When is auctioning preferred to posting a fixed selling price?
Robert Zeithammer
Pengxuan Liu
Graduate School of Business
Tepper School of Business
University of Chicago
Carnegie-Mellon University
November 1, 2006
Abstract: On eBay, identical goods are often sold simultaneously by two different mechanisms
– auctions and posted prices. This coexistence of two mechanisms is a puzzle because other
consumer markets tend to specialize in just one trading mechanism. We propose and empirically
test several possible explanations of this puzzle: 1) randomization arising from seller indifference
2) second-degree price-discrimination 3) sorting of both buyers and sellers into two separate submarkets, and 4) seller heterogeneity. In the explanation based on seller heterogeneity, we develop
a new theory of mechanism-choice based on differences between the structure of mechanismspecific costs: auctioning several identical units of a good separately involves a variable per-unit
cost due to risk, waiting and monitoring. In contrast, the demand-research necessary for postedpricing involves a cost which is fixed across multiple units. Therefore, we predict that usage of
posted prices in a given category should be positively correlated with seller scale and
specialization in that category. The empirical test is conducted on a unique dataset that captures
individual seller behavior across categories, allowing inference about sources of seller
heterogeneity. The data does not offer strong support for the first three potential explanations
because 1) choice of selling mechanism is not random either across or within seller 2) postedprice sales do not involve a consistent premium over auction sales, and 3) frequent eBay buyers
use both mechanisms. On the other hand, we do find that both observed and unobserved seller
heterogeneity are important correlates of mechanism-choice. The findings have implications on
the age-old marketing question of how to sell consumer goods. In particular, we confirm the
intuition that auction are used when the seller needs to establish a separate price for every item
sold.
Contact: Robert Zeithammer, Graduate School of Business, University of Chicago, 5807 South
Woodlawn Avenue, Chicago, IL 60637. e-mail: [email protected].
I. Introduction
On the dominant online-auction site eBay, identical goods are often sold simultaneously by two
different mechanisms – auctions and posted prices. For example, approximately a third of Canon
Point & Shoot Digital Cameras (CP&SD) are sold by pure auction, another third are offered at
fixed posted prices, and another third are offered by posted prices with an option to place a lower
bid and convert the sale into a pure auction (the so-called Buy-It-Now auction mechanism).
Auctioning and posted-price selling are both widely used selling-mechanisms in modern
markets, but they rarely coexist in the same narrowly-defined market like eBay CP&SD. In this
paper, we empirically investigate several possible explanations of this coexistence puzzle using a
unique dataset that focuses on the CP&SD category. The dataset is unique because it captures not
only which cameras are sold by which mechanism by the CP&SD sellers, but also whether and
how do those same sellers sell other goods on eBay.
Our analysis suggests that several obvious explanations do not explain the coexistence
puzzle: First, it does not seem that each seller is indifferent between the two mechanisms and so
chooses randomly on a sale-by-sale basis. Instead, most sellers stick to just one selling
mechanism for all their cameras. Randomization across sellers can also be ruled out because we
find that the mechanism used is correlated with seller characteristics. Second, we do not find
evidence of second-degree price discrimination, in which some buyers pay a premium for
posted-price buying in exchange for convenience and reduced risk, while other buyers are
willing to endure the additional hassle to pay less by buying through an auction. In contrast with
such a discrimination prediction, we find that posted-price buying does not involve a significant
premium consistent across different camera models. Instead, only rare camera-models involve
significant premia, with the profitability of discrimination apparently eliminated by intense
competition among the hundreds of sellers who sell popular/high-volume camera-models.
Finally, given that most sellers use just one mechanism, it is possible that so do the buyers, and
eBay really consists of two separate markets. This “sorting” explanation does not fit the data
either – we find that many camera buyers also recently bought other goods on eBay, and most of
such multi-item buyers have used multiple mechanisms to do so.
The main empirical regularity we find is that sellers who sell multiple cameras tend to
stick to just one selling mechanism. Why does seller A choose to sell all his CP&SD cameras by
posted prices while seller B sells them by auction? Does seller A carry subtly different products
1
from seller B, for example new versus used cameras? Or does seller A differ from seller B in
scale, experience with selling cameras, or some other characteristic? Or does each seller simply
have an idiosyncratic personal preference for one of the mechanisms? To investigate the sources
of variance in selling mechanism across sellers, we need a theory of rational choice between
auctioning and posting a fixed selling price. Interestingly, such theories are rare in the literature:
while the optimal use of each mechanism has been extensively analyzed, a seller not apriori
committed to either mechanism is left largely helpless. The literature does suggest, however, that
auctions and posted prices are equivalent or very similar in the revenue they generate (Wang 93,
Kultti 99). Therefore, a fruitful theory of profit-maximizing choice between auctioning and
setting posted prices is likely to emerge from considerations of differential costs of using the two
mechanisms. For example, Wang (93) considers the additional display costs of posted-price
selling versus the costs of running a live auction. We propose a theory based on costs faced by a
multi-item seller. The key new assumption of our theory is that sellers are uncertain about
demand, and neither figuring out the optimal posted price through market research, nor taking on
the risk of low auction-revenue and waiting for the auction’s conclusion, are costless. There is a
fundamental difference in the structure of these mechanism-specific costs when the seller has
multiple items to sell: finding the optimal price involves a fixed cost that can be spread over
several identical items, while auctioning involves a variable cost for each auction conducted.
This difference in the structure of costs implies that the larger and more homogeneous the
seller’s inventory, the more likely it is that the seller uses posted prices, and that sellers with
more experience should also use posted prices more often, because they know more about the
market and can thus price more easily.
eBay is a particularly good institution for studying seller choice among selling
mechanisms, because it literally offers the seller a menu of mechanisms to choose from for each
sale. Therefore, an analysis of variance in selling mechanisms across individual listings can
reveal which of the observable factors seem important to mechanism-choice. We test our
inventory-based theory by utilizing the unique feature of the CP&SD camera dataset: for every
seller, we know not only how she tends to sell cameras, but also whether and how she sells
Electronics, Books, Home & Garden items, and all other goods sold on eBay. Moreover, by
observing every transaction in the market for seven weeks, we can learn a lot about each seller’s
inventory, both in the focal camera category as well as in all other eBay categories. The
2
comprehensive view of each seller’s eBay activities allows us to separate category-specific
factors - like the scale of CP&SD inventory and the seller’s specialization in the category - from
global factors like the overall scale of the seller. In addition, knowing how each camera-seller
sells other goods allows us to control for each seller’s idiosyncratic taste for each selling
mechanism. The empirical analysis provides evidence for our theory’s relevance to eBay sellers,
and it also points to the importance of individual-specific taste-shocks which are not correlated
with observable seller characteristics. While quite important, these “taste-shocks” do not explain
all the variance in the data because sellers who sell cameras by only one mechanism do not
necessarily sell everything else by that same mechanism. Only a small part of the variance can be
explained by different sellers selling different goods.
Understanding how eBay sellers make the choice between auctioning and posted prices
can shed light on the fundamental marketing question of how to sell products to consumers. It is
clear that the scope of auctions has expanded in a modern economy thanks to the Internet, so it is
important to characterize when their use is beneficial to the seller. Such a characterization is
unlikely to emerge from analyses of traditional markets that tend to specialize in only one
mechanism. When cataloguing traditional auction markets, one quickly discovers that the set of
goods traditionally sold by auction is extremely diverse: fresh flowers at the wholesale level,
belongings of a deceased person, the daily catch of fish at the wholesale level, famous paintings,
fine wine, oil tracts in the Mexican Gulf, used farming machinery, fine diamonds, computing
equipment of a bankrupt firm, livestock, US Treasury Bills etc... This diversity makes a productspecific “auctionability” trait elusive: in the words of Paul Milgrom, “the only clear common
denominator for the kinds of objects sold at auction is the need to establish individual prices for
each item sold” (Milgrom 1989b). This paper proposes and tests a theory of auctionability which
is not inherent to the product itself. Following Milgrom’s idea, we study costs of establishing a
price for each item sold, and we find that these costs differ across the two mechanisms
depending on the seller’s experience and inventory.
The paper is organized as follows: Section II introduces the empirical phenomenon of
choice among selling mechanisms to focus the subsequent theoretical discussion in Section III.
Section IV then presents the analysis of eBay data, Section V discusses evidence against two
eBay-specific alternative explanations of the coexistence puzzle, and Section VI concludes.
3
II. Choice among selling mechanisms on eBay
eBay is not solely an auctioneer anymore, it has expanded to allow classified posted-price offers
as well. Sellers can now select from three different selling mechanisms, seemingly designed to
span the continuum between auctioning and posted-price selling. At the auction end of the
spectrum, sellers can sell their items by the ascending English auction facilitated by eBay’s
proxy-bidding system. Moving towards posted-price selling, the auction-sellers can also include
an option to buy immediately by using the “Buy-It-Now” (BIN) price, a hybrid mechanism
hereafter called “BIN auction”. As soon as bidding begins, this option disappears, reverting the
selling mechanism towards the pure auction. Finally, the sellers can simply post a fixed price by
means of a BIN listing without the option to bid. Throughout this paper, the last two mechanisms
will be called “posted-price” mechanisms, with eBay’s term “fixed-price” reserved for only the
last mechanism that most resembles traditional classified selling. The theoretical focus of this
paper is on guiding the choice between pure auctions and posted prices, not on the sub-choice
between BIN auctions and fixed posted prices. However, the empirical analysis will keep the two
eBay’s posted-price mechanisms completely separate, and it will remain agnostic about their
precise relationship. To complete the description of options available to eBay sellers, it is also
necessary to mention eBay “stores”, in which sellers can post fixed-price offers indefinitely for a
fraction of the normal listing cost after paying a monthly subscription fee. Store-listings are not
visible or searchable from the main eBay site, so their exposure to buyers is dramatically
reduced, and they will be ignored in this paper.
eBay is an ideal setting for studying the sellers’ choice among selling mechanisms
because all listings are offered to the same buyers regardless of mechanism chosen by the seller,
and eBay charges the seller almost the same amount for using each mechanism. The only
difference in accounting costs charged by eBay is that the BIN auction and fixed-price
mechanisms cost 5-25 cents (depending on the level of BIN price) more than a pure auction – a
negligible difference in the total accounting cost of selling which includes a listing fee as well as
a commission.1
The eBay situation is quite different from traditional markets, which tend to coordinate
on only one selling mechanism. Why did the traditional markets before 1995 tend to specialize in
1
For example, suppose you list an item for posted-price sale, asking for $20. Then, your listing fees will be 60 cents
baseline fee plus 10 cents for the BIN option. If the item sells, you will also pay eBay a commission of 5.25 percent,
so $1.05. Therefore, conditional on selling the item, using the BIN option adds only 6 percent to your cost.
4
one mechanism while eBay can use multiple mechanisms? One can speculate that eBay’s use of
auctions along with the fixed-price mechanism (used in traditional classifieds offered by
newspapers) is possible because of the reduced costs of auctioning due to the telecommunication
technology of the Internet that cheaply brings geographically dispersed bidders together.
Interestingly, the rise of eBay was not the first time in history when emergence of a more
efficient communication medium enlarged the scope of auctions: One of the most long-lasting
and geographically pervasive uses of auctions – selling the estates of bankrupt or deceased
persons - arose in England and France around 1650, as soon as there were newspapers to
efficiently advertise such sales to the public (Learmount 1985).
