Allocative Efficiency Considerations
in Online Auction Markets
Ram D. Gopal Department of Operations and Information Management
University of Connecticut Storrs, CT 06269 Tel: 860-4862408 Fax: 860-4864839
Email: [email protected]
Y. Alex Tung Department of Operations and Information Management
University of Connecticut Storrs, CT 06269 Tel: 860-4866470 Fax: 860-4864839
Email: [email protected]
Andrew B. Whinston* Department of Management Science and Information Systems
Graduate School of Business University of Texas at Austin
Austin, TX 78712 Tel: 512-4718879 Fax: 512-4710587
Email: [email protected]
Revised January 2004
* Corresponding author
Allocative Efficiency Considerations in Online Auction Markets
Abstract Allocative inefficiencies in online auction markets can result in the loss of revenues for sellers. It can also cause frustration for buyers who fail to win an item despite placing bids higher than other winners. The main contention of this work is that allocative inefficiencies present arbitrage opportunities, though not strictly in the traditional financial market sense, where risk-free profits are guaranteed. We develop a set of efficiency criteria to evaluate the auction activity of new and identically described items. Two principles, seller arbitrage and buyer arbitrage, are developed. These principles can be employed to evaluate the price behavior of temporally proximate auctions, and generate a useful benchmark to make allocative efficiency evaluations. Our empirical evidence suggests that arbitrage opportunities are present in a spectrum of online auctions. An empirically verifiable test of auction market allocative efficiencies is the major contribution of this research. Keywords: Online Auctions, Allocative Efficiency, Arbitrage, Price Dispersion
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Allocative Efficiency Considerations in Online Auction Markets
1. Introduction
Online auctions have become a popular e-commerce trading platform for a variety of
consumer and business trading activities. eBay, the world’s largest auction house has
over 45 million registered users, and is the most popular shopping site on the Internet as
measured by total user minutes, according to Media Metrix. Millions of items are listed
each day on eBay spanning thousands of categories such as automobiles, jewelry, musical
instruments, cameras, computers, furniture, sporting goods, tickets, and boats. The
volume of trade in the eBay community has grown from $5 billion in 2000 to over $9.3
billion in 2001, covering over 18,000 categories of goods. To sustain and grow the online
auction market, eBay has continually implemented mechanisms to increase the ease of
use and access to information, enhance privacy and security for the participants, reduce
fraud, and improve the legitimacy of trades conducted via their trading platform. Despite
these efforts, certain problems continue to plague the online auction market. For example,
winner’s curse is a well-known phenomenon where the winning bid of an auction
significantly exceeds the price of the same item easily accessible from other avenues.
The purpose of this work is to examine another less-discussed phenomenon,
allocative inefficiency. Allocative efficiency is an indicator of the degree to which items
are allocated to the higher value bidders. The central question we intend to address in this
work is whether online auction markets, such as eBay or uBid where transactions on a
plethora of goods and services take place, are indeed allocative-efficient. Before we
proceed further with this line of analysis, we need to place the research question in its
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proper context. Foremost is that our focus is on online auction markets, and not on the
mechanics of single auctions. Thus our interest is not on the details regarding a single
item auction, a combinatorial auction where bids are placed for a combination of items,
or a simultaneous auction where separate bids are placed for each individual item. Rather
our focus is on allocations across a number of independent, autonomous and temporally
proximate auctions. Further, to make reasonable efficiency evaluations across
independent auctions, we restrict our analysis to items (a) that are identical (at least in the
a priori sense) across these auctions, and (b) which are traded in sufficiently large
number of auctions. The former assures us that the comparisons are made on an apples-
to-apples basis, and the latter ensures sufficient liquidity in the market to make efficiency
evaluations. Thus, the underlying asset that we evaluate is new items that are identical
(based on the descriptions available to the bidders). Our analysis does not directly apply
to rare goods as they lack market liquidity, nor to used items since similarity is hard to
justify.
What causes us to question the allocative efficiency of online auction markets?
The simplest reason is the nascency of online auctions. Further reasons include reports
from a number of studies that suggest individual behaviors in auctions deviate from
rationality (in the economic sense). These include phenomenon such as herd behavior -
the tendency of individuals to gravitate towards certain auction listings, away from
alternate but more attractive auction listings. To motivate the research question, Table 1
reports potential allocative inefficiencies for auctions involving three different products.
For each product, the table reports the number of auctions conducted during the period
(3/1/02 – 3/14/02) by the most active seller. For example, the most active seller of Bose
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Radio conducted 29 successful auctions during the 2-week observation period. If the
auctions conducted by the seller were indeed efficient in allocating the items, then the 29
winners for Bose Radio should correspond to the 29 highest bidders who participated
with the seller. However, as reported in Table 1, only 21 of the top 29 bidders actually
won the item from this seller. Interestingly, none of the product auctions attained perfect
allocative efficiency, with efficiencies ranges from a low of 52.2% to a high of 82.5%.
Table 1: Allocative Efficiency of Item Allocation Item Number of Auctions by
the Most Active Seller Allocative Efficiency
Bose Radio 29 72.4% Palm 515 40 82.5% Play Station 2 136 52.2%
This phenomenon might be caused by a number of factors including herd
behavior, bidder timing constraints (unable to participate in auctions that end after the
bidder departs), and lack of awareness of all existing auctions (due to high search costs).
