Pricing Strategy under Reference-Dependent
Preferences: Evidence from Sellers on StubHub
Jian-Da Zhu∗
National Taiwan University
February 2017
Abstract
This paper uses both listing and transaction data on StubHub to study
how different types of sellers price their tickets. Two types of sellers,
single sellers and brokers, are identified from the data. The single sellers
only post a few listings in the whole season, while the brokers sell lots
of tickets in many listings. The results show that the listing prices set
by the brokers are higher than those set by the single sellers in the early
days before an event, but this reverses in the last few days before an
event. This study also proposes a dynamic pricing model based on the
reference-dependent preferences of sellers to support this finding. The
estimation result further leads to the conclusion that single sellers tend
to use the original purchase prices as reference points to determine the
listing prices every day before an event.
∗
Department of Economics, National Taiwan University. Email: [email protected]
1
1
Introduction
In the sports ticket market, official franchise websites are not the only marketplace for consumers to buy tickets. Secondary markets are even more
popular places for fans to search for cheaper tickets, so many people tend
to resell their sports tickets in a secondary market to earn money. For instance, StubHub is the most popular secondary market for sports tickets in
the United States. A seller can post a listing with all the ticket information
including a listing price, and then adjust this listing price at any time before
the game day, so dynamic pricing becomes very common on StubHub. This
paper uses data from StubHub, and aims to study how these heterogeneous
sellers price their tickets dynamically over time.
Compared with other secondary markets, StubHub is a quite professional
platform for selling sports tickets. For each venue and game, StubHub has
different web pages with detailed stadium maps to show where seating will be
in relation to the field. This allows sellers to list their tickets easily and lets
consumers search for tickets with a clear understanding of where their seats
will be. In order to attract sellers and ensure they they can make a profit,
StubHub provides comprehensive transaction records for the seller to set up
the initial price, and the seller can easily change the listing price. Unlike some
other secondary markets which reveal the rating of the sellers, no information
about each seller is provided on StubHub. StubHub guarantees that buyers
can certainly get the tickets from sellers. In addition, both sellers and buyers
are charged a commission after the ticket is sold.
Figure 1 shows an example of Major League Baseball tickets on StubHub. For one particular area in different games with the same face value,
the median listing price starts around $90 and decreases over time until the
game day. The main reason is that the existing sellers adjust their listing
prices downward over time, and new sellers tend to price lower in the market. Although the range of listing prices is quite large in the entire period,
consumers purchase those listings with cheaper prices. The daily average
transaction prices, as black dots, are mostly distributed lower than the median prices, especially in the last few days before a game. In addition to the
listing prices, most transactions happen within one month before a game.
2
Median Listing Prices (Dollars)
0
50
100
0
50 100
Aggregate Transaction Quantities (Seats)
150
Figure 1: Overview for StubHub Market
100
80
60
40
Days Prior to Game
Median
Face Value
Transaction Quantities
20
0
Percentiles 0.1 and 0.9
Average Transaction Prices
Not all the sellers have the same purpose in selling their tickets. Some
might want to sell their tickets simply because they cannot attend the game,
yet some sellers might want to make profits through the online secondary
market. Therefore, heterogeneous sellers can have different pricing strategies.
I have classified the sellers into two groups: single sellers and brokers. Those
who sell tickets only in a few listings during the whole season are defined
as single sellers, and those sellers who sell many tickets in many listings in
the season are defined as brokers. Because transaction data in the primary
market allow identification of how many tickets they buy in the primary
market, the two types of sellers can be classified according to the detailed
purchasing information. In addition, listing and transaction data on StubHub
are used to trace their behavior.
Comparing the price levels over time for the two types of sellers, I find
that prices set by brokers are higher than those set by single sellers in the
early days before an event, but this reverses in the last few days before the
game. I propose a model in which sellers decide the optimal prices based on
3
their reference-dependent preference to illustrate this phenomenon.
Reference-dependent preference comes from prospect theory, by Kahneman and Tversky (1979). According to a reference point, a seller has an
additional gain from gain-loss utility when the transaction price is higher
than the reference point, while the seller incurs a loss if the transaction price
is lower than the reference point. As most single sellers purchase single-game
tickets from the primary market, the natural reference points for them are
the original purchase prices in the primary market. This study shows that
single sellers tend to price close to the original primary market prices to ensure gains in the early listing days and to prevent losses in the last few days
before the game.
To show evidence of a reference-dependent preference, I use an econometric model to estimate the probability of sale for each listing on each day to
recover the opportunity costs for each seller. The result shows that the opportunity costs for single sellers are affected by the original purchase prices,
which is consistent with the theoretical model.
