This could apply to consumer electronics where the maximum valuation for any auction

participant should not be greater than the lowest posted price (which can easily be

determined using a shopping agent like www.shopper.com). On the other hand if the

domain is unique collectible items one could hypothesize that individuals' valuations will

be correlated to their counterparts' valuations and hence a discriminatory auction would

yield higher expected revenues.

Another candidate posted-price mechanism is the one utilized by companies like

Egghead.com where goods are said to be priced 'at cost' plus a small premium that is

26

revealed to the consumers. Egghead also has one of the premium B2C auction sites on the

web. An interesting research question would be examining the rationale behind the

consumers' decision to adopt either of these mechanisms. This would provide insights

into when and why consumers prefer the certainty of fixed prices to auctions.

Lastly, the reach of the controlled laboratory experimental setting can be extended

to create pricing models currently lacking for real-time information goods, like event

webcasts, that have to be delivered with a certain quality-of-service.

27

Appendix A – Example of Auction Mechanisms with Multi-item Demand

We consider the case when consumers are allowed to bid for more than one-item in an m-

item auction. Vickrey’s original definition of an incentive compatible mechanism, where

each bidder submits one bid, the top m bidders each win one good at a uniform price

equal to the first bid rejected, holds only when individuals are allowed to bid for only one

item.

Example 1: Consider an auction of 3 goods and let there be seven bidders with the

following final bids each for one quantity.

Consumer A B C D E (marginal

consumer)

F G

Final Bid 10 20 15 10 15 30 30

F, G, and B will be declared winners and they will all pay $15 (E’s bid) assuming that

ties are broken randomly. All bidders have it in their interest to bid their true valuations.

The auctioneer’s revenue is $45.

If however the bidders were allowed to bid for more than one item and that these bids

could be of different values then incentive compatibility does not hold.

28

Example 2: Consider an auction of 3 goods where bidders can submit as many individual

bids that they like. Let there be seven bidders and assume that each individual places bids

for 2 items.

Consumer A B C D E (marginal

consumer)

F G

Bid1 10 20 15 10 15 30 30

Bid2 10 5 5 10 15 10 20

For this mechanism to be incentive compatible that the top 3 bids {F1, G1, B1} are

declared winners, and that for the jth unit won by a bidder, she must pay an amount equal

to the jth highest of the rejected bids submitted by others. Thus F, G and B are charged

$20, $15, and $15 respectively. This results in the auctioneer’s revenue being $50.

29

Appendix B - Instructions for Multiple Item Progressive Electronic Auctions

(MIPEA)

General

This is an experiment in the economics of electronic markets. Various research

grants have provided funds for this research. The instructions are simple and if you

follow them carefully and make good decisions you might derive a considerable amount

of benefit, some of which will be in the form of cash given to you at the end of the

experiment.

In this experiment we are going to simulate a market that closely resembles many

of the current auctions conducted on the Internet. You and your fellow participants in the

experiment will be competing to buy a single unit of a homogenous product when

multiple units are being sold in a given trading period. By homogenous product we mean

that there is no difference of any kind between any two units. A single unit of the

product in this experiment is a set of 5 Maxell High Density floppy diskettes. Each

auction will attempt to sell 5 such units. The duration of the trading period will be

announced before hand. All participants have been provided the same information

regarding the experiment.

All participants will be given a sum of $5 for participating in the experiment. This

amount will be disbursed after the market clears at the end of the experiment. In addition,

at the end of the experiment we will determine the true market value of a single unit of

the product by randomly choosing a value ranging from $3 to $7. This range of true value

accounts for the variation in the market conditions such as price fluctuations that arise

from changes in demand and supply. Once the market value is determined and if you are

30

among the auction winners then you may receive an additional amount equal to the

difference between the market value and your winning bid. If your bid is higher than the

market value then the difference will be deducted from your participation payoff. In case

the difference is such that your net participation payoff is less than zero than your payoff

will be set to $0. Later, we will discuss examples that will further clarify the total payoff

for both winners as well as losers.

Registration

To participate in this expermient you have to register by providing your name and

social security number. Additionally, to protect your identity during the course of the

experiment you will be asked to select a 'user_id' that will serve as your anonymous

nametag. Please choose an id that does not reveal your true identity.

Market Organization

The market for this commodity is organized as follows: we open the market for

each trading period that lasts approximately 15 minutes. The number of units of the

commodity being auctioned, the bid increment, the current minimum required bid,

the current list of winning bids and the auction closing time will be displayed on your

web browser. If you have successfully registered and if the market is open you can place

a bid for a single unit of the commodity being auctioned. Bids are placed by entering a

bid amount and by pressing the submit button on your web browser. The bid has to be at

least as high as the current minimum bid. It can be higher than the current minimum bid.