The existence of such allocative inefficiencies provides opportunities for other players in
the market to take advantage of and benefit from. One such means of gaining from
allocative inefficiencies is through the process of arbitrage, which is discussed in detail in
the Section 3.
The remainder of the paper is organized as follows. Section 2 provides a brief
review of current literature on online auction studies. In particular, we especially focus on
studies that report winner’s curse and non-rational behavior in auctions. Section 3
presents a formal development of the arbitrage process that can yield risk-free profits
when significant allocative inefficiencies are present in online auction markets.
Section 4 presents the statistical analysis results to assess arbitrage in online auction
markets for three different products. Concluding remarks and directions for future
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research are presented in Section 5.
2. Literature Review
Literature on auctions is extensive. A number of auction related issues have been
addressed, and these include 1) winner’s curse, herd behavior, and other non-rational
behaviors; 2) impact of bidding parameters such as minimum bid increment, minimum
bid, reserve price, auction duration, and starting and ending time on auction outcomes; 3)
multi-units and multi-demand auctions; 4) auction security issues such as collusion and
shilling; and 5) issues related to seller reputation and trust.
Milgrom and Weber (1982), Cox and Isaac (1984) and Thiel (1988) examined
winner’s curse from a theoretical perspective. Kagel and Levin (1986), Dyer et al. (1989),
Lind and Plott (1991), and Julien et al. (2001) conducted experimental studies on
winner’s curse. Mehta and Lee (1999a, 1999b), Oh (2002), and Vakrat and Seidmann
(1999) empirically compared posted-price and auctions to evaluate the existence of
winner’s curse phenomenon. The existing evidence to date suggests that winner’s curse
phenomenon is prevalent in the current online auction markets.
Dholakia and Soltysinski (2001) provided evidence of herd behavior in online
auctions. Herd behavior is the tendency to gravitate towards auction listings with one or
more existing bids, virtually ignoring comparable and more attractive listings. The
authors identified two psychological mechanisms that account for herd behavior – the use
of others’ bidding behaviors as cues for pre-screening and escalation of commitment after
making the first bid. Kauffman and Wood (2001) found evidence of herd effect, and
observed that individuals tend to pay more for items sold on a weekend, for items with a
picture, and for items sold by experienced sellers. Similar herd behavior has been
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observed in financial market as well (Rubenstein, 2001).
The impact of bidding parameters has also been studied extensively. Bapna et al.
(2000, 2001, 2002), as well as Bajari and Hortacsu (2001, 2002), suggest that the
minimum bid and bid increment have a significant impact on seller’s revenues. Hendricks
et al. (1987) and Hendricks and Porter (1988) studied the effect of asymmetrically
informed bidders on the outcome of the auctions.
Recent work in auctions has extended the single-item auction settings (Rothkopf
and Harstad 1994; Guo, 2002). McAfee (1993) designed a mechanism for multiple sellers
and multiple buyers under the assumption that each seller only has one item of goods to
sell. He demonstrated that matching process in his designed mechanism is endogenously
done. In the model buyers and sellers can participate repeatedly until successful and
sellers are free to choose the auction mechanism. An equilibrium is found where sellers
hold identical auctions and buyers randomize over the sellers they visit. Alsemgeest
(1998) conducted an experimental comparison of auctions where bidders demand single
or multiple units. Cox et al. (1984), Rothkopf et al. (1998), Boyan and Greenwald (2001),
Greenwald and Boyan (2001), and Matsumoto and Fujita (2001) examined issues related
to simultaneous and combinatorial auctions. These auctions are for multiple or dissimilar
items. In combinatorial auctions, bids usually are placed for a combination of items (for
example, camera and flash memory) where simultaneous auctions require separate bids to
be placed for each individual item.
Wang et al. (2000) developed S-MAP protocol (Seal-bid Multi-round Auction
Protocol) to enhance security in online auctions. Snyder (2000) presents several strategies
to prevent online auction fraud. Bajari and Ye (2001) developed an approach to the
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problem of identification and testing for bid-rigging in procurement auctions. Bid rigging
(a.k.a. collusion or shilling) is a phenomenon of fraudulent bidding by an associate of the
seller in order to inflate the price of an item. Ba and Pavlou (2002) find evidence that
sellers with a higher reputation, measured based on the consumer feedback, fetch a price
premium as the perceived risk of safe transaction with such sellers is lower.
Tung et al. (2002) examine issues that arise in the face of multiple, overlapping
and independent auctions that are found in current online auction markets. They argue
that multiple, simultaneously active auctions significantly compound consumer
participation decisions. Decisions about which auctions to monitor, in what sequence,
how often, which auction to bid and re-bid are complex, and can have a non-trivial
impact on the acquisition and the final price of the item. Sticking it out with one auction
might result in missed opportunities to obtain the item much cheaper elsewhere; and
excess monitoring without making a commitment can also result in missed opportunities.
These can result in significant allocative inefficiencies that can provide arbitrage
opportunities. This process of arbitrage is detailed in the next section.
Sharpe and Alexander (1990) define arbitrage as the near simultaneous purchase
and sale of the same, or essentially similar, security in two different markets for
advantageously different prices. Modigliani and Miller’s (1958) classic work on the
financial structure of the firm based on arbitrage principles has served as an important
principle to discover relationships in asset pricing. Merton (1973) and Cox et al. (1979)
use arbitrage to bound option prices; Charupat and Milevsky (2001) use it to develop
price relationships in insurance and annuity markets. Varian (1987) provides an excellent
primer on the applications of arbitrage principle.