Selling perishable goods in a limited time is related to the literature on
dynamic pricing, which is also called revenue management in marketing literature. Monopolistic dynamic pricing models, starting with Gallego and
Van Ryzin (1994), study how a monopoly firm decides a price over time
under stochastic demand. The optimal pricing strategy can be characterized as a function of the inventory and time left in the horizon (Bitran and
Mondschein, 1997). Zhao and Zheng (2000) extend the model by considering
consumers whose reservation prices could change over time. In addition, an
extensive literature focuses on a competitive model (Netessine and Shumsky,
2005; Xu and Hopp, 2006; Perakis and Sood, 2006; Lin and Sibdari, 2009).
Recently, more literature further incorporates strategic consumers into a dynamic pricing framework (Levin, McGill, and Nediak, 2009; Deneckere and
Peck, 2012). Dynamic pricing is also applied to price discrimination in airline markets (Escobari, 2012). Soysal and Krishnamurthi (2012) show that
strategic consumers can lower retailers’ dynamic pricing revenues. Sweeting
(2012) finds that consumers in the sports ticket secondary market are not
strategic.
In the behavioral economics literature, reference-dependent preference
4
starts from Kahneman and Tversky (1979) and Tversky and Kahneman
(1991), and it is also related to the ”disposition effect” in finance (Barberis
and Xiong, 2009). A reference point could be exogenous, from the environment, or it could be based on people’s rational expectations (Kőszegi and
Rabin, 2006, 2007, 2009). Regardless of the types of reference points, both
experimental and empirical literature find evidences to support this theory.
Baucells, Weber, and Welfens (2011) use an experiment to demonstrate that
reference price is a combination of the first and the last price of the time
series. Crawford and Meng (2011) show that taxi drivers in New York target
both hours and income for reference points. Genesove and Mayer (2001) find
that sellers in the housing market tend to set higher asking prices to prevent losses, which is consistent with pricing behavior for single sellers in the
last few days before a game. In addition, several previous studies combine
dynamic pricing with reference point, and show how sellers impose dynamic
pricing when consumers consider the previous listing prices as the reference
points (Popescu and Wu, 2007; Bell and Lattin, 2000). Different from the
previous literature, this paper focuses on how the reference-dependent preference of sellers affects their dynamic pricing behavior.
The remainder of this paper is organized as follows. Section 2 summarizes the data in this study and shows the evidence of heterogeneous sellers.
Section 3 presents a theoretical model to illustrate how reference-dependent
preference affects pricing. Section 4 provides an empirical model to estimate
the probability of sale to recover the opportunity costs, which serves as evidence of reference-dependent preference. Section 5 concludes this research.
2
Data
The data in this study consist of three parts: the listing data on StubHub
for one anonymous Major League Baseball franchise’s home events in 2011,
the transaction data for those home events on StubHub, and the purchasing
information in the primary market.
On StubHub, sellers can post listings at any time before an event, and
consumers browse those available listings to make a purchase. The listing
data on StubHub contain all the information shown for consumers on the
5
website, including listing price, section number, row number, seat number,
and shipping options. To understand how sellers adjust the prices over time,
the listing data were collected from the StubHub website daily during the
period from March 25, 2011 to September 28, 2011. As StubHub hides the
information of sellers but guarantees that consumers can get tickets sold by
any sellers in the market, the listing data is not enough to identify the sellers.
In addition, the disappearance of available listings is not equivalent to
purchase, since sellers on StubHub can relist tickets with different listing
identification numbers; therefore, the transaction data on StubHub are used
to identify purchase for the listing data.1 Most of the purchased listings in
the sample can be matched with the detailed transaction information, such
as transaction time.
Purchasing data in the primary market can be used to identify the sellers
because all the tickets are sold initially by the franchise.2 Primary market transaction data include comprehensive purchase information, including
types of tickets, purchase prices, ticket characteristics, purchasing dates, and
identification number for buyers. Based on the buyers’ IDs, the amount of
tickets bought in the whole season can be calculated. Besides the purchasing
information, how many listings they have on StubHub can also be identified. However, not all the listings contain the detailed seat information, such
as row number and seat number, so only around 71.9% of listings can be
identified to know the information of sellers.
2.1
Summary Statistics
Table 1 shows the summary statistics for the information of listings on StubHub, including the listing price, starting date, original purchase price, face
value, sold status, and other ticket characteristics. I exclude some of the
1
The transaction data only include the transaction price, quantity, section number,
and row number. There is no seat number for each transaction, so I cannot match all the
purchased listing data with their transaction data. Besides the defect of transaction data,
I cannot guarantee that all the listings are collected during that periods because those
listings with earlier starting date might not be included in the sample.
2
Assume that tickets are not resold or transferred in other secondary markets.
6
listings with extremely high listing prices.3 The remaining sample is 159,223
listings in 81 home events, around 2,000 listings for each game.
