View
2
Download
0
Category
Preview:
Citation preview
1
Higher Revenue with the Same Demand: Distributing Bidders Evenly Across Multi-Object Sequential
Auctions
By: Eric Overby, Georgia Institute of Technology and Karthik Kannan, Purdue University
1.0 Introduction
Suppose you are a consultant advising a seller on how to use auctions to sell products. The seller has
multiple products to auction, and he has retained you to help him achieve higher prices. You might advise the
seller to implement strategies to attract more bidders to his auctions, as more bidders will translate into higher
prices, ceteris paribus. What you might not realize is that the seller can achieve higher prices without
increasing the number of bidders; instead he can achieve them by distributing existing bidders more evenly
across auctions.
In this study, we show both analytically and empirically how a more even distribution of bidders across a
series of auctions increases average prices. We also show how lower transaction costs online facilitate this
distribution of demand. The study contributes to the broader auction literature by investigating how the
distribution of demand influences outcomes in sequential auctions. The study also contributes to the research
literature related to reduced transactions costs in electronic channels (e.g., Clemons 1991; Malone et al. 1987.)
Much of this literature has focused on how electronic channels reduce buyer and seller search costs and the
corresponding effects on market outcomes (e.g., Bakos, 1997; Kuruzovich, Viswanathan, & Agarwal, 2010).
We extend this literature into a sequential auctions context by investigating how electronic channels reduce the
cost that buyers incur when waiting for a product to be auctioned, which we refer to as the “cost of waiting.” In
addition to research implications, the study has clear practical implications for auction sellers and for market-
makers whose transaction fees are based on a percentage of the selling price.
Section 2 presents the motivation and analytical model. Section 3 discusses the empirical context and the
data we use to test the insights from the model. Section 4 presents the empirical analysis and results. We
conclude in Section 5.
2
2.0 Motivation and Analytical Models
In many traditional auctions, products are auctioned sequentially. In other words, the first product is
auctioned, followed by the second product, followed by the third product, and so on. Collectibles, antiques,
wine, livestock, used vehicles, and agricultural commodities such as coffee beans are auctioned in this fashion.
Sequential auctions in which successive products are identical are referred to as “multi-unit” sequential
auctions. Those in which successive products are different are referred to as “multi-object” sequential auctions.
We focus on multi-object sequential auctions, specifically those for used vehicles, although our results can be
generalized to other types of multi-object sequential auctions.1
We investigate how bidder participation across the auctions in the sequence affects outcomes for the seller.
A straightforward approach for improving seller outcomes is to increase the number of bidders who
participate, as more bidders will lead to higher prices. We take a different view and investigate whether and
how the seller can achieve better outcomes without attracting more bidders. Instead, we examine how changing
the distribution of bidders across the auctions in the sequence can yield improved outcomes for the seller.
To illustrate, consider the following simple example. Assume that a seller is auctioning 5 products
sequentially and that she is able to attract a total of 25 bidders, each of whom participates in the bidding for
one of the products. The distribution of bidders across the products in the sequence can take multiple forms,
examples of which are shown in Figure 1. For example, if there is bidder attrition across the sequence, then the
bidder distribution will show a declining pattern. If bidder participation remains steady throughout the
sequence, then the bidder distribution will appear flat. If bidder participation increases over the sequence, then
the distribution will show an increasing pattern. In each case, it is critical to note that the total number of
bidders (n=25) is unchanged; the only difference is how these bidders are distributed across the products in the
sequence.
1 Modeling multi-unit sequential auctions can be challenging because bidders learn each other’s valuations as the auctions progress. This affects each bidder’s valuation, thereby complicating bidders’ strategies. This is not an issue with multi-object sequential auctions.
3
Figure 1: Examples of declining, flat, and increasing bidder distribution patterns.
Ceteris paribus, products with high bidder participation will fetch higher prices than products with low
bidder participation (Brannman, Klein, & Weiss, 1987). Thus, in the example above, products 1 and 2 will
fetch higher prices in the auction sequence with the “Declining” distribution pattern than in the auction
sequence with the “Flat” distribution pattern, while the converse will be true for products 4 and 5. At first
glance, it appears that these price differences will cancel each other out, such that total revenues will be the
same regardless of the bidder distribution. Interestingly, this is not the case, which we show analytically in the
proofs below.
