Allocative Efficiency Considerations in Online Auction Markets€¦ · allocative inefficiency....

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


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


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

15

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



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

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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


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


auctions with at

least two prior

auctions









79 36.71% $30.72 $19.07


49 12.24% $0.84 $0.57

20


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



0.284 0.261 0.473


0.065 0.031 0.214

Table 7: Seller Arbitrage Statistics and Z-test result for 24-Hour Time Frame and 2000 Seller Rating


auctions with at

least two prior

auctions









64 40.63% $35.89 $24.63


30 20% $1.02 $0.70


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



0.311 0.286 0.527


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

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