Sellers on StubHub can adjust the listing prices easily at any time, so the
observed daily listing prices might change over time for one listing. Table
1 reports summary statistics for maximum, minimum, and average prices of
each listing. Because the seller tends to set a higher price in the beginning
and lowers the price as the event date approaches, the average maximum
prices of all the listings ($76.52) and the average minimum prices ($58.38)
are all greater than the average face values ($42.28). Regarding the timing
of listing, most sellers tend to list their tickets well in advance of the event.
Around 58.2% of listings are listed more than one month prior to the event,
while 23.8% of listings are listed two weeks ahead. The starting dates are
strongly correlated with the starting listing prices because those listings listed
at different times might be from different sellers with different opportunity
costs.
The original purchase prices can only be obtained when the sellers’ information is known. Because prices for season tickets or group tickets are
cheaper than face values, the average original purchase price is $34.52, lower
than the mean face value, $42.28. Table 1 also presents quality characteristics for tickets, including the distance from seat to home plate,4 front row
dummy, and row quality. Row quality is the normalized measure to quantify
the row number. The value one in row quality represents the first row in that
section; the value zero shows the last row in that section. In addition, the
listing period and number of price adjustments vary based on the observed
periods for different events. The average listing period is about 35 days, and
the sellers adjust their listing prices around 2 times for one listing. Since each
listing has many tickets (seats), the seller can sell them separately in many
ways. On average, 32.4% of listings are sold out before the event, and around
35.5% of listings are sold partly during the observed periods on StubHub.
Based on the primary transaction data, the total number of identified
3
Those listings with prices exceeding $999 or 9 times larger than face value are excluded
from the sample.
4
This variable does not vary within the same section. I only calculate the distance from
seat to home plate by section.
7
Table 1: Summary Statistics for Listing on StubHub
Obs.
Mean
Std. Dev.
Min
Median
Max
Price for each listing
Maximum price ($)
Minimum price ($)
Average price ($)
159,223
159,223
159,223
76.52
58.38
70.40
48.85
40.98
44.46
2
1
2
65
49
60
677
677
677
Starting date for listing
(days prior to game)
100 plus
30 to 100
14 to 30
0 to 14
159,223
159,223
159,223
159,223
0.224
0.358
0.180
0.238
0.417
0.479
0.384
0.426
0
0
0
0
0
0
0
0
1
1
1
1
114,387
159,223
159,223
156,204
156,204
34.52
42.28
3.531
0.105
0.548
16.79
22.69
2.608
0.307
0.317
0
12
1
0
0
31
36
3
0
0.571
99
108
145
1
1
159,223
159,223
159,223
253.3
0.719
35.81
93.24
0.450
41.20
72.81
0
1
243.1
1
18
439.3
1
188
159,223
159,223
159,223
1.974
0.324
0.355
3.039
0.468
0.478
0
0
0
1
0
0
74
1
1
Original purchase price
in primary market ($)
Face value ($)
Number of seats
Front row dummy
Row quality
Distance from seat
to home plate (feet)
With sellers’ information
Listing periods (days)
Number of price adjustment
for each listing
Sold out or not
Sold partly
Note: The listing data are collected from March 25, 2011 to September 28, 2011. The
data include the daily seat information on the buying page, such as price, quantity, row
number, and seat number. The row quality is the measure to normalize the row number.
The value one in row quality represents the first row in that section; the value zero shows
the last row in that section.
8
Table 2: Summary Statistics for Sellers on StubHub (N = 10, 504)
Mean
Primary Market Purchase
Types of tickets
Only single-game tickets
Only package tickets
Both single-game
and package tickets
Purchase channel
Only from box office
Only from internet
Both box office and internet
Renewed packages
Number of games purchased
Number of tickets purchased
Average number of tickets
purchased in one game
Std. Dev.
Min
Median
Max
Information
0.426
0.359
0.495
0.480
0
0
0
0
1
1
0.167
0.373
0
0
1
0.280
0.386
0.136
0.449
0.487
0.343
0
0
0
0
0
0
1
1
1
0.545
29.50
140.0
0.498
31.44
486.8
0
1
1
1
20
42
1
81
33,064
6.199
29.83
1
3.200
1,889
88.03
14.37
159.6
0
1
1
2
2
7
5,519
81
8,308
37.19
1
2
1,398
0.881
1
1
27
5.842
1
2.500
142.5
StubHub Resale Information
Number of tickets sold
15.53
Number of games listed
7.946
Number of tickets listed
33.65
Number of listings in
the whole season
10.94
Average number of listings
in one game
1.174
Average number of tickets
listed in one game
3.890
Note: The number of identified sellers is 10,541. The information can be separated as two
parts: purchase information from the primary market and resale information on StubHub.