2.1 Analytical Models
We present two proofs. The first is based in a simple setting and is designed to demonstrate the intuition
behind our analytical result. The second relaxes the assumptions of the first setting to demonstrate the
robustness of the result.
2.1.1 Simple Setting: Two Products, n Bidders, Bidder Valuations Distributed Uniformly
Consider two scenarios in which two products are auctioned sequentially. Suppose in scenario 1 that the
number of bidders for each product are n and n with n < n , and that in scenario 2 the number of bidders for
each product is the same n. Next suppose that the total number of bidders for the two products is the same in
each scenario. Hence, 2 * n = n + n . Now, suppose bidders in both scenarios draw their valuations from the
same uniform [a,b] distribution. Then, the following proposition holds:
Proposition 1: The total expected seller revenue is higher in scenario 2 than in scenario 1. In other words,
a more even distribution of bidders across the auctions yields higher revenue than a less even distribution of
the same total number of bidders.
0
5
10
1 2 3 4 5
Declining
0
5
10
1 2 3 4 5
Flat
0
5
10
1 2 3 4 5
Increasing
4
Proof: Following theory pertaining to ascending auctions, the high bid is equal to the second-highest
valuation for each product. For n bids from a uniform [0,1] distribution, this will equal 11
+−
nn
in expectation.
For n bids from a uniform [a,b] distribution, this expression becomes )(*1)1( ab
nna −+−
+ . Thus, in the
second scenario, the total expected revenue from the two auctions is ⎟⎠⎞
⎜⎝⎛ −
+−
+ )(*1)1(*2 ab
nna . In the first
scenario, the total expected revenue from the two auctions is )(*1)1( ab
nna −+−
+ + )(*1)1( ab
nna −+
−+ =
⎟⎟⎠
⎞⎜⎜⎝
⎛−
++−
+ )(*)1)(1(
)1(*2 abnn
nna . The proof for the proposition is accomplished by showing that the first term
is greater than the second, i.e., that (after simplifying and canceling the a and b parameters) 11
+−
nn
>
)1)(1(1++
−nn
nn.
Consider the difference 11
+−
nn
−)1)(1(
1++
−nn
nn=
)1)(1)(1(22+++
−++−−nnn
nnnnnnnnn. As long as the numerator is
positive, we have proved the result. Substituting n = 2n − n and simplifying the terms, the condition
022 >−++−− nnnnnnnnn simplifies to nn > . QED.
Figure 2 provides a graphical illustration of the intuition behind the proof. If bidders draw their valuations
from the same uniform [0,1] distribution, then the expected price given the number of bidders is a concave
function. Thus, the price increase from adding an additional bidder to an auction with low participation
outweighs the price decrease from taking that bidder away from another auction with high participation. Figure
2 illustrates this by showing that the average expected price per product is higher when 10 bidders are
distributed across two auctions as 5 and 5 than when they are distributed as 3 and 7.
5
Figure 2: Graphical illustration of the concavity of the expected price given n bidders drawing valuations from a uniform [0,1] distribution.
2.1.2 Generalized Setting: m Products, n Bidders, Bidder Valuations Distributed Log-Concave
Consider again the two scenarios, 1 and 2, but each involving products that are auctioned sequentially.
Let us represent the number of bidders in scenario 1 by set and in scenario 2 by . Assume that, consistent
with the above, the total number of bidders in each scenario is the same, i.e., the sum of the elements in sets
and are equal. Suppose the distribution of bidders across the products is more even in scenario 2 than in
scenario 1. We capture this by making assumptions regarding the majorization of vectors (e.g., see Arnold
1987). In particular, we assume that set A majorizes B, i.e., A Bf . Suppose the bidder valuations are drawn
from a log-concave distribution with cdf . A wide range of commonly-used distributions such as uniform
and normal satisfy the corresponding properties. Then, the following proposition holds:
Proposition 2: The total expected seller revenue is higher in scenario 2 than in scenario 1.
Proof: We compare the sum of the winning prices across the two scenarios. Let and
be the sum of the winning prices in scenarios 1 and 2, respectively. Note that, for any set
, , is a function separable with respect to each product. Thus,
∑ , where is the expected winning price when the number of bidders is .