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3. Allocative Inefficiencies and Arbitrage in Online Auctions
Arbitrage can be broadly defined as buy-and-sell (or sell-and-buy) transactions of an item
that can be executed in a short time period, which result in risk-free or super-normal
profits. In online auction markets, such opportunities exist when the basic economic
concept – “the law of one price” is violated. This occurs when allocative inefficiencies
are prevalent and persistent, as indicated by significant price dispersion amongst auctions
for a given item.
To talk about arbitrage is to make a statement about potential opportunities in a
market to realize super-normal profits through executing a series of trades in near
simultaneous time. The power of the arbitrage methodology is that it obviates the need to
specify the inherent demand characteristics and long-term price behavior of the
underlying asset (Varian 1987). Instead it develops price relationships in the “short-term”
and the analysis requires specification of only the mechanics of the markets in which the
trades are executed, and costs to conduct these trades.
We begin the discussion by considering the costs associated with an auction. In a
typical online auction, the revenues earned by the auction house are obtained solely from
the seller. These generally take two forms: (1) a commission that is charged if the item is
successfully sold, and (2) a listing fee that is charged upfront to the seller. The listing fees
are applied independent of whether the item is successfully auctioned off or not. The
listing fees charged by auction houses are generally small. Ubid, for example, provides an
option to list items for free; eBay permits sellers to re-list unsold items once without
charging additional listing fees. Auction houses realize that high listing fees discourage
seller participation, especially given lack of guarantees on the success of auctions. If the
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auction completes successfully the buyer pays for the item, and typically also bears the
shipping and handling charges. This scenario is monetarily equivalent to seller bearing
the cost of shipping and handling, with the effective price received by the seller reduced
by these costs.
We will denote P to be the final price of the item, C(P) the commissions paid by
the seller to the auction house, L the listing fees paid also by the seller, and S(P) the
shipping and handling costs paid by the buyer. The commission charges are a non-
decreasing function of the final price.
We develop the arbitrage conditions by considering a base auction that ends
successfully with a price of Pbase. Let C(Pbase) and S(Pbase) be the associated commission
and shipping and handling costs, respectively. Let Π = {1,…,k}, denote a set of k
“homogeneous” and “identical item” auctions with the following properties: (a) each and
every auction in the set Π ends before the base auction; (b) the time gap between every
pair of auctions, those in set Π and the base auction, is minimal i.e. all the auctions end
in a “near simultaneous” amount of time; and (c) k ≥ 2. Each auction is for a single item,
and no auction other than those in the set Π ends before the base auction. The terms
“homogeneous”, “identical item auction”, and “near simultaneous” are used to develop
the theoretical arguments in relation to arbitrage. Their mapping to practice, and the
ensuing caveats on their applicability are discussed later in the section.
We develop two forms of arbitrage conditions, termed seller arbitrage and buyer
arbitrage. The arbitrageurs are, in the former case sellers from set Π, and in the latter case
buyers from set Π.
3.1 Seller Arbitrage Principle
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No seller arbitrage condition is
Py – C(Py) – Ly ≤ Pbase + S(Pbase)
where
Px – C(Px) – Lx ≥ Py – C(Py) – Ly where x , y ∈ Π and Py – C(Py) – Ly ≥ Pi – C(Pi) – Li ∀ i ∈ Π – { x , y }
Proof:
Consider the seller of auction i. Let Vi be the value of the item to the seller and Li denote
the listing fees in auction i. Clearly, the seller is better off selling the item only if the net
proceeds from the auction, Pi - C(Pi) - Li, exceed Vi. The arbitrage opportunity presents
itself once the item is sold in auction i. This opportunity arises if the seller, in near
instantaneous time, can buy the same item in the base auction, but at a much cheaper total
cost. If successful, the seller is back in her original state of possessing the item, but with a
positive net profit. If unsuccessful, the seller is no worse off as participating as a buyer in
an unsuccessful auction does not impose any cost (since the time gap between auctions is
minimal, the costs associated with time spent in the base auction are 0). Suppose that
seller i wins the item at the base auction, incurring a cost of Pbase + S(Pbase). Thus the net
benefit to the seller of auction i from engaging in this “roundtrip” is Vi - Pbase- S(Pbase) +
Pi - C(Pi) - Li. As long as this net benefit exceeds Vi, seller i has an incentive to
participate in the base auction as a buyer and realize arbitrage profits. Of course, other
sellers who satisfy the same condition also have an incentive to participate in the base
auction. All such sellers will compete in the base auction as buyers.
Let x and y be such Px - C(Px) - Lx ≥ Py - C(Py) - Ly ≥ Pi - C(Pi) - Li. Note that x
and y represent the auctions in the set Π with the largest and the second largest net
proceeds to sellers. As these sellers compete in the base auction to realize arbitrage
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profits, the price of the base auction should increase at least to the point where all sellers
except seller x drop out. Hence the result.
If we make an assumption that the listing costs are zero, and further that a seller
can employ a “buy now at this price” option at no cost, then we can derive another set of
arbitrage conditions that we term buyer arbitrage principle. Zero listing cost implies that a
seller does not incur any costs if the item is not successfully auctioned. While this
assumption does not apply to eBay, the largest online auction market, it does provide a
useful theoretical benchmark to assess arbitrage opportunities.