The puzzle that motivates the rest of this paper is that in the CP&SD camera data, all
three mechanisms are used to a significant degree (33% of listings are pure auctions, 37% are
BIN auctions, and 30% are fixed-price). This product-category is not special in this regard, we
have found significant shares of all three mechanisms in many other eBay categories. The next
section discusses several possible explanations of this coexistence.
III. Why do auctions and posted prices coexist in the same market?
Explanation 1: Sellers are indifferent
Suppose that a profit-maximizing seller faces a steady stream of risk-neutral buyers with private
valuations for the good. The seller can behave like a store-owner, post a fixed price and wait
until a buyer with high-enough valuation of the object appears. Alternatively, he can behave like
an auctioneer, set a future date of an auction and invite all buyers arriving before that date to
participate. Assume further that the seller faces the same costs regardless of mechanism, so his
decision comes down to differences in revenue. Wang (1993) shows that in such a stylized
world, the optimal auction will generate the same expected revenue as the optimal posted price.
Therefore, the seller is indifferent between the mechanisms. Kultti (1999) extends the revenueequivalence result to compare selling of many identical objects by repeated auctions and posted
prices, and the possibilities of co-existence of the two mechanisms. In his model, there are many
buyers and many sellers, and they meet repeatedly to trade. In every period, sellers choose how
to sell and buyers decide which mechanism they prefer to buy through. Kultti shows that there is
always an equilibrium, in which both mechanisms coexist by virtue of generating the same
expected revenue, and he remarks that auctions and posted prices are thus “practically
5
equivalent” mechanisms of trading. In summary, the revenue equivalence results suggest that
Adam Smith’s invisible hand is equally strong regardless of the glove it is wearing: in each
mechanism, the seller sets the rules of trading to maximize expected revenue subject to the same
fundamental market constraint that demand equals supply, and this constraint is strong enough to
force the expected revenue to be on average the same across mechanisms, at least under some
assumptions.
It should be noted that the assumptions of Wang and Kultti are not completely innocuous
because in the canonical auction model of N bidders participating in a single-shot auction, the
expected revenue from a second-price sealed-bid auction with an optimal reserve-price exceeds
not only the expected revenue from posted-price selling, but also the expected revenue from any
other direct revelation mechanism as shown by Myerson (1981). Therefore, potential differences
in mechanism-specific revenues should be considered in any theory of mechanism-choice.
Nevertheless, the above revenue-equivalence results suggest the baseline explanation for the fact
that all three selling mechanisms are used to sell essentially the same goods on eBay: the sellers
are indifferent between posted-price selling and auctioning, so they may just randomize across
mechanisms. If each seller randomizes across her inventory, we should observe most multi-item
sellers using multiple mechanisms. Alternatively, if the randomization of mechanism-use is
across sellers, we should observe each seller using just one mechanism, and the particular choice
of mechanism should not be correlated with any seller characteristics.
Explanation 2: Second-degree price discrimination
Another potential explanation for the coexistence arises when one allows the buyers to be
heterogeneous not just in valuations, but also in risk-aversion or patience. Since buying from a
posted-price listing involves less risk and less waiting than buying through a pure auction, the
seller facing very risk-averse or very impatient buyers can extract more revenue by posting a
BIN price as shown by Budish and Takeyama (2001) and Matthews (2003) respectively. Now, if
the buyers are heterogeneous in their risk-aversion or impatience, the sellers can second-degree
discriminate by setting a higher posted price than the expected price in a pure auction. When the
price-difference is not too large and the appropriate incentive constraints are thus satisfied, the
more risk-averse and/or impatient buyers would self-select to buy through a posted price, while
the remaining buyers would bid in auctions. Therefore, it is possible that the observed variance
6
in mechanism-use across listings arises simply from sellers using multiple mechanisms in order
to discriminate, either each seller using multiple mechanisms, or each seller specializing but the
population of sellers jointly using multiple mechanisms. The discrimination explanation makes
three testable predictions: 1) buyers with different observable characteristics related to patience
or risk-aversion should self-select into different mechanisms, 2) the expected auction price
should be lower than the posted price for the same good, and 3) large-scale experienced sellers
should use both mechanisms to sell the same good.
Explanation 3: Sorting
The simplest way to explain the coexistence of auctions and posted prices in the same market is
to challenge the “same market” part of the question. It may be that eBay is really composed of
two separate markets, one using auctions and one using posted prices, each with its own buyers
and sellers. This “sorting” explanation predicts that each seller uses only one mechanism to sell
all his goods, and each buyer uses only one mechanism to buy all goods purchased on eBay. In
particular, the buyers do not consider substitutes offered by alternative mechanisms. If this is the
case, it should also be true that the prices of the same good are different across mechanisms, i.e.
there is no arbitrage going on. Testing the previous two explanations will clearly go a long way
to testing this explanation. The only additional test is to look at the mechanism-choice of buyers,
both within and across eBay product-categories: if there are two separate markets, then each
buyer should stick to just one mechanism for all of her purchases.
Explanation 4: Heterogeneity in seller expertise and inventory-composition
The second-degree discrimination of Explanation 2 arises from differential mechanism-specific
buyer costs (which are in turn heterogeneous across buyers). Analogously, the sellers likely face
different costs depending on the mechanism they use. Wang (1993), for example, argues that an
auctioneer only faces a storage cost whereas the store-owner faces a storage cost plus a
displaying cost, so waiting for a live auction is always less costly than the same amount of
waiting for a posted-price sale. However, live auctions are also more expensive to conduct than
individual posted-price sales. Then, Wang predicts that the scope of auctions increases as the
distribution of buyers’ valuations becomes more dispersed. Wang’s theory does not apply well to
online environments, where there is no differential display cost, and where the auction is held
7
costlessly by a computer. The theoretical contribution of this paper is pointing out another source
of differential costs to the seller, arising from different amounts of market research, monitoring,
risk, and waiting needed in the two mechanisms.
In most of the above discussion, we have implicitly assumed that figuring out the optimal
price is costless to the seller, as is conducting an auction. But neither seems to be costless:
Consider pricing a Canon SD450 in a posted-price setting: it would be necessary to do some
market research in order to collect and analyze data about demand for the camera, about
competing sellers of substitute cameras and their strategies, and to then maximize the expected
profit. In other words, it is realistic to assume that the seller is uncertain about demand, and
needs to do market research to determine optimal posted prices. Such a seller could avoid the
cost of market research and just auction the camera off, incurring the additional revenue-risk
given a sale, the additional cost of monitoring the auction process, and the additional cost of
waiting for the outcome.2 Auctioning off the camera seems easier for a lay person, so why are
not all products sold by auction? Because some sellers sell multiple identical cameras, and the
cost of setting an optimal selling price can be spread over those units, whereas the cost of
auctioning is incurred for each unit. In other words, cost of pricing is a fixed cost when the
inventory is homogeneous, while the cost of auctioning is always a variable cost. Therefore, the
size and composition of the seller’s inventory clearly matters in deciding between auctioning and
posted prices. We believe that this observation is new to the literature. It gives rise to the
following theory of seller-heterogeneity in inventories as an explanation for the coexistence
puzzle.
Suppose there is a seller who is uncertain about demand, and she is endowed with an
exogenously-determined inventory of goods to sell. The inventory is either small or large. For
simplicity, assume small means one object while large means two objects. Large inventories are
either homogeneous in that the two objects are two identical units of the same good, or
heterogeneous in that the two objects are different, assume completely unrelated. Suppose further
that the goods need to be sold separately from each other, either each item by a single auction or
each item by a classified listing with its own posted price. When the seller decides to sell a unit
2
This argument implicitly assumes an auction without a reserve-price, because market-research and optimization
would also be necessary for the setting of the optimal reserve. This assumption can be justified both theoretically
and empirically: theory suggests that the power of reserve-prices to increase profits is greatly reduced in a multi-unit
context like eBay (McAfee and Vincent 1997, Peters and Severinov 2004). Empirically, reserve-prices are very rare
in the dataset studied here – less than 3 percent of the listings collected had a reserve price.
8
of the good by auction, he faces a cost α, arising from the need to monitor the auction, from the
risk that the unit sells for a price that is too low, and from need to wait for the auction to finish
(the latter source of the additional auction cost is specific to online environments, where auctions
usually last several days). When, on the other hand, the seller decides to sell the unit by posted
price, he incurs a cost β each time market-research is conducted to determine the optimal price to
charge. The seller with several identical units of a good only needs to conduct market-research
once, so the β cost is fixed across replications of the same good. The auctioning cost, on the
other hand, is always variable – incurred for every unit. To fix ideas, we develop the two-object
inventory example more rigorously by specifying a particular case of demand uncertainty, please
see the Appendix.
Let ∆R be the relative expected-revenue advantage of auctioning a single item, which is
likely positive because of the auction’s ability to resolve demand uncertainty. The simplest case
of the theory arises when ∆R ≈ 0 , i.e. when the difference in revenue is small relative to the
magnitude of α and β. Then, it is immediate that as long as α < β < 2α , only the seller with large
homogeneous inventory prefers to post prices, while the seller with small or large-andheterogeneous inventory prefers to auction both units. When ∆R > 0 , the following Proposition
applies:
Proposition: Suppose ∆R > 0 . When α + ∆R < β + 2∆R < 2α , then the homogeneous-inventory
seller prefers to post prices, but the heterogeneous-inventory seller prefers to auction both units.
Moreover, a single-item seller prefers to auction the item. For every ∆R , there exists a
continuum of (α , β ) pairs that satisfy the inequalities.
Proof: Let ∆R = Ra − R p , where Rm is the single-item revenue from mechanism m. The expected
profits in the case of homogeneous inventory are: auction both: 2 Ra − 2α , research demand and
post prices: 2 R p − β , and auction one, post price on the other: ( Ra + R p ) − α − β .
Heterogeneous inventory behaves the same except for one crucial difference, researching
demand and posting prices now yields 2 R p − 2 β .The Proposition follows from the expectedprofit comparisons. It only needs to be shown that no seller ever prefers to auction one item and
post prices on the other. Suppose the seller uses mixed mechanisms. When inventory is
homogeneous, 2 R p − β > 2 Ra − 2α ⇒ ( R p + Ra ) − α − β 2 < R p − β , so mixed mechanisms
9
would be dominated by posted-price selling even if the seller could only spend β/2 on learning.
When inventory is heterogeneous, an analogous argument shows that mixed mechanisms are
dominated by auctioning: 2 Ra − 2α > 2 R p − 2 β ⇒ ( R p + Ra ) − α − β < 2 Ra − 2α . QED
The intuition behind the above Proposition is straightforward. The first inequality says that when
the cost of auctioning one item α is less than the net cost of posting prices for one item, i.e. the
cost of market research β plus the revenue-advantage of auctioning, then heterogeneousinventory sellers and single-item sellers prefer to auction. The second inequality says that when
the cost of auctioning two items exceeds the net cost of posting prices for two homogeneous
items, then the homogeneous-inventory seller prefers to post prices.
When we consider inventories of Q potentially different units of a good, the theory
strengthens because optimal pricing now involves a combinatorial problem that is exponentially
difficult in Q, whereas the costs of auctioning rise only linearly in Q. For simplicity assume
∆R ≈ 0 and let α = δβ where δ < 1. The seller can auction all the units at the cost of Qα, so
unless they fall into at most δQ subsets that are internally homogeneous, the seller chooses to
auction them all. While α is probably a constant cost across all sellers, β clearly decreases with
expertise. “Expertise” is used in two meanings – general experience with setting a posted price
from learning by doing (useful across product-categories), and reduced demand-uncertainty due
to demand being correlated over time (specific to a category). As β decreases and α stays fixed,
posted prices become more profitable, so we should observe that more sellers with more general
and category-specific expertise are more likely to use posted prices, ceteris paribus.