Following auction theory about ascending auctions, is the 1 -th order statistic from
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Expe
cted
Rev
enue
Number of Bidders
Avg. revenu e given 5 and 5 bidders for products 1 and 2, respectively
Avg. revenu e given 3 and 7 bidders for products 1
and 2, respectively
6
draws. Given the log-concavity of the valuation distribution, is a concave function (see appendix
for this proof.) Then, according to Theorem 2.9 in Arnold (1987), ∑ ∑ .
This is the same as the condition . QED
3.0 Empirical Context and Data
3.1 Empirical Context
We test the insights from the analytical model in the context of the wholesale automotive market. The
buyers in this market are used car dealers, who use the market to source vehicles to sell to the retail public. The
sellers are other dealers or institutional sellers such as rental car companies and banks. Sellers use the market
to dispose of large numbers of vehicles at a predictable price. There are multiple intermediaries who broker the
transactions, typically referred to as automotive auction companies.
Sellers transport their vehicles to auction facilities operated by the automotive auction companies. There
are multiple facilities throughout the United States. Vehicles are auctioned sequentially in what is referred to as
a “sales event.” Each sales event consists of multiple vehicles, typically grouped based on seller. For example,
a sales event might consist of 200 vehicles being sold by Avis Rent A Car. Each vehicle in a sales event is
driven -- one at a time -- into a warehouse-type building, where a human auctioneer solicits bids on them. The
bidding for each vehicle takes approximately 45 seconds, after which the next vehicle is auctioned. An entire
sales event can last several hours. For each vehicle, the seller has the option to accept or reject the high bid;
there is no binding reserve price to which the seller must commit prior to the bidding. The position in the
sequence in which each vehicle is auctioned is referred to as the “run number.”
Bidders can bid on each vehicle in one of two ways. First, they can travel to the facilities and place bids in
person. We refer to these as physical bidders and physical bids. Second, they can use a web-based application
to place bids. This application simulcasts live audio and video of the sales event; bidders using this application
place bids in competition with bidders who are physically present at the facility. We refer to these as electronic
bidders and electronic bids. Electronic bidders place bids by clicking a Bid button that continuously refreshes
to show the current asking bid.
3.2 Data and Variables
7
Data were provided by an automotive auction company and consist of 19,297,068 vehicles auctioned in
the United States from January 11, 2005 to May 31, 2007 and January 1, 2009 to March 31, 2010. Complete
data for the June 1, 2007 to December 31, 2008 period were not available. For each auctioned vehicle i, the
data consist of the sales event j in which the vehicle was auctioned, the bid log (described below), the vehicle’s
run number (RunNumberi,j), the day the vehicle was auctioned (Dayi,j), which ranges from 1 (Jan. 11, 2005) to
1,906 (March 31, 2010), the vehicle’s mileage (Mileagei,j), and whether the auction resulted in a sale (Soldi,j).
For sold vehicles, the data include the sales price (SalesPricei,j) and a valuation estimate for the vehicle
calculated by the auction company based on prices of similar vehicles sold over the prior 30 days (Valuationi,j).
The vehicles were auctioned in 163,766 sales events, for an average of approximately 118 vehicles per sales
event.
Some institutional detail is necessary to understand the data contained within the bid log. Prior to the
introduction of the webcast channel, individual bids were not recorded; i.e., there was no bid log. Only the
winning bid for each vehicle was recorded, along with the identity of the winning bidder. This changed when
the electronic “webcast” channel was introduced. Each time a physical bidder placed a bid, an auction clerk
would manually register the bid amount in a database. This generated a running bid log for each vehicle as it
was being auctioned. The bid log is displayed in the webcast application to assist electronic bidders with
tracking the bidding activity. Importantly, the auction clerk does not record the identity of physical bidders,
only the bid amounts, unless the bidder was the winning bidder. Thus, it is impossible to tell from the bid log
which bidder placed a physical bid if that bid was not a winning bid. By contrast, when an electronic bidder
places a bid via the webcast channel, this bid is automatically registered into the bid log along with the identity
of the bidder based on the credentials s/he used to log into the webcast channel. Thus, each row of a vehicle’s
bid log contains the bid amount (BidAmount), whether the bid was placed by a physical or electronic bidder
(BidType), and the ID number of the bidder for electronic bids only (BidderID). Table 1 provides a sample bid
log.