3.2 Buyer Arbitrage Principle
No buyer arbitrage condition is
Pbase – C(Pbase) ≤ Py + S(Py)
where
Px + S(Px) ≥ Py + S(Py) where x , y ∈ Π and Py + S(Py) ≥ Pi + S(Pi) ∀ i ∈ Π – { x , y }
Proof:
Consider the buyer of auction i. It follows that the costs incurred by the buyer Pi + S(Pi)
do not exceed the buyer’s value, denoted as Vi, for the item. The arbitrage opportunity
presents itself once the buyer has successfully purchased the item in auction i. This
opportunity arises if the buyer, in near instantaneous time, can sell the same item at a
much higher price. If successful, the buyer is back in her original state, but with a
positive net profit. If unsuccessful, the buyer is no worse off as participating as a seller in
an unsuccessful auction does not impose any cost. Suppose the buyer of auction i sells the
item for a price P, incurring a cost of C(P) as commissions. The net benefit to the buyer
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of auction i from engaging in this “roundtrip” is P - C(P) - Pi - S(Pi). As long as this net
benefit is positive, buyer i has incentive to sell the item and realize arbitrage profits.
Consider the base auction, and suppose Pbase - C(Pbase) ≥ Pi + S(Pi). In such a case
the buyer i has an incentive to start an alternate auction, and offer a “buy now” option
with a price lower than Pbase. If buyer i can initiate this alternate auction prior to the
completion of the base auction, it will attract the individual who would otherwise bid and
win in the base auction. Of course, every buyer from the set Π can do the same as long as
the Pbase remains high.
Let x and y be such Px + S(Px) ≤ Py + S(Py) ≤ Pi + S(Pi). Note that x and y
represent the auctions with the smallest and the second smallest payments made by the
buyers in the auction set Π. Clearly buyer x can offer the lowest “buy now” price
amongst the buyers of auction set Π. To out compete others, she must offer a “buy now”
price no larger than what buyer y would have offered. Hence the result.
The preceding discussion specifies arbitrage opportunities available to parties that
take a position in the auction market. In other words, these arbitrage opportunities are
available only to parties that consider buying or selling items via auctions, even if
arbitrage opportunities do not present themselves. However, mispricings between posted-
prices and auction prices can provide opportunities for third-party arbitrageurs who
would otherwise not engage in the auction market, if the listing fees were zero. The
mechanics are as described before and the process is as follows: An arbitrageur initiates
an auction with a reserve price that is the sum of the posted-price, commissions (fees paid
to the auction house if the auction is successful), and the cost to obtain the item from the
retailer. If unsuccessful, the arbitrageur is no worse-off as she does not purchase the retail
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item unless it is sold in the auction. If successful, the arbitrageur can realize risk-free
profits. Such an arbitraging strategy can be effective when there are significant location-
based price discrepancies. Farming products, for example, are significantly cheaper in
rural communities than in urban locations. Also, occasionally there are deep-discounts in
certain physical locations for a period of time (such as a weekend) when the retail price,
along with the associated costs, are significantly lower than the price at which it can be
sold in an auction. When there are no legal restrictions for resale (reselling software
purchased with an educational discount for the full retail price, for instance, is illegal and
thus not risk-free), arbitrage arguments can be employed to specify price relationships
between retail and auction prices.
Our development of the arbitrage principles is rooted in idealized settings, where
“homogenous” and “identical item” auctions take place, and where auctions are plentiful
in that the time gap between the ending times of any two successive auctions is very
small. What caveats do these assumptions impose on the practical applicability of the
arbitrage principles?
Consider the notion of identical items. This implies perfect substitutability
between all items that are available in the analyzed pool of auctions. This clearly rules
out a direct application to used items. Our arbitrage analysis can be applied to new items
that are described identically (make, model, year etc.) in all the auctions.
The homogeneity assumption employed in our analysis translates to bidders
perceiving the sellers as undifferentiated, except in the price. This is not a reality that
correctly paints the picture of current online auctions. Given the anonymity of sellers and
occurrence of fraud, consumers do perceive a ‘risk’ in engaging in online auctions. In
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fact, current evidence points to a willingness of consumers to pay a premium for auctions
with high seller ratings. Seller rating is a composite score that is compiled based on a
seller’s prior transaction history with other consumers, and is indicative of the seller’s
reputation and hence the trust that consumers place on the seller. How does it impact the
process of arbitrage? Consider the second-step execution of the arbitrage process (buy
transaction for sellers, and sell transaction for buyers). In the case of seller arbitrage, the
arbitrageur can significantly mitigate the risks by bidding only in auctions from highly
reputed sellers. While this may restrict the pool of sellers to arbitrage from, the same
basic principles would continue to be applicable. In the case of buyer arbitrage, the risks
arise from nonpayment by a buyer and from a buyer backing out of the transaction. In
most online auctions, sellers typically ship the item only after the payment from the buyer
can be confirmed. In case a buyer backs out after the completion of the auction, the loss
faced by the seller is in terms of wasted effort, and the effort involved in initiating
another auction. To the extent that the processes of initiating, executing, and managing
online auctions are automated, these costs in the buyer arbitrage case should be minimal.
The assumption that all the auctions end in a “near simultaneous” amount of time
deals with the liquidity of online auction markets. As online auctions become more
commonplace and the volume of transactions increase, this assumption should not place a
significant hurdle for the practical use of our arbitrage principles. Note that when we talk
of liquidity, we mean the combined volume of transactions from all online auction
houses, and not just from a single auction house such as eBay. This is because the sell
and buy transactions do not have to be executed in the same auction house, but can
spread across different auction houses as conditions warrant.