The theory of pricing costs related to inventory can explain some of the patterns of
auctioning observed in traditional markets. Note that the concept of “unit” is not fixed here, it is
meant in the sense that buyers have unit demand, so what may be a unit for a wholesaler is a set
of many units for a retailer. By endogenizing the definition of the “unit”, the theory explains why
perishable commodities like fish are sold by auction at the wholesale level but for a posted price
on the street: fishermen bring in multiple wholesaler-units of the good varying in quality and
weight in the form of baskets of fish grouped by type, but the retailer is selling multiple identical
retail-units of the good in the form of pounds of fish, easily sold by posted per-pound prices.
Another pattern consistent with the theory is that standardized goods are usually sold by
posted prices. In his primer on auction theory, Milgrom (1989a) observes that “Posted prices are
10
commonly used for standardized inexpensive items sold in stores …When goods are not
standardized or when the market clearing prices are highly unstable, posted prices work poorly,
and auctions are preferred.” Standardization seems intuitively to be an aspect of production, but
the key interpretation here is that it is a property of the seller’s inventory. Not all sellers have
such a luxury. An example of non-standardized products linked by “production” to the same
seller can be seen in the aforementioned estate sales and in all natural (as opposed to
manufactured) products like fish, cut-flowers, wine, citrus fruit, and many others, all of which
are traditionally auctioned on the wholesale level.
When inventories are not exogenous, the inventory-based explanation cannot be
empirically separated from different sellers being differently able to use each selling mechanism:
Sellers exogenously endowed with the ability to auction should acquire small and heterogeneous
inventories while sellers endowed with the ability to set posted prices well should acquire
homogeneous inventories. Assuming exogenous inventories, we can test the explanation in our
data by correlating inventory-size and seller experience to mechanism choice. Since digital
cameras are mass-produced in only a few models, large inventories of new cameras are
automatically homogeneous. However, used cameras are much more heterogeneous, so
controlling for size of inventory, used cameras should be sold by auctions more often. Moreover,
the space of all used products is much larger than the space of new versions of the same
products, making accurate market research much more difficult, and hence suggesting that
auctions would be a better way of selling used products because β should be larger for used
products.
IV. Empirical analysis of eBay mechanism-choice data
Data
Using eBay’s XML API interface, we collected all listings of CP&SD camera category during a
7-week period between September 5 and October 24, 2005. The data includes the selling
mechanism (pure auction, BIN auction, or fixed price)3, text information about the attributes of
each camera sold (model, new vs. used, whether or not accessories are included), and the final
price. About each seller, we collected data containing their feedback, time since registration on
eBay, and data about all of their other active listings at the time when their CP&SD listings were
3
BIN auctions with BIN price less than 1 percent above minimum bid are classified as fixed-price listings.
11
listed. These other listings were grouped by eBay category (Digital Cameras, Computers &
Electronics, Home & Garden, …), and each seller’s proportion of each selling mechanism was
computed for every category. About each buyer, we then collected information about their other
eBay purchases on eBay within the three months after the CP&SD data-period.
After carefully cleaning the data and selecting the 27 most popular (of 53 total) cameramodels (87% of listings), 13,843 listings remain, listed by 2951 different sellers. The total
number of cameras sold was 8,360 (averaging 170 per day). Of all the buyers, 3174 have bought
at least one other item on eBay within the three months after the study, and for each of those
buyers, we recorded the number of purchases, the mechanisms used in every purchase, and the
eBay category of each purchase. Some CP&SD listings were excluded from analysis: Listings of
sellers whose feedback score was less than 10 were excluded because these sellers are not
allowed to use the Fixed-price format (eBay rules). As already mentioned, of the 53 CP&SD
camera-models, the bottom 26 selling models were excluded from analysis because they consist
of only 13.1% of total number of listings. Private listings and Multiple-Item-Auction listings
were excluded, there were only about 1 percent of such listings. To supplement the data with
more information about the cameras, we collected the spot-market price for a new unit of each of
the camera-models (retail price on Amazon.com from either Amazon.com or any other 5-star
seller, in November 2005), as well as the date when the model was released to market by Canon.
As mentioned in the Introduction, there is a lot of variance in selling mechanisms across
the listings: 30% of the listings are fixed-price, 37% BIN-auction, and 33% pure auction.
Summary statistics of the data are presented in Table A1 in the Appendix. It is clear that both
used and new cameras are well represented, most of the cameras considered are currently offered
by Canon, and the different models do not vary too much in price. Most of the sellers sell
multiple cameras as well as other electronics, more than half of the sellers are camera specialists
in that cameras represent more than half of their inventory, and only 24 percent of the sellers are
selling just one camera and nothing else on eBay during the 7 weeks of the data.
A more informative way to summarize the data involves calculating the averages by
selling mechanism. It is further useful to split sellers according to their total unit sales in the
focal Canon P&S category, because non-professional sellers who only want to get rid of their
camera are likely to behave very differently from professional camera-stores, who sell several
cameras a day. We split sellers into three groups: “small” sellers who sold at most one Canon
12
P&S digital camera during the whole time of the data, “medium” sellers who sold between 2 and
50 cameras, and “large” sellers who sold in excess of 50 cameras. Table 1 presents summary
statistics of product- and seller- specific observables, by seller-size and selling mechanism.
Merely glancing at Table 1 reveals a lot of systematic co-variation between the sellingmechanisms and the characteristics of both sellers and products sold: for example, most sellers
stick to just one selling mechanism, but different-size sellers stick to different mechanisms.
Increasing seller-size (number of cameras sold) shifts the preferred mechanism from auction to
posted price: the proportion of pure auctions is 53% among small-, 43% among medium-, and
13% among large-seller listings. Some of the variation across seller-sizes seems to correlate with
the kinds of goods the sellers sell: large sellers are much less likely to sell discontinued cameramodels, which tend to be sold by auction, and the same is true about used cameras. Instead, large
sellers tend to sell bundles (i.e. camera with a case or a memory card) involving a new camera
more often, and such bundles are overwhelmingly more likely to be sold by posted price. While
variation in depreciation and scarcity seem to be strongly related to selling mechanism, the actual
model of the camera (like “Powershot S 30” or “A 520”) does not seem to be strongly correlated
with selling mechanism: for any given model that is sold by a particular (mechanism, size of
seller), the proportion of the other same-mechanism listings of the same model in the data hovers
between 30 and 40 percent – not distinguishable from baseline chance (recall that the proportions
of the three selling mechanisms in the data are 30, 37, and 33 respectively).
A major feature that distinguishes our dataset from other available eBay datasets is the
ability to look at each seller’s behavior far beyond the focal category – to Computers and
Electronics, or to non-electronic items like “Home, Garden, and Clothing”. We find that the way
the seller sells other goods seems to strongly correlate with the mechanism selected for CP&SD
cameras: For example, when a medium seller lists one camera using the fixed-price mechanism,
the proportion of all digital cameras (not just CP&S) in that seller’s inventory that are also listed
by fixed price is 87 percent on average. The strength of the correlation between selling
mechanism in the focal category and seller’s mechanism-habit in other categories diminishes as
the other categories get become more different from the focal category (there is one exception:
large-scale fixed-price sellers stick to fixed prices across the board, perhaps because these are
retailers merely using eBay as another channel an just posting the same prices on eBay as in their
store).
13
Table 1: Means of observed variables across listings, by seller-size and selling mechanism
Number of sellers
Percent single-mechanism
% both posted & auction
Total listings
Total sales
Three groups of sellers by Canon P&S Digital Camera sales
Up to one sale
2-50 sales
Over 50 sales
1977
946
28
99%
79%
68%
1%
14%
21%
2216
6370
5257
1814
4378
2168
Fixed
BIN
Pure
Fixed
BIN
Pure
Fixed
BIN
Pure
price auction auction price auction auction price auction auction
10%
37%
53%
25%
32%
43%
44%
43%
13%
Mechanism share
Product characteristics
Current camera model
93%
74%
68%
96%
88%
79%
97%
99%
81%
new (as opposed to used)
65%
45%
36%
85%
69%
65%
66%
67%
67%
bundled w/ accessories
22%
28%
19%
51%
33%
22%
73%
85%
11%
new X bundled
15%
12%
8%
43%
24%
18%
44%
62%
5%
% of model by fixed price
27%
24%
29%
25%
31%
25%
31%
33%
37%
% of model by BIN auction
36%
33%
37%
35%
37%
35%
35%
38%
42%
% of model by pure auct.
33%
38%
30%
33%
26%
27%
43%
40%
40%
Amazon price new
$306
$326
$305
$312
$317
$288
$373
$325
$296
Seller characteristics
# all listings / seller
158
93
71
2888
5559
1124
9336 22486 17690
median ( # listings / seller)
1
1
1
14
34
8
350
533
99
# CP&SD cameras sold/seller 0.85
0.86
0.93
21.77 18.37
12.44
89.31 200.96 138.17
Seller eBay age (years)
3.4
4.1
3.7
3.2
4.1
3.3
3.9
4.3
3.7
Percent positive feedback
99.00% 99.20% 99.10% 99.20% 99.30% 99.20% 98.30% 99.30% 98.20%
log(total feedback)
4.9
4.9
4.8
7.1
7.3
5.9
9.1
10.2
7.8
# Digicams/ # inventory
45%
61%
54%
49%
47%
47%
66%
48%
66%
DigicamSpecialist (Pr>0.5)
30%
51%
43%
56%
50%
43%
90%
72%
70%
Unit total inventory dummy
17%
30%
28%
% digicams by fixed price
2%
1%
5%
6%
19%
10%
94%
87%
86%
% digicams by BIN auction
2%
3%
4%
5%
12%
4%
91%
87%
73%
% digicams by Auction
4%
7%
9%
9%
1%
7%
96%
89%
86%
The following percentages calculated conditional on carrying the category:
NonCanon P&S DC fix price 91%
6%
5%
9%
6%
18%
21%
90%
95%
NonCanon P&S DC BIN auct. 3%
9%
4%
3%
4%
8%
65%
83%
71%
NonCanon P&S DC Auction
9%
24%
8%
9%
1%
11%
86%
89%
72%
Percent has NonCanon P&S
34%
17%
22%
80%
80%
66%
97%
100%
53%
Comp-electro by fixed price
8%
7%
9%
10%
17%
13%
74%
82%
92%
Comp-electro by BIN auct.
7%
7%
7%
6%
7%
11%
61%
76%
80%
Comp-electro by Auction
19%
31%
12%
16%
1%
3%
85%
85%
77%
Percent has Comp-Electro
43%
36%
41%
85%
67%
80%
83%
100%
56%
Non-electro by fixed price
13%
4%
4%
10%
54%
24%
58%
75%
92%
Non-electro by BIN auction
8%
4%
13%
10%
8%
16%
53%
70%
46%
Non-electro by Auction
33%
40%
19%
26%
0%
0%
92%
81%
56%
Perc. Has Non-electro
12%
15%
24%
16%
23%
31%
25%
71%
25%
14
The diminishing correlation suggests that the story behind the seller’s choice of mechanism is
not just a simple mechanism-specific taste invariant across categories. For example, a mediumsize seller who sells a Canon P&S camera by fixed price is very likely (90% chance) to sell other
point-and-shoot cameras by fixed price, but if he also has sells some non-electronic items, he is
much less likely (75% chance) to sell these also by fixed price.