8
BidAmount BidType BidderID 10,000 P (for physical) 10,100 E (for electronic) 111 10,200 E 222 10,300 P 10,400 P 10,500 P 10,600 E 111
Table 1: Example of the bid log for a vehicle.
3.2.1 Bid Log Variables: For each vehicle, we recorded the sequence of physical and electronic bids as a
string variable (BidPatterni,j.) For example, for the bid log shown in Table 1, BidPatterni,j = “PEEPPPE”. We
recorded the starting bid (StartingBidi,j) and high bid (HighBidi,j) , the difference between Valuationi,j and
StartingBidi,j (ValuationMinusStartingBidi,j), and the bid increment (BidIncrementi,j). We also counted the
number of physical bids (PBidsi,j), the number of electronic bids (EBidsi,j), and the number of electronic
bidders (EBiddersi,j.) We imputed the number of physical bidders (PBiddersi,j) by using the information
contained within the bid pattern and the relationship between the number of electronic bids and electronic
bidders. Imputation was trivial for three cases. If a vehicle had no physical bids (n=49,303), we set PBiddersi,j
= 0. If a vehicle had only one physical bid (n=1,313,520), we set PBiddersi,j = 1. If a vehicle had only two
physical bids that were placed in succession (n=1,145,492; this would include bid patterns such as “PP,”
“PPEE,” and “EEPPEE”), then those bids had to have been placed by two physical bidders, because a single
bidder would not immediately outbid himself. We set PBiddersi,j = 2 for these vehicles. We used the
relationship between electronic bids and electronic bidders to impute the other cases. We estimated this
relationship as follows. First, we constructed TwoConsecutiveEBidsi,j, which is a dummy variable set to 1 for
vehicles in which at least two electronic bids were placed in succession (0 otherwise.) Examples of bid patterns
for vehicles with TwoConsecutiveEBidsi,j = 1 include “PEE” and “PEPEEEEE.” This represents vehicles for
which at least two electronic bidders placed bids. We then regressed EBiddersi,j on EBidsi,j and
TwoConsecutiveEBidsi,j, after removing observations in which: a) EBidsi,j = 0, b) EBidsi,j = 1, and c) EBidsi,j =
2 and TwoConsecutiveEBidsi,j = 1.2 This yielded a sample of n=2,422,176 and ensured that the sample
2 We used different explanatory variables in the regression, including: a) dummy variables for each level of EBidsi,j, thereby permitting its relationship to EBiddersi,j to be estimated as a fully flexible spline, and b)
9
contained the appropriate data for imputing the value of PBiddersi,j for those observations not covered by the
trivial cases. Results using both an OLS and a Poisson specification appear in Table 2. EBidsi,j and
TwoConsecutiveEBidsi,j are both positively and significantly correlated with EBiddersi,j. Because
TwoConsecutiveEBidsi,j is a dummy variable, it effectively shifts the intercept when TwoConsecutiveEBidsi,j =
1. Thus, if two of the electronic bids placed on a vehicle are consecutive, the intercept in the OLS specification
becomes 2.115 (i.e., 1.117 + 0.938 = 2.115). This makes sense given that a vehicle with two consecutive
electronic bids must also have at least two electronic bidders. If none of the electronic bids are consecutive, the
intercept is 0.938. We used the OLS coefficients to impute PBiddersi,j. Specifically, PBiddersi,j = 0.938 +
(1.177 * TwoConsecutivePBidsi,j) + (0.049 * PBidsi,j), where TwoConsecutivePBidsi,j is defined analogously to
TwoConsecutiveEBidsi,j.
A: OLS Specification B: Poisson Specification Coefficient Coefficient
EBidsi,j 0.049 (0.000) *** 0.015 (0.000) *** TwoConsecutiveEBidsi,j 1.177 (0.001) *** 0.739 (0.001) *** Intercept 0.938 (0.001) *** 0.053 (0.000) *** n 2,422,176 2,422,176 R2 0.63 n/a Log Likelihood n/a -2960840.7 Robust standard errors in parentheses. * p < 0.01, ** p < 0.05, * p < 0.10.