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One might argue that, regardless of the caution exercised by arbitrageurs and
effective mechanisms enforced by auction houses to prevent deviant behavior, there may
continue to be risks and additional costs to engaging in arbitrage. Simple modifications to
our arbitrage principles can accommodate any additional costs that may arise from the
arbitrage activity. The notion of risk-less arbitrage developed in the current work would
need to be expanded to include risks in online auctions. In such a model, a “risky
arbitrage” opportunity exists when the potential gains are significantly larger than the
underlying risk. If arbitrage is persistent and cumulative gains are potentially substantial,
the presence of risk may spawn the development of “specialists” willing to hedge the
risks of arbitrage. It would be reasonable to state that the element of risk would only
stretch the concept of arbitrage from risk-free to risky arbitrage, but does not obviate its
important role in driving the online auction markets towards allocative efficiency.
4. Empirical Analysis
In this section we report on our empirical study that examines the existence of arbitrage
opportunities in online auctions hosted by eBay, the largest online auction house. The
data was collected for a two-week time period in early 2002 for three items described in
Table 2. All the items were posted as new and described identically for potential buyers.
The significant average price differential amongst the items, and the volume of observed
transactions for each drove the choice of the particular items we selected for the analysis.
Table 2: Auction Items
Item Average Final Price Number of Auctions
Olympus C-700 Digital Camera $383.23 119 Palm Vx PDA $138.57 378 DVD movie Moulin Rouge $15.03 175
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In designing the empirical methodology we were particularly cognizant about
utilizing only the information that is publicly and rather easily available to all the buyers
and sellers. Reliance on publicly available information makes the efficiency evaluations
both robust and verifiable. The following data items were collected for each auction: final
bid price, seller rating, ending time, listing fees, shipping and handling fees, and
commission fees. The seller rating information consists of both positive and negative
number of comments from unique users, and is part of the feedback mechanism
implemented by eBay.
4.1 Hypothesis Development
In empirically evaluating the existence of arbitrage, we limit our attention to the seller
arbitrage condition. This is mainly due to the significant listing fees charged by eBay.
The arbitrageur in the seller arbitrage condition realizes risk-free profits by engaging in a
purchase transaction immediately after successfully selling the item. To realize arbitrage
profits, these transactions can take place at different auction houses. However, in our
analysis we restrict all transactions to eBay as over 90% of all online auctions take place
at this auction house. Even though an evidence of efficiency in eBay transactions is not
indicative of overall efficiency of the online auction markets; but an evidence of
inefficiency is.
The evaluation of seller arbitrage conditions on eBay necessitates specification of
two important parameters: nature of the seller from whom the subsequent purchase is
made, and the time interval between the sell and buy transactions. The former may
impose risks in undertaking a buy transaction to realize arbitrage, and the latter may
impose ‘waiting costs’ if the time interval between sell and buy transactions is
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substantially large. For our baseline analysis, we restrict the set of sellers that an
arbitrageur considers to those with a positive rating of 1000 or above and a negative
rating of no worse than the arbitrageur, and the limit of the buy transaction to be within
24 hours after the sell transaction is successfully completed. Ba and Pavlou (2002)
suggest that approximately 470 responses are indicative of a long selling history at eBay.
Thus the seller rating of positive 1000 should serve as a reasonable cutoff to determine a
safe arbitrage process as it indicates that the seller was in good stead with a large number
of previous buyers. Note that we also limit the negative number of comments to those
with no worse than the seller of the base auction to ensure that when buying back the
item, no add-on risks were perceived as the items were bought back from “better”
reputated sellers. Our temporal constraint is that once an item is sold the seller is
restricted to one day to subsequently buy back the item to realize arbitrage profits. We
selected a time frame of 24 hours as shipping an item usually takes at least a day, and a
typical auction in our set lasted about 5 days. In this environment, a time lag of 24 hours
should not impose any significant time-based costs to the arbitrageur. While our
parameter setting are reasonable within the current operating environment of online
auctions, our choices were ultimately dictated by liquidity concerns. Significantly lower
time window and/or higher cutoff for seller rating will reduce the number of observations
to draw conclusions from. As the online auction market liquidity increases, one can fine-
tune these parameters to tighten the arbitrage conditions. We do conduct a sensitivity
analysis by lowering the time window and increasing the minimum seller rating by a
factor of two, and evaluate the ensuing impact of the overall efficiency conclusions.
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Seller Arbitrage Hypothesis: There are significant seller arbitrage opportunities when
the buy transaction is with a seller whose positive rating is at least 1000 and the negative
rating is no worse than the buyer, and the time lag between sell and buy transactions is
no more than 24 hours.
4.2 Data Analysis
To test the hypothesis, we first compute the arbitrage numeric using the following
process. For each item, we select the subset of successfully completed auctions with a
positive seller rating of 1000 or more. Each of these is labeled as a base auction. For each
base auction, we identify the set of auctions that were successfully completed in the
previous 24-hour time period, and where the negative rating of the seller is no better than
the seller of the base auction. These are labeled the candidate auctions. If the number of
candidate auctions for a base auction is less than two, then no arbitrage numeric is
computed for that base auction. For the remaining base auctions, we compute the value Pi
- C(Pi) – Li – Pbase – S(Pbase) for each auction i that has negative seller rating that is no
better than the seller of the base auction. These computed numbers are rank ordered, and
the second highest number in the ordered list is the arbitrage numeric.