While individual tastes for mechanism are obviously important in that their impact remains
above chance, the choice of selling mechanism correlates with observable seller-characteristics
as well: Larger total feedback, overall scale of camera sales, and being a camera-specialist are
correlated with posted-price selling both within and across seller-groups. These correlations with
seller characteristics are preliminary evidence for the inventory-based explanation proposed in
the previous section.
Results: first three explanations for the coexistence puzzle are rejected by the data
The first possible explanation suggests that sellers randomize across mechanisms. We can rule
out randomization within seller across listings, because of the 573 sellers observed selling at
least three cameras, only 25 percent use more than one mechanism, and only 21 percent ever use
both the pure auction mechanism and a posted-price mechanism. Randomization across sellers
can be ruled out as well, because the use of the auction mechanism is strongly correlated with
small seller scale and lower seller experience (Table 1).
The second possible explanation for the variance is second-degree discrimination arising
from buyer heterogeneity in risk-aversion or patience. The prediction is that buyers self-select
into mechanisms most suitable for them. To test this possibility directly, we attempted to find
differences among the buyers in terms of their observable characteristics. The results are shown
in Table 2, and they indicate that the buyers who buy by posted price have lower feedback score
(square root 2.19 vs. 2.30), higher positive feedback percentage (99.1% vs. 98.8%), are more
likely to be first-time eBay users (8 vs. 4 percent) and the observed purchase is more likely to be
their only camera-purchase on eBay within the seven weeks of the data (92 vs. 88%). The
observed differences are consistent with auctions being more difficult to participate in and less
familiar than posted-price offerings. While the above differences are significant given the large
sample, they are quite small in magnitude. Therefore, we conclude that there does not seem to be
too much self-selection among the buyers into mechanisms. However, none of the observed
buyer-characteristics is a direct measure of patience or risk-aversion, so self-selection on these
15
key characteristics may remain unobserved. Another way to detect price-discrimination is to
consider the final prices of new cameras sold by different mechanisms.
Table 2: Which buyers end up buying by which mechanism?
Bought by posted price
Fixed price
2701
2.19
99.2%
2.76
0.38
50.3
0.08
0.92
Number of observations
Total feedback of buyer (4th root)
Positive feedback percentage
Time since eBay registration (years)
Seller (1=has sold on eBay, 0=otherwise)
Percentage of feedback from buyers
First-time (1=no feedback, 0=otherwise)
Single purchase (1=only seen once in data)
Bought in an auction
BIN auction BIN auction
Pure auction
BIN-sold auction-sold
1472
909
4338
2.19
2.30
2.28
99.1%
98.8%
98.8%
2.81
3.01
2.76
0.39
0.43
0.38
60.9
34.0
30.2
0.08
0.04
0.04
0.91
0.91
0.88
Note to Table 2: The Seller variable is deduced from the existence of “feedback from buyers”.
The proportion of such feedback form buyers indicates the relative volume of selling this buyer
has done as a percentage of all his/her eBay transactions. Single purchase is an indicator of only
being observed once in the data at hand. Because there are the multiple item listings and one
buyer can buy more than 1 item in such listings, Table 2 is calculated by each item sold, not each
listing sold.
Since posted prices save the waiting/hassle cost and they lower the risk to the buyer of
not winning a camera, posted-price transactions should involve higher prices than auction
transactions. To test this prediction, we focus on 4620 sold new non-bundled cameras, and
calculate their final prices (including shipping), both by selling-mechanism and by actual method
of sale. The following linear regression of total price of observation i of model m on model
fixed-effects, model-specific dummies indicating sale by a BIN price, and a time-trend is used to
estimate the model-specific premia:
( price + shipping )m,i = α m + β m ⋅1( PostedSoldi ) + γ ⋅ tm,i + ε m,i
(1)
where PostedSold is a dummy for sale by BIN price pooling across the two mechanisms that
offer a BIN price. The regression results are presented in Table A2 in the Appendix, and they
reveal mixed evidence: Of the 27 popular models, only nine are sold with a statisticallysignificant premium, and two are sold with a significantly negative premium. Moreover, the
premium estimates vary widely (see Figure 1 for the distribution of premia across models).
16
Figure 1: Distribution of posted-price premium across camera-models
9
Number of models
8
$ premium
7
6
5
4
3
2
1
0
-$30
-$20
Number of models
$0
$10
$20
$30
More
10%
More
Posted-price premium
8
7
-$10
% premium
6
5
4
3
2
1
0
-10%
-5%
-2%
0%
2%
5%
Posted-price premium
17
One way to explain the inconsistent posted-sold premia found in Figure 1 is to consider
competition. While a monopolist seller can use the different mechanisms to discriminate,
competition among sellers reduces both the posted and the auction prices towards cost. We
consider two measures of competition: the overall volume of sales for the given model and the
time since the model has been released by Canon. Time since release not only increases the
availability of new units, but also proxies for the competition from used models of the same
camera. The correlation of volume and model-age is -0.35 in the data, with a vaguely inverse-Ushaped relationship. Instead of estimating model-specific premia, the regression we run to check
for competitive effects is:
( price + shipping )m,i = α m + β ⋅1( PostedSoldi ) + γ ⋅ tm,i + δ ⋅1( PostedSoldi ) × compi + ε m,i
Table 3: Do posted-price sales involve a premium? Effect of competition.
Estimate (SE) Estimate (SE) Estimate (SE)
Variable:
27 model-specific fixed effects, mean $295, st. deviation $110
-0.58 (0.03) -0.58 (0.03) -0.59 (0.04)
time (days)
5.75 (0.89) 7.74 (2.00)
binsold dummy
-2.36 (2.20)
binsoldXmodel age (yrs)
-3.18 (0.95)
binsoldXmodel volume (std)
5.69 (1.00)
fixed price dummy
6.85 (1.21)
BIN auction dummy
BIN auction binsold
BIN auction aucsold
fix priXmodel age (yrs)
BIN aucXmodel age (yrs)
fix priXmodel volume (std)
BIN aucXmodel volume (std)
Estimate (SE) Estimate (SE)
-0.58 (0.03)
-0.57 (0.04)
5.69 (1.00)
7.86 (2.35)
16.67 (2.52)
8.51 (1.50)
4.63 (1.69)
-2.18
-11.98
-4.14
-3.56
(2.59)
(2.72)
(1.09)
(1.25)
Note to Table 3: Linear regression, dependent variable is price+shipping in dollars, multi-item
fixed-price listings considered as separate sales. Volume is normalized to mean zero and unit
standard deviation.
Table 3 shows the results of several price-regressions, both on the method of actual sale (BINsold vs. auction-sold) and on the method of initial listing (fixed-price, BIN-auction, auction). The
results of controlling for competition are consistent with the idea that competition reduces a
seller’s ability to price-discriminate. On average, selling a camera by posted price involves a
very small $5.75 (1.9 percent) premium. However, and as predicted, this premium is higher for
18
less popular cameras, declining about $3 per standard deviation of sales-volume. Separating the
posted-price sales by mechanism reveals that BIN auctions involve a higher premium of $8.51
compared to the fixed-price mechanism’s $5.69. Unexpectedly, the BIN auctions that revert to
auctions also involve a substantial premium – about $4.63. While the BIN auction premium is
high, is declines very fast with the time since the model’s release ($12 per year), and with
popularity of the camera. Altogether, a year old camera that sells one standard deviation more
units compared to the average camera involves no posted-price premium. Therefore, pricediscrimination cannot explain the variance in selling mechanisms across all popular and nonrecent cameras.4
Given that buyers seem to be self-selecting at least somewhat, and at least some cameras
are sold with a posted-price premium, the sellers have an incentive to each use multiple sellingmechanisms. As pointed out in the discussion of the first explanation, this does not seem to be
the case: the number of multi-unit sellers using more than one mechanism is very small. In
particular, of the 573 sellers observed selling at least three cameras, only 25 percent use more
than one mechanism, and only 21 percent ever use both the pure auction mechanism and a
posted-price mechanism. There is very little correlation of multi-mechanism selling with salesvolume, the percentage of sellers using multiple mechanisms remains below thirty as only the
larger- and larger-volume sellers are considered. Therefore, the discrimination story can only
explain the variance in mechanism-choice if each seller specializes in one mechanism, and the
sellers find a way to jointly coordinate in offering multiple mechanisms. Alternatively, the
variance can be explained by differences among sellers as suggested in Explanation 4. Before
examining this possibility, we also rule out the sorting explanation.
Given that most sellers specialize in just one mechanism, it is possible that eBay really
consists of two unrelated parallel markets – one using auctions and one using posted prices. The
fact that popular new cameras trade for statistically identical prices in these two sub-markets
contrasts with this explanation, but the definitive evidence comes from considering the buyers.
We do not find evidence that most buyers stick to only one method of purchasing: Of the 3174
camera buyers, we observed 1990 buying at least 2 other items on eBay within the next three
months, and 1387 bought at least three items. Negligibly few of these multi-unit buyers used
4
These results are in contrast with the findings of Lee and Malmendier (2006), who find that auction-prices tend to
be higher than posted prices for the same good in a market for a specific boardgame called “Cashflow”. Therefore, it
seems that buyers of digital cameras are not as “irrational” as buyers of boardgames.
19
only posted-price offers to purchase, and only about a third of them used only auctions. Table 4
implies that among frequent buyers, about 70 percent use multiple formats. Therefore, it does not
seem that eBay buyers stick to only one format – as suggested by the lack of significant postedprice premia, there are enough buyers willing to switch mechanisms for a bargain, and eBay
should be analyzed as a single market.
Table 4: Which mechanism do the buyers use to buy other things on eBay?
Min # other purchases # buyers % Auction only % Posted (BIN) only
2
3
4
5
6
7
8
9
1990
1387
1026
772
616
490
407
355
44
38
35
32
30
29
29
30
5
2
1
1
1
0
0
1
To summarize the discussion of empirical evidence so far, it does not seem that sellers
are randomizing across selling mechanisms, either across listings or across sellers. Instead, most
multi-unit sellers stick to just one mechanism, and the mechanism chosen is correlated with
several observable seller-characteristics. It also does not seem that the two mechanisms coexist
to price-discriminate between buyers based on personal preferences for auctions versus posted
prices (for example preferences based on risk-aversion or impatience). The average posted-price
premium is only 1.9 percent of the final price, and the positive premia are restricted to rare or
discontinued camera-models (a year old camera-model that sells one standard deviation more
units compared to the average model involves almost no posted-price premium). Moreover, there
is very little evidence that buyers self-select into only one mechanism: the auction-buyers differ
only marginally from posted-price buyers in terms of observable characteristics, and about 70
percent of those buyers who buy other things on eBay make use each mechanism at least once.
Finally less than a quarter of very experienced sellers use multiple mechanisms to sell their
cameras, so it does not seem that experience makes the sellers exploit the potential pricediscrimination profits. Altogether, we conclude that the CP&SD eBay market is too competitive
for price-discrimination to provide significant profit-gains. The data is also inconsistent with the
sorting explanation: while most sellers use just one mechanism, most multi-unit buyers use
multiple mechanisms to buy their goods. Therefore, the analysis of eBay as a single market
20
linked by the demand-side is warranted. Having rejected the three “obvious” explanations, we
now focus on the fourth possible explanation – the theory of different sellers facing different
mechanism-specific costs because of their heterogeneous inventories.