By placing a bid you express a desire to obtain a set of 5 floppies at your

given bid level and you understand that your net payoff will be affected by your bid

amount. After the auction closes the list of winners, that is the 5 highest bidders will be

31

announced and the market will clear. The bids are ranked by bid amount and by time

within bid amount. This implies that if person A bids $x before person B bids $x than A

will be higher on the winners list.

Example 1 of Section 3.2 was presented to the subjects here.

32

Appendix C - Instructions for Multiple Vickrey Auctions (MVA)

General

This is an experiment in the economics of electronic markets. Various research

foundations have provided funds for this research. The instructions are simple and if you

follow them carefully and make good decisions you might derive a considerable amount

of benefit, some of which will be in the form of cash given to you at the end of the

experiment. In this experiment we are going to simulate a market that closely resembles

many of the current auctions conducted on the Internet. You and your fellow participants

in the experiment will be competing to buy a single unit of a homogenous product when

multiple such units are being sold in a given trading period. By homogenous product we

mean that there is no difference of any kind between any two products. A single unit of

the product in this experiment is a set of 5 Maxell High Density floppy diskettes. Each

auction will attempt to sell 5 such units. The duration of the trading period will be

announced before hand. All participants have been provided the same information

regarding the experiment.

All participants will be given a sum of $5 for participating in the experiment. This

amount will be disbursed after the market clears at the end of the experiment. In addition,

at the end of the experiment we will determine the true market value of a single unit of

the product by randomly choosing a value ranging from $3 to $7. This range of true value

accounts for the variation in the market conditions such as price fluctuations that arise

from changes in demand and supply. Once the market value is determined and if you are

among the auction winners than you may receive an additional amount equal to the

difference between the market value and the price of the product determined by the

33

auction. The auction price of the product will be uniformly set to the 6th highest bid.

Thus all the 5 winners, that is the 5 highest bidders, will receive the product at a price

equal to the bid made by the 6th highest bidder. If the auction price is higher than the

market value than the difference will be deducted from your participation payoff. In case

the difference is such that your net participation payoff is less than zero than your payoff

will be set to $0. Later, we will discuss examples that will further clarify the total payoff

for both winners as well as losers.

Registration

To participate in this expermient you have to register by providing your name and

social security number. Additionally, to protect your identity during the course of the

experiment you will be asked to select a 'user_id' that will serve as your anonymous

nametag. Please choose an id that does not reveal your true identity.

Market Organization

The market for this commodity is organized as follows: we open the market for

each trading period that lasts not greater than 10 minutes. The auction will automatically

close after bids from all 10 participants are received. The number of units of the

commodity being auctioned will be displayed on your web browser. If you have

successfully registered and if the market is open you can place a bid for a single unit of

the commodity being auctioned. Bids are placed by entering a bid amount and by

pressing the submit button on your web browser. Since this is a sealed-bid auction no

information regarding the bids will be displayed during the course of the auction. Also,

you can place only one bid for the commodity and this bid cannot be revised.

34

By placing a bid you express a desire to obtain a set of 5 floppies at your

given bid level and you understand that your net payoff will be affected by your bid

amount. After the auction closes the list of winners, that is the 5 highest bidders will be

announced and the market will clear. The price charged to each of the 5 winners will

be equal to bid of the 6th highest bidder, that is the first losing bidder. The bids are

ranked by bid amount and by time within bid amount. This implies that if person A bids

$x before person B bids $x than A will be higher on the winners list.

Example 2 of Section 3.2 was presented to the subjects here.

Example 2

Let the randomly determined true market value be $5.00. Table C1 below shows the

bidders' list after the close of the market and the corresponding payoffs. The bids are

ordered by bid amount and by time within bid amount. Hence, the first 5 bids (shaded)

are the winning bids and the last 5 bids are the losing bids. Observe, that ZZ (the 6th

highest bidder) is the marginal consumer at a level of $10. Hence the auction price

for all 5 winners will be equal to ZZ's bid, that is $10.


Final Bid = $10. Since the true market value was determined (randomly) to be $5, and the

auction price (ZZ the marginal consumer's bid) is $10, Jane in effect over bid by an

amount equal to $10-$5 = $5. Since Jane is among the top 5 bidders she will receive the

set of 5 floppy disks. However, the amount she overbid by, that is $5, will be subtracted

to her participation money of $5. Hence Jane Smith's net payoff will be the Set of 5

35

floppy diskettes + [$5(participation money) + $5 (true market value) - $10 (uniform

auction price) = $0].





Final Bid = $10. Since this a uniform-pricing auction the price for Ram will be the same

as the price for Jane Smith. Hence Ram Singh's net payoff will be the Set of 5 floppy

diskettes + [$5(participation money) + $5 (true market value) - $10 (uniform auction

price) = $0].

Insert Table C1 Here.