Note that the arbitrage numeric could be positive or negative. When positive, it
implies that one of the sellers of the candidate auction could realize arbitrage profits by
leveraging the base auction. Interestingly, while a negative value indicates absence of
arbitrage, the magnitude of negative number provides no meaningful information.
However, the value of positive numbers does provide useful information in that it
indicates the magnitude of arbitrage present. Table 3 provides summary statistics
regarding arbitrage for each of the items. We perform a Z-test to evaluate the significance
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of positive values in the set of computed arbitrage numbers. The results are illustrated in
Table 4 and indicate that the proportion of base auctions amenable to arbitrage is
statistically significant. The lower limit for the 95% confidence interval for the
proportion with positive arbitrage is significantly larger than zero, highlighting
inefficiencies amongst the auctions for each of the items. For the lower-priced item, both
the proportion and the average arbitrage profits are small. This can be attributed to
transaction cost (shipping/handling, commission and listing fees) being significant in
relation to the price of the item. For the high-priced item, while the average arbitrage
profits are the highest, they are not substantially different from the mid-priced item. But
the prevalence of arbitrage is significantly lower for the most expensive item in
comparison to the mid-priced item. It appears that buyers seem to exercise caution in
bidding for the high-priced item. Thus a mid-priced item appears to serve as a useful
instrument to engage in arbitrage activity as both the prevalence and average net proceeds
are substantial.
Table 3: Seller Arbitrage Statistics 24-Hour Time Window and 1000 Seller Rating
Statistics Auction Item # of base
auctions with at least
two prior auctions
% of base auctions with
positive arbitrage profits
average arbitrage profits
(only positive arbitrage is considered)
standard deviation for
average arbitrage profits
(only positive arbitrage is considered)
Olympus C-700 Digital Camera
79 43.04% $35.03 $22.44
Palm Vx PDA 63 84.13% $32.04 $14.98 DVD Movie: Moulin Rouge
49 16.33% $0.83 $0.70
19
Table 4: Z-test Result for 24-Hour Time Window and 1000 Seller Rating
Z-test for proportions of base auctions with positive arbitrage profits 95% confidence interval for
the proportion Auction Item Cut-off proportion (Q) where test
result is significant (p < 0.05). Null hypothesis: Proportion of
base auctions with positive arbitrage profits <= Q Lower limit Upper limit
Olympus C-700 Digital Camera
0.343 0.321 0.540
Palm Vx PDA 0.752 0.751 0.932 DVD Movie: Moulin Rouge
0.095 0.06 0.267
We also conducted a sensitivity analysis by narrowing the time window and
increasing the seller rating for base auctions. Tables 5 and 6 illustrate the result for the
12-hour case. The results from setting the minimum seller rating to 2000 are shown in
Tables 7 and 8. The results from this sensitivity analysis continue to support our main
findings that inefficiency does exist in current online auctions.
Table 5: Seller Arbitrage Statistics and Z-test result for 12-Hour Time Frame and 1000 Seller Rating
Statistics Auction Item # of base
auctions with at
least two prior
auctions
% of base auctions with
positive arbitrage profits
average arbitrage profits
(only positive arbitrage is considered)
standard deviation for
average arbitrage profits
(only positive arbitrage is considered)
Olympus C-700 Digital Camera
79 36.71% $30.72 $19.07
Palm Vx PDA 63 63.49% $27.03 $13.03 DVD Movie: Moulin Rouge
49 12.24% $0.84 $0.57
20
Table 6: Z-test Result for 12-Hour Time Window and 1000 Seller Rating
Z-test for proportions of base auctions with positive arbitrage profits
95% confidence interval for the proportion
Auction Item Cut-off proportion (Q) where test result is significant (p < 0.05). Null hypothesis: Proportion of
base auctions with positive arbitrage profits <= Q Lower limit Upper limit
Olympus C-700 Digital Camera
0.284 0.261 0.473
Palm Vx PDA 0.531 0.516 0.754 DVD Movie: Moulin Rouge
0.065 0.031 0.214
Table 7: Seller Arbitrage Statistics and Z-test result for 24-Hour Time Frame and 2000 Seller Rating
Statistics Auction Item # of base
auctions with at
least two prior
auctions
% of base auctions with
positive arbitrage profits
average arbitrage profits
(only positive arbitrage is considered)
standard deviation for
average arbitrage profits
(only positive arbitrage is considered)
Olympus C-700 Digital Camera
64 40.63% $35.89 $24.63
Palm Vx PDA 54 90.74% $33.55 $14.45 DVD Movie: Moulin Rouge
30 20% $1.02 $0.70
Table 8: Z-test Result for 24-Hour Time Window and 2000 Seller Rating
Z-test for proportions of base auctions with positive arbitrage profits
95% confidence interval for the proportion
Auction Item Cut-off proportion (Q) where test result is significant (p < 0.05). Null hypothesis: Proportion of
base auctions with positive arbitrage profits <= Q Lower limit Upper limit
Olympus C-700 Digital Camera
0.311 0.286 0.527
Palm Vx PDA 0.822 0.830 0.985 DVD Movie: Moulin Rouge
0.107 0.057 0.343
21
5. Conclusions
Based on the principles of arbitrage, we develop a set of efficiency criteria to evaluate the
auction activity of new and identically described items. Two arbitrage principles, seller
arbitrage and buyer arbitrage, are developed. These principles can be employed to
evaluate the price behavior of temporally proximate auctions to derive the operating
efficiency of these auctions. The seller arbitrage conditions can be directly applied within
the current operating environment of most online auctions. The buyer arbitrage principle
applies to the case when the auction house does not impose a listing fee on the sellers.