Results: seller heterogeneity in inventories correlated with mechanism-choice
So far, the main positive finding regarding the source of variance in selling mechanism across
listings is that each seller tends to stick to just one selling format when selling CP&SD cameras,
but different sellers stick to different formats. Why do different sellers use different formats?
Table 1 provided some preliminary evidence that the use of posted prices is associated with
larger sellers, more experienced sellers, and camera specialists. Alternatively, each seller may
simply have an unexplained personal preference for a mechanism. The multi-category nature of
our data allows us to at least partially separate such a personal “taste-shock” from the effect of
inventory-size and the seller experience specific to the focal-category.
Table 5: Classification of CP&SD camera sellers based on cross-category selling behavior
Size of eBay Inventory
Variation in mechanisms used
to sell eBay inventory
Percent of all camera sellers
Cameras sold / seller
Log ( total listings )
Log ( total feedback )
How do they sell cameras?
Fixed price
BIN auction
Pure auction
2951 sellers found selling CP&SD cameras
Single-Item
Multi-item
eBay Inventory
eBay Inventory
Single-mechanism Both mechanisms
for all listings
used
21%
0.97
0
4.0
41%
2.58
2.12
5.0
38%
5.51
3.44
5.7
6%
40%
54%
15%
23%
63%
16%
33%
51%
Note to Table 5: In “How do they sell cameras?”, multi-mechanism bidders are classified by
their favorite camera mechanism (only 17% of them use multiple mechanisms to sell cameras).
The above-described reluctance of individual sellers to use multiple mechanisms within a
category extends to their behavior across categories: Of the 2951 total sellers listing at least once
in the focal category (CP&SD), 2334 (79 percent) list at least one more item on eBay, and of
those 2334, 52 percent stick to just one mechanism in that they either always auction (752) or
never auction (449). Of those who never auction, 32 percent always use a fixed-price, 51 percent
21
always use a BIN-auction, and only 17 percent use both fixed-price and BIN-auction. Please see
Table 5 for details. To summarize, about half of all the sellers with multiple listings use the same
mechanism to sell all their goods, and so knowing how a seller sells other goods is a very good
predictor of the way that seller sells Canon P&S digital cameras. This can be illustrated by
plotting percentage of each seller’s listings sold by auction in the Computer & Electronics
category against the percentage of the same seller’s listings sold by auction in the focal category,
please see Figure 2.
Figure 2: Persistence of selling mechanism across categories
Proportion of auctions among Canon P&S listings
1
Plot jittered by Uniform[-0.05,0.05]
0.75
0.5
0.25
0
0
0.25
0.5
0.75
1
Proportion of auctions among seller’s Computer & Electronics listings
Note to Figure: Each dot is a seller, the Figure shows 697 sellers who sell 2-50 Canon
P&S cameras within the data, and also list some Computers & Electronics.
22
The raw correlation of the proportions across sellers is 0.92, while the analogous correlation
between non-electronic goods and the focal category is 0.81.
The sellers can thus be divided into three distinct groups following Table 5: those who list only
one item on eBay within the entire data-period of seven weeks (623 sellers), those who list
multiple items, but stick to one mechanism for all their products (1201 sellers), and those who
list multiple items and vary the mechanism at least somewhat (1127). These distinct sellergroups are now analyzed separately, in turn.
The single-item sellers use a lot of pure auctions as predicted by their small inventories,
but they also use a lot of BIN auctions. The popularity of the BIN-auction among these sellers is
somewhat unexpected, especially because the BIN option is actually executed about half of the
time, a propensity similar to that among larger-volume sellers. Therefore, these sellers are not
just setting very high BIN prices in the hopes of running into uninformed buyers, they post
competitive prices. The fact that 95% of these sellers’ listings result in a sale irrespective of
mechanism used suggests that these sellers are eager to sell, and so they use low minimum bids
and/or low posted prices.
A parsimonious way to capture the correlates of mechanism-choice among the second
group of sellers, i.e. sellers who stick to only one mechanism, is to perform the analysis at the
seller level. Table A4 in the Appendix shows that the BIN-auction sellers are not at all similar to
the fixed-price sellers, making an analysis of posted-price versus auctions tenuous. In fact, BINauction sellers tend to be the smallest-scale, least diversified, and least experienced of all three
groups. It is not clear what other conclusions we can draw from these single-mechanism sellers.
It is only clear that the personal preference for format is not random – the mechanism used is
strongly correlated with both product and seller characteristics.
Finally, the third group of sellers is most promising in that their behavior demonstrates
familiarity with both selling mechanisms. It is therefore reasonable to suggest that these multimechanism bidders are actively making a choice about how to sell their CP&SD cameras.
Moreover, since their method of selling other goods is not perfectly predictive of their method of
selling cameras, there is a hope of separating the relative influence of a personal taste-shock
common across categories from the influence of category-specific inventory and experience. To
be able to construct this personal-taste variable for every seller in the analysis, we restrict the
subsequent analysis of this third group of sellers to the 812 (72 percent) of them who also have at
23
least one listing in the Computer & Electronics category. These sellers together account for 8561
listings.
Table 6: Different products or different sellers? Seller-level analysis
How seller sells CP&SD cameras:
Fixed price BIN auction Pure auction
% of seller’s Computers and Electronics listed by:
Fixed price
BIN auction
Pure Auction
Seller characteristics:
log (feedback)
log ( # all listings)
median # all listings
log ( # digital camera listings)
median # digital camera listings
# CP&SD camera listings
# CP&SD cameras sold
# CP&SD cameras sold / specialist
specialist seller (digicams >50% of inventory)
% digital cameras in inventory
% also has non-Canon P&S digital cameras
# sold units per model
median # sold units per model
% has non-electronic items
Product characteristics:
Amazon price new
current camera model (dummy)
days since release of camera by Canon
new (as opposed to used )
bundle (with accessories)
newXbundle
% of the camera model listed by:
Fixed price
BIN auction
Pure Auction
Number of sellers
59%
7%
34%
5.91
3.86
29
2.54
8
19.7
10.09
26
0.19
0.34
0.63
3.07
(0.15)
(0.15)
287.3
0.94
340.1
0.77
0.15
0.12
(7.62)
(0.02)
(11.66)
(0.03)
(0.03)
(0.02)
(0.15)
(6.36)
(1.87)
(6.95)
(0.03)
(0.02)
(0.04)
(0.34)
2
0.27 (0.04)
31%
36%
33%
157
9%
51%
40%
5.93
3.61
28
2.01
5
14.37
6.27
19.52
0.19
0.30
0.51
1.78
(0.11)
(0.12)
300.8
0.80
393.6
0.58
0.15
0.09
(6.86)
(0.02)
(13.73)
(0.03)
(0.02)
(0.02)
(0.12)
(4.41)
(1.81)
(8.64)
(0.03)
(0.01)
(0.03)
(0.18)
1
0.33 (0.03)
28%
35%
37%
248
14%
13%
73%
6.07
4.17
51
2.27
8
4.68
4.51
6.6
0.15
0.26
0.60
2.15
(0.10)
(0.09)
281.8
0.76
410.7
0.57
0.10
0.07
(4.41)
(0.02)
(11.63)
(0.02)
(0.01)
(0.01)
(0.07)
(0.41)
(0.43)
(1.10)
(0.02)
(0.01)
(0.02)
(0.13)
1
0.44 (0.02)
25%
35%
40%
407
Note to Table 6: N=812 sellers, who also have at least one listing in the Computer & Electronics
category. In “How do they sell cameras?”, the sellers are classified by their favorite camera
mechanism (only 19% of them use multiple mechanisms to sell cameras, 16 % both posted prices
and auctions). Standard errors of the means are in parentheses and italics.
24
Three possible factors remain as explanatory variables for this mechanism choice: 1)
cross- category unexplained taste-shock, 2) seller characteristics like experience with cameras,
total scale & experience, or CP&SD-specific scale, and 3) product characteristics like new vs.
used or bundling with accessories. To assess the influence of different factors on mechanismchoice, we perform two analyses: a simple univariate ANOVA analysis with each seller as an
observation, and a multivariate choice-model analysis with each listing as an observation. The
seller-level analysis is presented in Table 6, and it reveals that all three classes of factors are
correlated with mechanism choice. The influence of an unexplained cross-category taste-shock
seems strong: the mechanism used for selling cameras is used to sell more than half of the same
seller’s Computer & Electronics inventory, 73 percent of it when the mechanism is a pure
auction.
The seller characteristics are also influential: consistently with the proposed inventory
theory, pure auctions are correlated with smaller camera inventories (Fewer CP&SD cameras
sold. Cameras sold are a better measure than cameras listed because the different mechanisms
differ in probability of sale), lack of specialization in cameras, and especially with the interaction
of these two variables. Interestingly, the overall scale (measured by either feedback or the total
number of listings), is positively correlated with selling CP&SD cameras by pure auctions.
Overall scale confounds camera scale with lack of specialization: The correlation of the overall
scale with the CP&SD scale in logs is 0.46, so larger overall sellers also sell more CP&SD
cameras. However, the correlation of the overall scale with camera specialization (% digital
cameras in inventory) is -0.32. Therefore, the ability to set posted prices in a given category
seems less related to the general experience on eBay, and more related to specialization in that
category. Of course, the multivariate analysis will be able to separate these effects more
conclusively.
In terms of product characteristics, pure auctions are significantly correlated with used
products, discontinued models, and unbundled cameras, but not with specific camera-models.
We do not have strong theories why bundling with accessories should make the seller use a
posted price, but we include the variable in all subsequent analyses as a control.
25
Choice-model multivariate analysis
To see how well all the above univariate correlations hold up when they are asked to explain the
variance in selling-mechanism jointly, we need a multivariate analysis. The multinomial logit is
a natural model for capturing the correlations of variables with choice-obervations across
listings. The model is agnostic about the potential relationship among the three mechanisms,
treating them as independent choices faced by the seller. Let the underlying random-utility
function of seller s selling the i-th instantiation of product (camera-model) p by mechanism
m ∈ { 0 ( = fixed price ) ,1( = BIN auction ) , 2 ( = pure auction )} be specified as follows:
U m,s, p,i = α m, p + β H m,s + γ m Zi + δ mWs + ε m,s, p,i
(3)
where the covariates are defined as follows:
•
α m, p are model-mechanism fixed effects. These control for all model-level productcharacteristics, both unobserved and those specifically observed in our data, like Amazon
price or time since release by Canon. The main question we are asking is why different
sellers sell the same goods differently, so product-specific variation in mechanism is a
nuisance parameter we want to control for without interpreting the coefficients.
•
H m,s is the “habit” of the seller, i.e. the proportion of the seller s’s Computer &
Electronics listings offered by mechanism m. This is our key control for a global (ebaywide) personal preference for a mechanism of each seller.
•
Z i is a vector of instantiation characteristics, and γ m is thus the vector of effects of these
characteristics on utility of mechanism m (normalized by γ 2 = 0 ). The productcharacteristics used are: new (dummy, description matches “new” or “mint” and does not
contain “not”) , bundle (dummy, description mentions accessories like case, memory
card…), and their interaction.