Table 2: Results of OLS and Poisson regression of EBiddersi,j on EBidsi,j and TwoConsecutiveEBidsi,j.
4.0 Empirical Analysis and Results
4.1 Vehicle-Level Analysis
Figure 3 shows the average number of physical and electronics bids (first row) and bidders (second row)
by run number for vehicles auctioned in the first quarters of 2005 and 2010. Figure 3 also displays linear
regression trend lines and R2 statistics.
dummy variables corresponding to the number of consecutive electronic bids in each vehicle’s bid pattern. None of these variables improved model fit, so we used the more parsimonious expression.
10
Q1 2005 Q1 2010
Figure 3: Average number of total, physical, and electronic bids by run number for the first quarters of 2005 and 2010.
As shown in Figure 3, the average number of physical bids and bidders declines over the sequence, with
the slope of this decline similar in 2010 (regression slope = -0.0078 for bids and -0.0007 for bidders) and in
2005 (regression slope = -0.0079 for bids and -0.0006 for bidders.) The average number of electronic bids
increases over the sequence, with the slope of the increase larger in 2010 (regression slope = 0.0031 for bids
and 0.0012 for bidders) than in 2005 (regression slope = 0.0014 for bids and 0.0007 for bidders.)
This indicates attrition among physical bidders and the converse for electronic bidders. One potential
explanation relates to the transaction cost of waiting for subsequent vehicles in the sequence to be auctioned.
This cost of waiting consists of the opportunity cost of not performing other activities while waiting for
vehicles to be auctioned. This cost is high for many bidders, as time spent away from the dealership may result
Avg. num
ber of bids
Run Number
y = ‐0.0079x + 10.455R² = 0.9146
y = 0.0014x + 0.4682R² = 0.7727
0123456789101112
0 25 50 75 100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
y = ‐0.0078x + 9.3928R² = 0.8891
y = 0.0031x + 0.6915R² = 0.7961
0123456789101112
0 25 50 75 100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
Physical BidsElectronic Bids
Run Number
Avg. num
ber of bidde
rs
Run Number
y = ‐0.0006x + 2.5533R² = 0.9234
y = 0.0007x + 0.1589R² = 0.8813
0
0.5
1
1.5
2
2.5
3
3.5
4
0 25 50 75 100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
y = ‐0.0007x + 2.5028R² = 0.8939
y = 0.0012x + 0.2269R² = 0.8888
0
0.5
1
1.5
2
2.5
3
3.5
4
0 25 50 75 100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
PhysicalBiddersElectronic Bidders
Run Number
11
in missed sales opportunities. The cost of waiting is lower for electronic bidders than for physical bidders,
because electronic bidders can perform other tasks at their dealerships during the sales event. Not only are
electronic bidders better able to wait until later in the sequence to bid, but they also have an incentive to do so
to avoid competing with physical bidders who are active at the beginning of the sequence. This could explain
the patterns shown in Figure 3.
There are alternative explanations, including the possibilities that the patterns are idiosyncratic to the first
quarters of 2005 and 2010 and that vehicles that appeal to electronic (physical) bidders are auctioned later
(earlier) in the sequence. The latter possibility is important to consider because prior research has shown that
the electronic channel is often used to purchase low mileage, relatively high-value vehicles whose quality is
predictable and can be adequately represented online (Overby and Jap 2009). We used the following regression
specifications to examine these possibilities.
PBiddersi,j = α + β1*RunNumberi,j + β2*Dayi,j + β3*(RunNumberi,j * Dayi,j) + β4*Mileagei,j + β5*Mileage2
i,j + β6*Valuationi,j + β7*Valuation2i,j + β8* ValuationMinusStartingBidi,j +
β9*BidIncrementi,j + ε.
(1a)
EBiddersi,j = α + β1*RunNumberi,j + β2*Dayi,j + β3*(RunNumberi,j * Dayi,j) + β4*Mileagei,j + β5*Mileage2
i,j + β6*Valuationi,j + β7*Valuation2i,j + β8* ValuationMinusStartingBidi,j +
β9*BidIncrementi,j + ε.