The application of the seller arbitrage principle to three variably priced items auctioned in
eBay reveal the presence of allocative inefficiency. We find that the mid-priced items are
ideal targets for arbitrageurs as both the prevalence and the average arbitrage profits are
substantial. Arbitrage profits for low priced items are impeded by the relatively
significant transaction costs. For high priced items potential consumers seem to exercise
caution in their bidding behavior. While we can make a case for the presence of
inefficiency for the three items we explicitly evaluated, we cannot paint the overall online
auction markets with the same broad brush of inefficiency. Though our evidence is quite
telling, further evaluations that consider a larger set of goods that are traded are clearly
needed to accurately gauge the overall allocative efficiency of these markets.
A compelling evidence of allocative inefficiency raises the immediate question of
what corrective actions to take in order to move these markets towards efficiency. This
issue is deserving of further study. As mentioned earlier, allocative inefficiency might be
attributed to factors such as herd behavior, bidder timing constraints, and information
asymmetries. The online auction houses can pursue initiatives that take these factors into
22
consideration. These initiatives can serve as useful starting points to drive the online
auction markets towards allocative efficiency.
A number of other issues also deserve further investigation. Extensions of our
arbitrage principles to incorporate transaction risks can enable efficiency evaluations in
more realistic settings. Given the predominance of used-item transactions in online
auctions, generation of arbitrage conditions to evaluate these auctions can be useful. This
can be achieved if, for instance, the items can be ‘value clustered’ based on information
made available to bidders. If item value comparisons across clusters can be objectively
performed, at least in a relative sense, one can begin to derive arbitrage conditions.
Arbitrage arises when a trader can sell a relatively lower valued item at high price, and
subsequently re-purchase a higher valued item at a low price within a relatively short
period of time. As online auction markets gain traction, and as trading activity increases,
we expect interest on how efficiently these markets function to grow as well.
23
References
Alsemgeest, P., Noussair, C., and Olson, M. “Experimental Comparison of Auctions Under Single- and Multi-Unit Demand,” Economic Inquiry, Vol. 36, No. 1, 1998, pp. 87-97.
Ba, S., “Establishing Online Trust Through a Community Responsibility System,”
Decision Support Systems, Vol. 31, No. 3, 2001, pp. 323-336. Ba, S. and P.A. Pavlou, “Evidence of the Effect of Trust Building Technology in
Electronic Markets: Price Premiums and Buyer Behavior,” MIS Quarterly, Vol. 26, No. 3, 2002.
Bajari, P. and Hortacsu, A. "Auctions Models When Bidders Make Small Mistakes:
Consequences for Theory and Estimation," Working Paper, Stanford University, 2001.
Bajari, P. and Hortacsu, A. "The Winner's Curse, Reserve Prices and Endogenous Entry:
Empirical Insights From eBay Auctions," Working Paper, Stanford University, 2002. Bajari, P. and Ye, L. “Competition Versus Collusion on Procurement Auctions:
Identification and Testing,” Working Paper, Stanford University, 2001. Bapna, R., Goes, P., and Gupta, A. “A Theoretical and Empirical Investigation of Multi-
item On-line Auctions,” Information Technology and Management, Vol. 1, No. 1, 2000, pp. 1-23.
Bapna, R., Goes, P., and Gupta, A. “Online Auctions: Insights and Analysis,”
Communications of the ACM, Vol. 44, No. 11, 2001, pp. 42-50. Bapna, R., Goes, P., and Gupta, A. “Comparative Multi-item Online Auctions: Evidence
from the Laboratory,” Decision Support Systems, Vol. 32, No. 1, 2001, pp. 135-153. Bapna, R., Goes, P., Gupta, A., and Karuga, G. “Optimal Design of the Online Auction
Channel: Analytical, Empirical and Computational Insights,” Working Paper, University of Connecticut, 2002.
Brynjolfsson, E. and M. Smith, “Frictionless Commerce? A Comparison of Internet and
Conventional Retailers,” Management Science, Vol. 46, No. 4, 2000, pp. 563-585. Boyan, J. and Greenwald, A. “Bid Determination in Simultaneous Auctions,”
Proceedings of the Third ACM Conference on Electronic Commerce, Tampa, October, 2001, pp. 210-212.
24
Charupat, N. and M.A. Milevsky, “Mortality Swaps and Tax Arbitrage in the Canadian Insurance and Annuity Markets,” Journal of Risk and Insurance, Vol. 68, No. 2, 2001, pp. 277-302.
Cox, J., S. Ross., and M. Rubinstein, “Option Pricing: A Simplified Approach,” Journal
of Financial Economics, 1979, 7, pp. 229-263. Cox, J. and Isaac, R. “In Search of the Winner’s Curse,” Economic Inquiry, Vol. 22, No.