•
Ws is a vector of seller-characteristics, and δ m is thus the effect of seller-characteristics on
utility of mechanism m (normalized by δ 2 = 0 ). The seller-characteristics include:
inventory size (log of the number of CP&S-cameras sold by the seller within the data),
feedback (log of the total feedback, a measure of total sales on eBay to date), specialist (a
26
dummy for more than 50 percent of the seller’s current listings being digital cameras),
and hasNonElectro (dummy for the seller currently also carrying non-electronics).
•
ε m ,s , p ,i is the standard independent extreme-value error that leads to logit probabilities of
a particular mechanism m being selected when sellers maximize U m ,s , p ,i . The
independence assumption is probably most tenuous within the same seller, an issue that
could be avoided by only using one randomly-drawn observation for each seller. Such an
analysis (not reported) seems to yield very similar conclusions, but more data (N is
reduced to 812) would be needed to use this more conservative analysis instead.
For ease of interpretation, the inventory size, and feedback variables were normalized to standard
deviation of unity (across listings), with the mean set to ensure they were positive for all
observations. Uniform positivity is crucial for interpreting interactions. Please see Table A5 in
the Appendix for the descriptive statistics of the final regression variables. Table A5 also shows
mutual correlations of all the regression variables, and it reveals that the Computer & Electronics
habit variable is quite correlated with the seller and product characteristics. This makes it harder
to separate their effects and necessitates the analysis of the characteristics both with and without
the habit variable in the model.
Table 7: Multivariate analysis of variance in mechanism across listings
Model:
MAD
baseline
model fixed effects
model fixed effects + seller char
model fixed effects + instantiation char
model fixed effects + seller char + inst. char
model fixed effects + seller char + inst. char +seller habit
baseline + seller habit
0.429
0.383
0.301
0.350
0.29
0.129
0.146
Reduction ↓ in MAD
in MAD wrt wrt model
baseline
w/fixed
effects
11%
30%
21%
18%
9%
32%
24%
70%
66%
66%
Table 7 captures the contribution of each of the above variables to the explained variance in
mechanism choices. For each model specification, we calculated the mean absolute deviation
(MAD) between the observed choices and the choices predicted by the model. The seller’s
Computer & Electronics mechanism-habit is by far the most influential variable – alone, it
reduces MAD by 66 percent, while all the additional variables contribute only four further
percentage points. Without the habit variable in the model, the seller characteristics contribute a
27
21-percent MAD reduction beyond model fixed effects, also a substantial amount of explanatory
power. The instantiation characteristics only contribute two percentage points beyond the seller
characteristics. We therefore conclude that the most important correlate of mechanism-choice is
global eBay “habit” of the seller, the second most important correlate is the category-specific
experience and inventory of the seller, and finally, the instantiation-characteristics are the least
important. Interestingly, the model fixed effects explain quite little given how many parameters
(54) they involve.
Table 8: What correlates with mechanism? Net marginal effects on mechanism share
baseline (data)
Seller factors
all Comp & Electronics items
listed by pure auction
no camera specialists
all sellers camera specialists
log(camera inventory)+1 std
all spec. & log(c. inve.+1std)
all sellers have Non-Electro
no sellers have Non-Electro
all seller feedback + 1 std
Product-instantiation factors
all used, no bundles
all new, no bundles
all used, all bundles
all new, all bundles
Model without
habit variable
Fixed
BIN
Pure
price
auction auction
Model with
habit variable
Fixed
BIN
Pure
price
auction auction
34.90%
34.90%
43.30%
21.90%
-26.70%
-28.50%
55.10%
43.30%
21.90%
-8.20%
9.70%
-8.20%
-1.90%
-12.60%
9.00%
0.20%
2.00%
-6.70%
7.50%
9.60%
8.80%
-7.20%
7.70%
6.10%
-3.10%
0.50%
-7.90%
3.80%
-1.80%
-8.00%
-0.90%
2.90%
-5.40%
-3.90%
-2.90%
1.60%
3.90%
-1.40%
-1.00%
4.10%
6.50%
2.80%
-1.70%
-2.70%
2.10%
-2.10%
1.20%
-2.70%
0.00%
0.00%
-1.30%
-9.20%
1.80%
7.30%
-7.00%
6.80%
0.10%
-7.30%
-0.90%
11.60%
1.50%
14.80%
-1.10%
5.70%
-14.00%
-10.50%
-0.40%
-0.80%
4.80%
-2.50%
9.20%
-2.10%
2.70%
-8.50%
-2.80%
Note to Table 8: All percentages are share of each mechanism in the population of all listings.
Italics indicate counterfactuals based primarily on insignificant logit parameters, please see Table
A4 for details.
The parameter estimates are presented in Table A4 in the Appendix, but the raw parameters are
not particularly illuminating about the strength of correlations between the mechanism and the
characteristics. To assess the strength of the correlations of the seller and instantiation
28
characteristics with mechanism choice, we performed several counterfactual computations using
both the model with and the model without the seller-habit variable. We let the dummies be
either all zero or all one, and we changed the continuous variables by one standard deviation.
Table 8 presents the results. In interpreting Table 8, we just look at the highlighted “pure
auction” column, lumping the “fixed price” and “BIN-auction” columns together because we do
not have a theory of choosing between those two. However, the logit analysis analyzed these two
mechanisms as separate choices, and it is clear that they do not always “move together”.
Therefore, we find that BIN auction is not the same thing as fixed price to the sellers, and it is
possible our results contain a direction for further study of the difference.
The main qualitative finding of Table 8 is that most of the univariate correlations found
in Table 6 survive the multivariate analysis. The seller’s “habit” from the Computer &
Electronics category has by far the greatest impact on the way the same seller sells CP&SD
cameras: making all sellers sell all their C&E products by pure auction is estimated to boost the
pure-auction listings of cameras from 22 percent to 77 percent! The seller characteristics are also
important correlates, some even in the presence of the C&E habit. Because of the correlations
between the habit and most seller characteristics shown in Table A6, including the C&E habit in
the model mostly attenuates the magnitude of correlation between seller-characteristics and
mechanism.
The most robust seller characteristic is camera specialization: making no sellers camera
specialists raises the share of pure auctions by 6 percent without C&E habit, and by 2 percent
with C&E habit. As predicted by the inventory theory of mechanism choice, specialization
interacts with category-specific scale to produce a super-additive effect: when all sellers are
camera specialists and their inventories of cameras are all larger by one standard deviation, pure
auctions lose 7.9 percent of share (2.7 with C&E habit). A variable related to specialization in
cameras is hasNonElectro – an indicator of a diversified seller. As predicted by the idea that
setting the right posted price requires category-specific expertise, carrying non-electronic boosts
the share of pure auctions (when all sellers have non-Electro rather than only 42 percent of
sellers as is the case in the data, pure-auction share is boosted by 3.8 percent). Finally, general
eBay experience / overall eBay scale as measured by feedback also reduces the share of auctions
in line with predictions. The correlation is quite strong – increasing everyone’s feedback by one
standard deviation reduces the share of auctions by 8 percent (1.3 percent with C&E habit). The
29
correlations of mechanism and product-instantiation characteristics are not the main focus of our
study, but we also find significant effects similar the univariate correlations in Table 6. In
particular, products bundled with accessories are more likely to be sold by posted price bundling all the products with accessories was estimated to reduce the share of pure auctions by
over 10 percent (from a baseline of 22 percent), a very large effect. Interestingly, the logit model
indicates that new products are slightly more likely to be sold by auction than by posted price,
but the parameters are mostly insignificant.
Before concluding, it is interesting to consider the economics of the eBay camera
business. Is it true that consumer goods like digital cameras are generally overpriced on eBay as
anectodal evidence from the press would suggest? To answer these questions, we employ
Amazon pricing data collected (unfortunately) after the sample-period, in the end of November
2005. These Amazon prices are the lowest prices of a new camera of the given model (without
accessories) on the Amazon site (either from Amazon or from other participating sellers) subject
to the constraint that the seller selling through Amazon has five stars, i.e. the best possible
quality rating. They do not include any shipping charges, but the prices are so high that a buyer
would qualify for free shipping. On the eBay side, we compute all the fees charged by eBay for
every listing, and we recorded the listed shipping cost, which is borne by the buyer on eBay and
so is a component of seller revenue. We also take into account the different numbers of cameras
sold by different fixed-price listings. The results of the revenue analysis are presented in Table
A3 in the Appendix, first for all listings, and then for the listings of sold new cameras only. It is
clear from Table A3 that small-scale (single-camera) sellers just want to get rid of their camera,
and so they price quite a bit (about 8 percent) below Amazon. Medium and Large sellers, on the
other hand, turn a profit by posting very high prices and re-listing their cameras until it gets sold.
For example, very large sellers using a BIN auction sell only 37 percent of their listings, but
collect a 20-percent premium over Amazon per camera sold. A clear winner is eBay – collecting
$8 per listing whether the listing results in a sale or not. Since the Amazon prices were not
collected concurrently with the data, it is possible that the 20-percent premium exaggerates the
potential gains (cameras get cheaper over time, about 58 cents per day according to Table 3), so
we do not recommend starting an arbitrage business to our readers. Also, the strategy of posting
high prices and mostly not selling involves a non-trivial inventory-holding cost assumed to be
zero in our calculations. However, we do find that buying from large-scale sellers on eBay does
30
involve a premium over small-scale sellers, and it is possible that large-scale sellers could turn a
profit by buying on Amazon and reselling on eBay.
V. eBay-specific alternative explanations of the coexistence puzzle
Before concluding, we rule out two eBay-specific alternative explanations of the coexistence:
multiple-item listings, and free re-listings. These explanations are not generalizable to other
settings because they are based on peculiarities of the eBay marketplace.
eBay-specific alternative explanation #1: Multiple-item listings
EBay’s fixed-price listings allow the seller to list more than one item within the same listing, and
most of the large-scale camera sellers use this option: 36 percent of sellers who used the fixedprice mechanism used a multiple-item listing, and these sellers are more likely to be large-scale
sellers because multiple-item listings account for 77 percent of the fixed price listings. Therefore,
fixed-price listings differ from the BIN-auction and pure-auction listings not only in mechanism,
but sometimes (endogenously) also in quantity offered. This fact complicates the analysis of
selling probabilities: 36 percent of fixed-price listings result in a sale, but only 13 percent of the
listed items are sold.
Table 9: Multiple-item listings
Single item listing Multiple item listing
# of listing
931
3190
# of listings sold
613
888
listing sold rate
65.8%
27.8%
# of items offered
931
20669
# of items sold
613
2138
item sold rate
65.8%
10.3%
What makes multiple-item listings attractive to the sellers? Since there is no extra charge for an
additional item in a listing (in the digital camera price range), sellers may want to list more items
than they have in stock to capture potential unexpected spikes in demand (i.e. obtain additional
items from their suppliers if demand ends up being high and their stock sells out). In addition
there are economies of scale arising from only paying for listing-upgrades per listing rather than
per item: we find that multi-item listings are much more likely to be “Featured” or “Highlighted”
than single-item listings (though these upgrades are used rarely even with multiple-item listings
31
– in less than 5 and 3 percent of listings respectively). On the other hand, listing many items has
a downside in the form of strategic buyer-behavior: strategic buyers who see a lot of units
available may respond by waiting for a lower price in the future – a classic durable-goods
problem.
We don’t observe blatant over-listing the data: the vast majority of multi-listing sellers list less
than 10 items (maximum 34). However, only 6 percent of all the multi-item listings are all sold
out, which indicates excess stated supply, and hence is consistent with some over-listing.