(1b)
Specifications 1a and 1b are identical except for the dependent variables PBiddersi,j and EBiddersi,j. The
interaction between RunNumberi,j and Dayi,j allows the relationship of RunNumberi,j to the dependent variables
to change continuously over time. Mileagei,j and Valuationi,j (and their squares) control for the possibility that
physical or electronic bidders are attracted to vehicles of certain quality and/or value.
ValuationMinusStartingBidi,j controls for the possibility that bidders are attracted to vehicles for which the
auctioneer starts the bidding substantially below market value. BidIncrementi,j controls for the possibility that
smaller increments allow a higher number of bidders to bid. We estimated specifications 1a and 1b
simultaneously using seemingly unrelated regression (“SUR”) and individually using Poisson regression.3 We
scaled Dayi,j, ValuationMinusStartingBidi,j, Mileagei,j, and Valuationi,j by dividing by 1000, 1000, 10000, and
10000, respectively. Results appear in Table 3. Including the variables containing Valuationi,j reduces the
3 EBiddersi,j is a count variable, but PBiddersi,j is not as a result of the imputation. We rounded PBiddersi,j to the nearest integer when using Poisson regression.
12
sample size because Valuationi,j is only recorded for vehicles that sold. For robustness, we also estimated the
models without these variables. Results are qualitatively unchanged and are not reported.
PBiddersi,j EBiddersi,j SUR Poisson SUR Poisson
Coefficient Coefficient Coefficient Coefficient
RunNumberi,j -0.00023 (0.0000)
*** -0.00011 (0.0000)
*** 0.00029 (0.0000)
*** 0.00076 (0.0000)
***
Dayi,j -0.05248 (0.0000)
*** -0.02125 (0.0000)
*** 0.17020 (0.0005)
*** 0.19860 (0.0037)
***
RunNumberi,j * Dayi,j 0.00004 (0.0000)
*** 0.00005 (0.0000)
*** 0.00010 (0.0000)
*** 0.00016 (0.0000)
***
Mileagei,j 0.01997 (0.0000)
*** 0.00986 (0.0000)
*** -0.02890 (0.0001)
*** -0.15006 (0.0003)
***
Mileage2i,j
-0.00029 (0.0000)
*** -0.00015 (0.0000)
*** 0.00039 (0.0000)
*** 0.00148 (0.0000)
***
Valuationi,j 0.00248 (0.0003)
*** 0.01643 (0.0006)
*** 0.19360 (0.0006)
*** 0.57278 (0.0025)
***
Valuation2i,j
-0.00442 (0.0001)
*** -0.00284 (0.0001)
*** -0.01371 (0.0001)
*** -0.07307 (0.0005)
***
ValuationMinusStartingBidi,j 0.05620 (0.0000)
*** 0.02593 (0.0000)
*** 0.03031 (0.0000)
*** 0.06233 (0.0000)
***
BidIncrementi,j -0.00013 (0.0000)
*** -0.00015 (0.0000)
*** -0.00007 (0.0000)
*** -0.00091 (0.0000)
***
Intercept 2.49706 (0.0006)
*** 0.87043 (0.0011)
*** 0.07887 (0.0010)
*** -1.48459 (0.0037)
***
na 11,484,013 11,484,013 11,484,013 11,484,013 R2 (or Pseudo-R2) 0.07 0.07 0.10 0.10 Standard errors in parentheses. * p < 0.01, ** p < 0.05, * p < 0.10. a Sample size is reduced due to the inclusion of variables including Valuationi,j, as discussed in the text.
Table 3: Results of specifications 1a and 1b.
Results indicate that the negative relationship between RunNumberi,j and PBiddersi,j shown in Figure 3
holds after controlling for vehicle quality, the starting bid, and the bid increment. The same is true for the
positive relationship between RunNumberi,j and EBiddersi,j. Both relationships become more positive over
time, although the magnitude of this interaction effect is greater for EBiddersi,j. This increases our confidence
that the physical and electronic bid patterns can be explained by differences in the transaction costs associated
with waiting rather than by other factors.
4.2 Sales Event Level Analysis
The above results show that physical bidders participate more heavily early in the sequence while
electronic bidders participate more heavily later in the sequence. This has the effect of distributing the bidders
more evenly across the sequence. Building on the analytical results presented in Section 2, we next examine
13
whether the evenness of the bidder distribution positively impacts average revenues in sales events in our
empirical context.