1, 1984, pp. 579-592. Cox, J., Smith, V., and Walker, J. “Theory and Behavior of Multiple Unit Discriminative
Auctions,” Journal of Finance, Vol. 39, No. 4, 1984, pp. 983-1010. Dholakia, U.M., and K. Soltysinski., “Coveted or Overlooked? The Psychology of
Bidding for Comparable Listings in Digital Auctions,” Marketing Letters, Vol. 12, No. 3, 2001, pp. 225-237.
Dyer, D., Kagel, J., and Levin, D. “A Comparison of Naïve and Experienced Bidders in
Common Value Offer Auctions: A Laboratory Analysis,” The Economic Journal, Vol. 99, No. 1, 1989, pp. 108-115.
Greenwald, A. and Boyan, J. “Bidding Algorithms for Simultaneous Auctions,”
Proceedings of the Third ACM Conference on Electronic Commerce, Tampa, October, 2001, pp. 115-124.
Guo, X. “An Optimal Strategy for Sellers in an Online Auction,” ACM Transactions on
Internet Technology, Vol. 2, No. 1, 2002, pp. 1-13. Hendricks, K. and Porter, R. “An Empirical Study of an Auction with Asymmetric
Information,” The American Economic Review, Vol. 78, No. 5, 1988, pp. 865-883. Hendricks, K., Porter, R., and Boudreau, B. “Information, Returns and Bidder Behavior
in OCS Auctions: 1954-1969,” Journal of Industrial Economics, Vol. 35, 1987, pp. 517-542.
Julien, B., Kennes, J., and King, I.P. “Auctions and Posted Prices in Directed Search
Equilibrium,” Topics in Macroeconomics, Vol. 1, No. 1, 2001, pp. 1-14. Kagel, J. and Levin, D. “The Winner’s Curse and Public Information in Common Value
Auctions,” The American Economic Review, Vol. 76, 1986, pp. 894-920. Kauffman, R.J., and C.A. Wood, “Doing Their Bidding: An Empirical Examination of
Factors that Affect a Buyer’s Utility in Internet Auctions,” Working Paper, 2001, University of Minnesota.
25
Lind, B. and Plott, C. “The Winner’s Curse: Experiments with Buyers and with Sellers,” The American Economic Review, Vol. 81, No. 1, 1991, pp. 335-346.
Matsumoto, Y. and Fujita, S. “An Auction Agent for Bidding on Combinations of Items,”
Proceedings of the 5th International Conference on Autonomous Agents, Montreal, Canada, May-June, 2001, pp. 552-559.
McAfee, R.P., “Mechanism Design by Competing Sellers,” Econometrica, Vol. 61, No.
6, 1993, pp. 1281-1312. Mehta, K. and Lee, B. “Efficiency Comparison in Electronic Market Mechanisms: Posted
Price versus Auction Market,” Proceedings of WISE, Charlotte, NC, 1999a. Mehta, K. and Lee, B. “An Empirical Evidence of Winner’s Curse in Electronic
Auctions,” Proceedings of ICIS, Charlotte, NC, 1999b. Merton, R., “Theory of Rational Option Pricing,” Bell Journal of Economics and
Management Science, Vol. 4, No. 1, 1973, pp. 141-183. Milgrom, P. and Weber, R. “A Theory of Auctions and Competitive Bidding,”
Econometrica, Vol. 50, 1982, pp. 1089-1122. Modigliani, F and M.H. Miller, “The Cost of Capital, Corporation Finance and the
Theory of Investment,” American Economic Review, Vol. 48, No. 3, 1958, pp. 261-297.
Oh, W., “C2C Versus B2C: A Comparison of the Winner’s Curse in Two Types of
Electronic Auctions,” IJEC, Vol. 6, No. 4, 2002. Rao, A.R. and K.B. Monroe, “Causes and Consequences of Price Premiums,” Journal of
Business, Vol. 69, No. 4, 1996, pp. 511-535. Rothkopf, M.H. and Harstad, R.M. “Modeling Competitive Bidding: A Critical Essay,”
Management Science, Vol. 40, No. 3, 1994, pp. 364-384. Rubenstein, M., “Rational Markets: Yes or No? The Affirmative Case,” Financial
Analysts Journal, May/June 2001, pp. 15-29. Sharpe, W. and G. Alexander, Investments, 4th edition, 1990, Prentice Hall, Englewood
Cliffs, NJ. Snyder, J.M. “Online Auction Fraud: Are the Auction Houses Doing All They Should or
Could to Stop Online Fraud?” Federal Communications Law Journal, Vol. 52, No. 2, 2000, pp. 453-472.
26
Thiel, S. “Some Evidence on the Winner’s Curse,” The American Economic Review, Vol. 78, 1988, pp. 884-895.
Tung, Y.A., R.D. Gopal, and A.B. Whinston, “Multiple Online Auctions: Inaction and
Reaction,“ IEEE Computer, Vol. 36, No. 2, 2003, pp. 100-102. Vakrat, Y. and Seidmann, A. “Can Online Auctions Beat Online Catalogs?” 12th
Proceedings of International Conference on Information Systems, Charlotte, North Carolina, 1999.
Varian, H.R., “The Arbitrage Principle in Financial Economics,” The Journal of
Economics Perspectives, Vol. 1, No. 2, 1987, pp. 55-72. Wang, W., Hidvegi, Z., and Whinston, A.B. “Economic Mechanism Design for Securing
Online Auctions,” Proceeding of International Conference of Information Systems, December, Brisbane, Australia, 2000.
27