Moreover, our data indicates that the reported number of units is probably not an accurate
indication of the available units in inventory: the histogram of the number of listed items has a
local spike at every multiple of 5, so accounting and inventory-management convenience seems
to play a role. While the pros and cons of multiple-items listings pose an interesting pricing
problem in themselves, we abstract away from the multiple-item issue because an average
multiple-item listing has about the same expected revenue as the average single-item listing in
our data: Table 9 shows that if the expected revenue given a sale of one unit is R, a single-item
listing delivers about 0.65R expected revenue, and a multiple-item listing delivers (2138/3190)R,
i.e. 0.67R. Therefore, in the data at hand, it is reasonable to simply treat a multiple-item listing as
a single-item listing for the purposes of expected revenue – the key part of a seller’s objective
function. In particular, it does not seem that sellers with large homogenous inventories have an
incentive to use posted prices because of eBay’s idiosyncratic rules. In addition, the problem of
setting the posted price remains even with free multiple-item listings.
eBay-specific alternative explanation #2: Free re-listings
Of the total 13843 listings, 5499 listings are not sold. Of these 5499 unsold listings, 2558
listings (46.5%) have been re-listed by two weeks after their ending time (the maximum waiting
time before re-listing is 90 days, so the 46 percent figure probably somewhat underestimates the
actual extent of re-listing). The complicated part about re-listing is that when a re-listing of an
unsold item results in a sale, eBay refunds the second listing fee. The eBay rules thus give
sellers a free second chance to sell, so the variance in mechanisms across listings may be simply
due to the fact that sellers open with a high fixed price, and then follow up with an auction in
case the first listing ends up with no sale – just like a tennis player who hits the first serve as hard
as he can to try his luck, and then gives a slow but safe second serve. Luckily for the purposes of
32
this paper, this explanation for the variance in selling mechanisms across listings can be ruled out
in our data, because the sellers do not seem to systematically change mechanisms after re-listing:
Among the 2523 listing-relisting pairs that we detected, only 3.7 percent changed selling
mechanisms (Table 10). Moreover, the sellers who switch mechanisms after a re-listing tend to
be the less experienced sellers (lower total feedback and more feedback from other sellers rather
than buyers). Also going against the discrimination explanation, among the 974 sellers who sell
two or more cameras within the data, only 14 percent use both auctions and posted prices.
Table 10: Re-listing mechanism-switching matrix
Original
Relisting
Fixed
BIN
Auction
Total
Fixed
BIN
Auction
970
7
12
989
2
1383
15
1400
1
57
76
134
VI. Discussion
By giving sellers a choice among selling mechanisms, eBay has created a level playing field for
posted prices and auctions to compete with each other. The result is a co-existence of both
mechanisms even at a detailed level of a product-category like Canon Digital Point-and-Shoot
cameras. It is easy to see at a glance that such co-existence is happening in most other product
categories as well. This coexistence is a puzzle to us, because most other markets tend to
specialize in only one trading mechanism. We propose four different explanations of this puzzle,
and our analysis rules three of them out: It does not seem that the sellers choose mechanisms
randomly listing-by-listing, or that each seller randomly chooses how to sell all his cameras.
Also, we do not find evidence of second-degree price-discrimination because there is no
premium for posted-price buying, and we reject the idea that eBay is sorted into two separate
mechanism-specific markets because most buyers are observed using multiple mechanisms.
Instead, we find that sellers seem to specialize in only using one mechanism, and a lot of this
choice can be explained by seller-level factors like specialization in the category and scale of
camera inventory. A large portion of the variance in mechanism across sellers remains
unexplained, and seems to be driven by a cross-category personal preference for a given
mechanism.
33
The correlations between inventory properties and mechanism use are consistent with a
theory of mechanism-specific costs proposed in this paper. The key new theoretical observation
is that neither posting fixed prices nor auctioning are costless to the seller, and their respective
costs differ in structure: the cost of posted-pricing is fixed over many identical units, but the cost
of auctioning is a variable cost incurred for every unit sold. This observation leads almost
immediately to the robust prediction that the more larger and more homogeneous the inventory,
the more likely it is that the seller uses posted prices. This is exactly what happens in the data at
hand, not only at the univariate level, but also when a choice-model is used to control for all
other observed factors than may influence mechanism choice.
All theories laid out in this paper remain agnostic about the choice between the fixedprice and BIN-auction mechanisms, treating both as “mechanisms with posted prices”. However,
the data-analysis separates them by using a trinomial logit, and it is possible that the results
presented here will prove useful in the future when a more precise understanding of the
difference between these two mechanisms is developed. One thing is clear already: the BIN
auction is not necessarily “between” pure auctions and fixed posted prices because many of the
explanatory variables have a non-monotonic impact on the shares of the three mechanisms. More
research needs to be done to account for BIN auctions.
The main weakness of the empirical analysis is its merely correlational nature. Causal
words like “effect” thus need to be understood with the usual disclaimer that, for example,
seller’s specialization has the measured effect on mechanism-choice only as long as the observed
variation in specialization is exogenous to mechanism-choice. If that assumption is wrong, the
causal link could be either exactly opposite, i.e. sellers might first choose their selling
mechanism for some other reason, and then build their inventories accordingly. This endogeneity
argument limits the definitive interpretability of all variables derived from properties of products,
like depreciation, bundling, and inventory-homogeneity because the seller has choice over which
products to sell and whether to bundle them with accessories or not. On the other hand, personal
characteristics of the seller determined before the data-period, like feedback or overall scale, are
not subject to this endogeneity critique.
34
References
Budish, E. and Takeyama, L. (2001): “Buy Prices in Online Auctions: Irrationality on the
Internet?, ” Economics Letters, 72, 325-333.
Engelbrecht-Wiggans R. (1993) : “Optimal Auctions Revisited”, Games and Economic
Behavior, vol. 5, 227-239.
Wang, R. (1993): “Auctions versus Posted-Price Selling”, American Economic Review, vol. 83
(4), 838-851.
Kultti, Klaus (1999) “Equivalence of Auctions and Posted Prices,” Games and Economic
Behavior 27, 109-113.
Learmount, Brian, “A History of the Auction”, Barnard & Learmount, 1985.
Lee, Hanh and Malmendier, Ulrike (2006). The Bidder’s Curse. Stanford working paper.
Mathews, T. (2003) : “The Impact of Discounting on an Auction with a Buyout Option”,
forthcoming in Journal of Economics - Zeitschrift für Nationalökonomie.
McAfee, R.P. and Vincent, D. (1997): “Sequentially Optimal Auctions”, Games and Economic
Behavior, vol. 18(2), 246-276.
Milgrom, Paul “Auctions and Bidding: A Primer”, The Journal of Economic Perspectives, Vol.
3, No. 3, 1989a, 3-22.
Milgrom, Paul “Auction Theory” in Advances in Economic Theory Fifth World Congress,
Truman Bewley ed., Cambridge University Press, 1989b, 1-32.
Myerson, R (1981): “Optimal Auction Design”, Mathematics of Operations Research, No. 6,
1981, 58-73.
Wilson, Robert (1989) “Game-theoretic analyses of trading processes,” in Advances in
Economic Theory Fifth World Congress, Truman Bewley ed., Cambridge University Press,
1989, 33-70.
35
Appendix
Example: 2-object inventory, seller uncertain about number of buyers
In this example, we develop the model with 2-object inventory while assuming a particular
source of demand-uncertainty – uncertainty about the number of buyers. Consider a monopolist
seller endowed with two items to sell, 1 and 2, who is deciding whether to use the second-price
sealed-bid auction or posted-price selling to sell each of the items. Auctioning costs the seller α
per auction, whereas pricing research and computations cost β each time they are conducted. The
demand for each object i arises from a different group of Ni unit-demand buyers, whose private
values for a unit of the good are drawn independently from some continuous distribution F on
the [ 0,1] interval.5 The results presented below will hold for any distribution, but let F be
uniform for tractability reasons. The seller is uncertain about the number of buyers in each
group, which is either NL or NH, with equal prior probability, where 2 ≤ N L < N H . When the
seller incurs the market-research cost of β for item i, he learns Ni. The two items are either
identical in the sense that N1 = N2, or unrelated in the sense that N1 is independent of N2. When 1
and 2 are identical and the seller’s inventory is thus homogeneous, the seller can spend β only
once and learn both Ni, but a seller with a heterogeneous inventory would have to spend 2β in
order to set prices optimally.
The expected revenue from auctioning one item is the expected value of the second
highest bidder, so the profit for Ni =N becomes Π auction ( N ) =
N −1
− α ≡ Ra* ( N ) − α , the
N +1
tractability of which follows from the uniform assumption6, and the expected profit before
knowing Ni is Π auction = E ⎡⎣ Ra* ( N )⎤⎦ − α ≡ Ra* − α . When the seller knows Ni, the optimal price to
1
⎛ 1 ⎞N
post maximizes the expected revenue: p * ( N ) = arg max p (1 − p N ) = ⎜
⎟ , where
p
⎝ N +1⎠
(1 − p ) = (1 − F ( p )) is the probability that at least one buyer has a value over p. Therefore,
N
N
5
The separate populations are used here for convenience because this avoids the two auctions / posted-price sales
from competing with each other. Since such competition involves the same demand forces regardless of mechanism,
considering just one population should not change the conclusions found here.
6
The pdf of second highest draw z of N iid uniform draws is N ( N − 1)(1 − X 2 ) z N −2 , so the expected revenue can
be evaluated as Ra* ( N ) = E ( z ) =
1
∫ N ( N − 1)(1 − X ) z
2
N −2
0
36
zdz =
N −1
.
N +1
the expected profit from doing demand research and then selling a single item by posted-price is:
1
N ⎛ 1 ⎞N
*
Π post ( N ) =
⎜
⎟ − β = R p ( N ) − β . Analogously with the auction case, let the ex-ante
N +1⎝ N +1⎠
expected profit be E N ⎡⎣ R*p ( N ) ⎤⎦ ≡ R*p . The optimal price to charge without spending β to learn Ni
⎛
p NL + p NH
would be p ** = arg max p ⎜1 −
2
p
⎝
⎞
*
⎟ , leading to smaller expected revenue R ** < R p .
⎠
Assume that β is small enough that this option is always dominated by learning, so
β < R*p − R ** .