The unit of analysis here is the sales event. For each sales event j, we constructed several variables.
AvgHighBidj is the mean of the high bids for the vehicles in sales event j. VehiclesAuctionedj is the number of
vehicles auctioned in sales event j. AvgValuationj is the mean of the valuation of the vehicles sold in sales
event j. As above, Dayj is the day on which sales event j occur, scaled by dividing by 1000. TotalBiddersj is the
number of bidders who participated in sales event j. GiniBiddersj is the gini coefficient of the bidder
distribution for sales event j. This measure the (un)evenness of the bidder distribution across the vehicles in
sales event j. Smaller values represent a more even distribution. For example, assume that sales event A
consists of 5 vehicles on which 4, 2, 3, 5, and 2 bidders bid, and that sales event B consists of 5 vehicles on
which received 3, 3, 3, 3, and 4 bidders bid. For sales event A, GiniBidsj = 0.20. For sales event B, GiniBidsj =
0.05. We regressed AvgHighBidj on GiniBiddersj, TotalBiddersj, AvgValuationj, Dayj, VehiclesAuctionedj, and
VehiclesAuctionedj2. Including TotalBiddersj allowed us to determine whether GiniBiddersj had an effect while
holding constant the total number of bidders participating in the sequence. Results appear in Table 4.
Coefficient GiniBiddersj -6289.43 (102.96) *** TotalBiddersj 0.32 (0.09) *** AvgValuationj 0.99 (0.00) *** Dayj 181.09 (7.59) *** VehiclesAuctionedj 6.63 (0.27) *** VehiclesAuctionedj
2 -0.01 (0.00) *** Intercept 180.28 (17.20) *** N 154,742 R2 0.91 Robust standard errors in parentheses. * p < 0.01, ** p < 0.05, * p < 0.10.
Table 4: Results of regressing AvgHighBidj on GiniBiddersj, TotalBiddersj, AvgValuationj, Dayj,
VehiclesAuctionedj, and VehiclesAuctionedj2.
The coefficient for GiniBiddersj is negative and significant, indicating that a more even bid distribution
(i.e., a smaller value for GiniBiddersj) is associated with higher bids. The standard deviation of GiniBiddersj is
0.052; thus, a one standard deviation decrease in GiniBiddersj is associated with a $326 increase in the average
high bid across the sequence.
14
5.0 Conclusion
Intuition suggests that the key to achieving higher prices in a sequential auction setting is to increase
demand by attracting more bidders. However, this is not strictly required. Our analytical and empirical results
show that redistributing existing bidders more evenly also yields higher prices. We provide evidence in our
empirical context that electronic bidding has facilitated a more even distribution of bidders across the
sequence, theoretically because the electronic channel’s low transaction costs help bidders shift their bids from
early to late in the sequence where competition is lower. Our analysis contributes to the theoretical
understanding of multi-object sequential auctions and transaction costs in online environments and also yields
an alternative strategy for sellers seeking to improve outcomes in sequential auctions without necessarily
having to attract new bidders.
REFERENCES
Arnold, B. (1987), "Majorization and the Lorenz Order: A Brief Introduction". Springer Verlag Lecture Notes
in Statistics, vol. 43.
Bakos, Y. (1997), "Reducing Buyer Search Costs: Implications for Electronic Markets," Management Science,
vol. 43(12): 1676—1692.
Brannman, L., Klein, J. D., & Weiss, L. W. (1987). The price effects of increased competition in auction
markets. The Review of Economics and Statistics, 69(1), 24-32.
Clemons, E. (1991), “Evaluation of strategic investments in information technology” Communications of the
ACM, vol. 34 (1): 22–36.
Kuruzovich, J., S. Viswanathan, R. Agarwal. 2010. Seller search and market outcomes in online auctions.
Management Science vol. 56 (10) forthcoming.
Malone, T.W., Benjamin, R.I., & Yates, J. (1987), “Electronic Markets and Electronic Hierarchies,”
Communications of the ACM, vol. 30(6): 484—497.
Overby, E. & Jap, S. (2009). Electronic and physical market channels: A multiyear investigation in a market
for products of uncertain quality. Management Science, 55(6), 940-957.
Recommended