Example 3

Let the randomly determined true market value be $5.00 once again. Table C2 below

shows the bidders' list after the close of the market and the corresponding payoffs. The

bids are ordered by bid amount and by time within bid amount. Hence, the first 5 bids

(shaded) are the winning bids and the last 5 bids are the losing bids. Observe, that ZZ

(the 6th highest bidder) is the marginal consumer at a level of $3.25. Hence the

auction price for all 5 winners will be equal to ZZ's bid, that is $3.25.


Final Bid = $3.50. Since the true market value was determined (randomly) to be $5, and

the auction price (ZZ the marginal consumer's bid) is $3.25, Jane in effect under bid by

36

an amount equal to $5-$3.25 = $1.75. Since Jane is among the top 5 bidders she will

receive the set of 5 floppy disks. However, the amount she underbid by, that is $1.75, will

be added to her participation money of $5. Hence Jane Smith's net payoff will be the Set

of 5 floppy diskettes + [$5(participation money) + $5 (true market value) - $3.25



Final Bid = $3.25. John is not among the top 5 bidders hence he shall not receive the

floppy diskettes. Hence John Doe's net payoff will be the $5(participation money).


Final Bid = $3.5. Since this is a uniform-pricing auction the price for Ram will be the

same as the price for Jane Smith. Hence Ram Singh's net payoff will be the Set of 5

floppy diskettes + [$5(participation money) + $5 (true market value) - $3.25


Insert Table C1 Here.

37

User-ID Final Winning Bid Net Payoff ($5 +True Value - Final Winning Bid )

AA $7.5 $1.5 + Floppies CC $6.5 $2.5 + Floppies Jane Smith $6 $3 + Floppies BB $4.5 $4.5 + Floppies Ram Singh $3.75 $5.25 + Floppies ZZ $3.5 $5 FF $3.25 $5 John Doe $3.0 $5 RR $2.75 $5 QQ $2 $5

38

User-ID Final Winning Bid Net Payoff ($5 + True Value - Marginal Consumer's Bid )

AA $7.5 $4.75 + Floppies CC $6.5 $4.75 + Floppies Jane Smith $6 $4.75 + Floppies BB $4.5 $4.75 + Floppies Ram Singh $3.75 $4.75 + Floppies ZZ $3.5 $5 FF $3.25 $5 John Doe $3.0 $5 RR $2.75 $5 QQ $2 $5

39

t-Test: Two-Sample Assuming Unequal Variances

MIPEA MVA Mean 24.485 19.95 Variance 13.76503 7.552778 Observations 20 10 Hypothesized Mean Difference

0

df 24 t Stat 3.774544 P(T<=t) one-tail 0.000465 t Critical one-tail 1.710882 P(T<=t) two-tail 0.00093 t Critical two-tail 2.063898

40

t-Test: Two-Sample Assuming Unequal Variances

k=10 k=25 Mean 24.53 24.44Variance 16.35789 12.69711Observations 10 10Hypothesized Mean Difference

0

df 18t Stat 0.0528P(T<=t) one-tail 0.479237t Critical one-tail 1.734063P(T<=t) two-tail 0.958473t Critical two-tail 2.100924

41

Treatment 1 Treatment 2 F-statistic p-value MVA MIPEA (bid increment

= $0.10) 2.165 0.132

MVA MIPEA (bid increment = $0.25)

1.681 0.225

MIPEA (bid increment = $0.10)

MIPEA (bid increment = $0.25)

1.288 0.356

42

User-ID Final Winning Bid Net Payoff ($5 + True Value –

Marginal Consumer's Bid ) AA $10 $0 + Floppies CC $10 $0 + Floppies Jane Smith $10 $0+ Floppies BB $10 $0 + Floppies Ram Singh $10 $0 + Floppies ZZ $10 $5 FF $5 $5 John Doe $5 $5 RR $5 $5 QQ $5 $5

43

User-ID Final Winning Bid Net Payoff ($5 + True Value -

Marginal Consumer's Bid ) AA $4 $6.75 + Floppies CC $3.75 $6.75 + Floppies Jane Smith $3.5 $6.75 + Floppies BB $3.5 $6.75 + Floppies Ram Singh $3.5 $6.75 + Floppies ZZ $3.25 $5 FF $3 $5 John Doe $3 $5 RR $3 $5 QQ $3 $5

44

45

46

47

48

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52

Titles for Figures: Figure 1 - Login Screen for Online Auction Experiment

Figure 2 Snapshot of MIPEA Auctions Conducted in the Laboratory

Figure 3- Interactive Console for Controlling Online Auctions in the Laboratory

Figure 4. The screen for the MVA reminds subjects of its sealed-bid nature

53

Titles for Tables: Table 1. Example list of final bids for the MIPEA

Table 2. Example list of final bids for the MVA.

Table 3. Results of MIPEA v. MVA

Table 4. Results with Bid Increment as the Treatment Variable

Table 5. Pair-wise F-test for equality of variance test

Table C1. Example list of bids for the MVA

Table C2. Example list of bids for the MVA

Documents

Comparative Multi-item Online Auctions: Evidence from the