Table A1: Summary statistics of data (averages over N=13,834 listings)
variable
Data about camera sold:
Model currently offered by Canon
Days since model release
Amazon price new
new (dummy)
bundled w/ accessories (dummy)
newXbundle
Data about listing
# units offered (can be ≥ 1 if fixed-price)
# units sold
≥ 1 units sold (dummy)
sold by BIN pride (dummy)
single sale by the seller in 7 weeks (dummy)
Data about seller
log(feedback)
percentage positive feedback
time since eBay reg. in days
total listings by seller within data period
total camera listings by seller within data
percentage of digital cameras in inventory
camera specialist (above %>0.5)
number of CP&SD listings
number of CP&SD sales
seller has Non-Canon P&S cams. in inventory
seller has Computer&Electro in inventory
seller has Non-Electro in inventory
mean
stdev
median
min
max
0.88
345.58
319.6
0.65
0.42
0.29
0.33
216.33
121.58
0.48
0.49
0.45
1
266
295.94
1
0
0
0
16
139.94
0
0
0
1
971
639.94
1
1
1
2.26
0.72
0.6
0.11
0.05
3.12
0.91
0.49
0.31
0.21
1
1
1
0
0
1
0
0
0
0
50
31
1
1
1
7.6
99.3
1415
559
200
0.55
1
38
26
1
1
0
2.3
85
19
1
1
0
0
1
0
0
0
0
11.63
100
9411
123728
18444
1
1
630
319
1
1
1
7.4
2.48
99.01
1.4
1380.77 595.78
7489.09 13911.71
3021.01 4571.48
0.53
0.29
0.60
0.49
187.47 228.41
62.37
83.14
0.73
0.45
0.75
0.43
0.32
0.46
37
Table A2: Posted-price premium (new non-bundled cameras)
Model
SD400
A520
SD300
SD500
SD200
S2IS
SD550
S60
S1IS
A510
S500
A95
A400
A610
G6
SD450
SD20
S70
A85
A75
A620
A410
Pro1
S410
S400
S50
A70
time (days)
Fixed effects
BIN-sold effects
Estimate (SE)
Estimate (SE)
328.03
211.98
275.69
396.09
218.44
488.45
444.32
270.09
269.57
187.69
286.99
317.60
144.30
298.06
469.21
371.80
271.45
382.41
210.00
192.36
380.88
161.93
563.47
252.42
228.47
216.11
154.01
-0.58
(1.67)
(1.83)
(1.93)
(1.93)
(2.17)
(2.37)
(2.62)
(3.68)
(4.07)
(3.47)
(3.41)
(4.52)
(3.62)
(4.18)
(4.15)
(5.74)
(9.15)
(4.59)
(5.02)
(6.08)
(5.72)
(7.53)
(6.85)
(6.18)
(7.50)
(8.38)
(7.81)
-3.34
-0.79
13.51
27.92
4.58
-3.46
13.68
-6.28
11.45
6.96
21.98
-15.40
11.70
9.64
15.51
6.29
-5.28
-6.51
13.55
-16.64
32.50
14.29
29.06
-1.54
-0.10
58.87
-38.10
(2.21)
(2.42)
(2.81)
(3.09)
(2.84)
(3.13)
(3.80)
(4.44)
(5.09)
(5.17)
(6.15)
(5.78)
(6.40)
(6.24)
(6.52)
(7.18)
(9.91)
(7.73)
(7.50)
(8.32)
(8.91)
(9.40)
(10.26)
(11.39)
(14.87)
(13.14)
(21.76)
# sold
693
611
448
439
411
339
254
184
135
128
106
102
96
88
82
67
64
62
60
48
44
40
32
31
20
20
16
Model age
(days)
202
238
352
202
351
138
17
485
576
230
576
384
384
30
384
32
352
384
415
577
33
26
580
576
945
926
936
(0.03)
Note to Table A2: Linear regression, dependent variable is price+shipping, multi-item fixedprice listings considered as separate sales. R2=0.92, the models are ordered in descending
popularity.
38
Table A3: Economics of selling on eBay
Sellers classified by total unit sales within CP&SD category
0-1 sale
2-50 sales
51+ sales
Mean per listing
(N=13,843 listings)
Fixed BIN
price auct.
Pure
auct.
Fixed BIN
price auct.
Pure
auct.
Fixed BIN
price auct.
Pure
auct.
Amazon unit price
$306
$326
$305
$312
$317
$288
$373
$325
$296
BIN price
$278
$295
$319
$329
$425
$393
Minimum bid
$159
$69
$263
$30
$297
$1
% w/ reserve
0%
7%
4%
0%
3%
0%
0%
13%
0%
% sold
65%
76%
89%
45%
49%
97%
28%
37%
100%
% BIN-sold
37%
27%
29%
# units offered
2.82
1
1
3.78
1
1
6.48
1
1
# units sold
0.76
0.76
0.89
0.91
0.49
0.97
0.63
0.37
1
$9
$9
$8
$9
$7
$8
$9
$8
$9
total eBay fees
Only sold & new
cameras (N=6228)
# of new cameras sold
1 sale
2-50 sales
51+ sales
90
280
389
971
620
1726
1050
646
456
Amazon price/unit
sold
$300
$318
$299
$290
$305
$292
$318
$303
$302
net revenue / unit sold
$287
$290
$280
$311
$311
$303
$315
$367
$326
Revenue/Amazon
95.7
91.2
93.9
107.2
102.2
103.7
98.90% 121.4
108.2
39
Table A4: Sellers who use only one format for all their eBay listings
Fixed price
BIN auction
Pure auction
173
957
272.76
10
50.58
4
4.93
5.53
$286
92%
350
73%
12%
9%
5.5
46%
34%
42%
64%
13%
270
437
7.92
3
4.16
2
2.01
1.62
$324
72%
444
44%
10%
5%
4.7
62%
47%
17%
41%
8%
750
1680
242.83
6
10.7
2
2.32
2.24
$300
71%
444
41%
8%
3%
5.07
44%
30%
31%
57%
27%
Number of sellers
Number of focal cameras
mean # listings/seller
median # listings/seller
mean # camera listings/ seller
median # camera listings/ seller
# focal listings/ seller
# sold focal cams / seller
Amazon price new
current camera model
days since release
new
bundle
newXbundle
log(feedback)
% digicams in inventory
specialist (digicams >50%)
% has non-Canon P&S
% has Comp & Electro
% has non-electro
40
Table A5: Raw logit coefficients
Model with Model without
Habit variable Habit variable
Variable
Coeff
tstat Coeff tstat
S500 _fix
1.13
3.56
1.45
6.19
S500 _bin
0.49
1.63
0.08
0.32
S60 _fix
0.20
0.38
-0.32 -0.93
S60 _bin
-2.17 -3.93 -1.56 -4.78
A95 _fix
-2.25 -3.23 -3.29 -5.14
A95 _bin
-1.43 -4.07 -1.51 -5.57
S400 _fix
-0.23 -0.55
0.21
0.76
S400 _bin
-1.13 -3.22 -0.61 -2.76
A400 _fix
-1.55 -2.12 -2.24 -4.14
A400 _bin
-2.79 -6.47 -2.58 -7.46
A70 _fix
0.04
0.10
-1.09 -3.57
A70 _bin
-1.51 -4.15 -1.67 -6.30
A85 _fix
0.73
1.89
1.37
5.06
A85 _bin
0.04
0.12
0.21
0.79
G6 _fix
-0.95 -2.51
0.51
1.69
G6 _bin
-0.66 -1.77
0.02
0.05
A610 _fix
0.16
0.24
-0.71 -1.53
A610 _bin
-1.32 -2.44 -1.79 -4.97
A75 _fix
-1.18 -1.59 -3.21 -5.78
A75 _bin
-1.77 -3.57 -2.39 -7.06
S50 _fix
0.51
0.96
1.21
3.47
S50 _bin
1.07
2.09
1.49
4.35
SD450_fix
-0.98 -1.48 -0.24 -0.59
SD450_bin
-2.24 -4.00 -2.03 -4.71
S410 _fix
-0.09 -0.24
1.10
4.02
S410 _bin
-1.17 -3.12 -0.53 -1.88
Pro1 _fix
-0.05 -0.12
0.57
2.25
Pro1 _bin
-1.42 -3.89 -0.97 -3.81
S70 _fix
-0.74 -0.97 -1.64 -2.39
S70 _bin
0.01
0.02
1.50
3.84
A620 _fix
0.62
1.06
1.63
4.43
A620 _bin
-0.46 -0.84
0.47
1.28
SD20 _fix
1.83
2.70
1.71
3.36
SD20 _bin
1.65
2.67
1.93
4.26
Number of observations 8561
8561
Likelihood
-3188
-6310
MAD
0.129
0.29
Model with Model without
habit variable habit variable
Variable
Coeff tstat Coeff tstat
format_prop_seller 3.33 55.97
new_fix
0.29 1.70 0.19 1.63
new_BIN
-0.88 -6.27 0.09 0.86
bundle_fix
1.85 7.25 2.16 11.82
bundle_BIN
1.38 6.20 2.12 12.51
newXbundle_fix -0.64 -2.10 -0.21 -0.97
newXbundle_BIN -0.61 -2.22 -0.94 -4.65
feedback_fix
0.57 6.60 0.76 12.13
feedback_BIN
-0.01 -0.13 0.94 16.20
hasNE_fix
-0.44 -3.32 -1.34 -14.32
hasNE_BIN
0.27 2.32 -0.09 -1.05
specialist_fix
0.98 3.24 0.91 4.29
specialist_BIN
-1.12 -3.89 -3.02 -11.89
large_fix
-0.58 -5.86 -0.18 -2.32
large_BIN
-0.30 -3.36 -0.37 -5.72
largeSPEC_fix
0.11 0.77 0.41 4.17
largeSPEC_BIN
0.85 6.55 1.55 14.86
fixed_baseline
-1.22 -4.41 -2.49 -12.93
BIN_baseline
1.74 7.50 -1.47 -8.84
SD400_fix
-0.13 -0.58 -0.08 -0.51
SD400_bin
-0.67 -3.16 -0.30 -2.03
A520 _fix
-0.56 -2.30 -0.05 -0.29
A520 _bin
-1.11 -4.82 -0.48 -2.93
SD300_fix
0.01 0.05 0.03 0.15
SD300_bin
-0.43 -1.76 -0.01 -0.05
SD500_fix
1.03 4.03 0.52 2.79
SD500_bin
-0.52 -2.07 -0.35 -1.97
SD200_fix
-0.87 -2.93 0.18 0.81
SD200_bin
-0.20 -0.79 0.60 3.01
S2IS _fix
0.46 1.45 0.77 3.48
S2IS _bin
-0.79 -2.64 -0.05 -0.25
S1IS _fix
1.04 3.40 0.56 2.80
S1IS _bin
-0.13 -0.45 -0.32 -1.64
A510 _fix
0.66 2.09 0.96 4.48
A510 _bin
0.22 0.74 0.56 2.72
SD550_fix
-1.99 -5.00 -2.11 -7.70
SD550_bin
-1.86 -5.64 -2.98 -11.34
41
Table A6: Correlations of the regression variables
variable
mean
new
0.68
bundle
0.57
newXbundle
0.41
log feedback
2.75
has Non-Electro
0.42
specialist
0.57
log CP&SD inventory
2.41
spec x inventory
1.61
Prop Auction Comp & Electro 0.23
std
0.47
0.50
0.49
1.00
0.49
0.50
1.00
1.52
0.36
min
0
0
0
0
0
0
0
0
0
max median
1
1
1
1
1
0
4.228 2.945
1
0
1
1
3.829 2.771
3.829 1.798
1
0.017
Correlations:
Prop
Auction
has
log
new X
spec x
Comp
new bundle
feedback Non- specialist CP&SD
bundle
inventory
Electro
inventory
&
Electro
new
1.00 0.07
bundle
1.00
newXbundle
feedback
has Non-Electro
specialist
log CP&SD inventory
spec x inventory
Prop Auction Comp & Electro
0.56
0.72
1.00
-0.05
0.59
0.44
1.00
0.00
0.12
0.10
0.28
1.00
0.22
0.36
0.41
0.19
-0.22
1.00
0.07
0.58
0.44
0.73
0.16
0.49
1.00
0.22
0.46
0.49
0.38
-0.12
0.93
0.67
1.00
-0.10
-0.52
-0.39
-0.52
0.00
-0.37
-0.54
-0.45
1.00
Note to Table: feedback and inventory are rescaled to have standard deviation of unity and no
negative values. Substantial correlations which are not easily explained are highlighted in bold.