Box office and internet are two biggest channels for selling tickets, but there are some
other channels not listed. Single-game tickets and package tickets are two major ticket
types in the primary market; other types of tickets are not listed. For the sellers, each
listing might contain many tickets (seats), and those tickets could be partly sold.
9
sellers is 10,504. Table 2 shows the summary statistics for all the identified sellers. In the primary market, three different kinds of tickets can be
purchased: single-game tickets, package tickets, and group tickets.5 Prices
for the single-game tickets and the package tickets are different. Consumers
can buy the single-game tickets for any particular game, but the package
tickets are designed for multiple games. Consumers with different needs can
purchase different kinds of tickets. 42.6% of sellers only buy the single-game
tickets in the primary market; 35.9% of sellers only buy the package tickets. Besides the types of tickets, consumers also have their usual channels to
buy their tickets. Most sellers buy tickets from the website, but still around
28.0% of sellers buy tickets only from the box office.
In addition to the purchase information in the primary market, listing
and transaction data on StubHub indicate how many tickets those sellers
tend to sell in the secondary market. The average number of listings in the
whole season is 10.94, with around 33.65 tickets per seller. Some sellers only
have one listing in that year, but some sellers have lots of listings. The most
active seller posted 8,308 tickets in 81 games by 1,398 listings.
Table 3 shows the distribution of the number of listings among all the
sellers. Among 10,504 sellers, 4,403 sellers (41.92 percent) only have one
listing during the whole season, but 75 sellers (0.71 percent) post more than
150 listings. However, those 4,403 single-listing sellers only have 3.85% of all
the listings, but those 75 top sellers have around 20.19% of all the listings
(23,101 listings). According to the number of listings, I define two types
of sellers: single sellers and brokers. The single sellers have fewer than 15
listings on StubHub in one season, while the brokers have more than 110
listings. 6 Under this definition, around 25% of listings are from the single
sellers, and around 25% of listings are from the brokers. The rest of the
sellers are defined as the middle sellers with around 50% of listings in the
5
Table 2 does not show the summary statistics for the group tickets information because
the proportion of the group tickets is relatively small in the sample.
6
The result in this research is robust based on different definitions for single sellers and
brokers. The single sellers can also be defined as those either with fewer than 10 listings
(around 20% of total listings) or with fewer than 22 listings (around 33% of total listings).
The brokers can also be defined as those either with more than 150 listings (around 20%
of total listings) or with more than 80 listings (around 33% of total listings).
10
Table 3: Types of Sellers
Number of Sellers
Number of listings for
one seller in whole season
1
2-5
6-10
11-15
16-22
23-50
51-79
80-109
110-149
150+
Total
4,403
2,768
1,167
576
442
658
274
96
45
75
10,504
41.92%
26.35%
11.11%
5.48%
4.21%
6.26%
2.61%
0.91%
0.43%
0.71%
Number of Listings
4,403
8,426
8,988
7,317
8,240
21,831
17,464
8,819
5,825
23,101
3.85%
7.36%
7.86%
6.40%
7.20%
19.08%
15.26%
7.71%
5.09%
20.19%
100.00% 114,414
100.00%
market.
Table 4 shows the summary statistics for single sellers, middle sellers,
and brokers. Even though the single sellers and the brokers have similar
numbers of listings in the market, the number of single sellers is 8,914, much
greater than the number of brokers, 120. The first panel presents the average
information for different types of sellers. For instance, the single sellers on
average have 3.7 tickets sold, while the brokers on average have 463.2 tickets
sold in one season. In general, each broker has more listings than a single
seller. Each broker has around 243.1 listings in one season, but each single
seller only has around 3.3 listings.
The second panel in Table 4 shows the average purchase information for
different types of sellers. As expected, the brokers buy more tickets than
the single sellers in the primary market. Based on the types of tickets they
have, the single sellers usually buy single-game tickets, but most brokers have
package tickets. In addition, most of the single sellers use one particular way
to buy tickets, either from the box office or from the internet, but the brokers
often use multiple ways to buy tickets.
11
Table 4: Summary Statistics by Single Sellers, Middle Sellers, and Brokers
Single Sellers
Middle Sellers
Brokers
8,914
1,470
120
Observations
Average Resale Information on StubHub
Number of tickets sold
3.717
(6.326)
3.051
(3.223)
9.580
(11.18)
3.272
(3.416)
Number of games listed
Number of tickets listed
Number of listings in
the whole season
50.62
(52.77)
32.47
(18.03)
109.8
(91.91)
38.49
(22.04)
463.2
(647.2)
71.19
(13.58)
888.2
(1,133)
243.1
(216.9)
Average Purchase Information
in Primary Market
Number of games purchased
23.33
(28.37)
94.74
(404.2)
63.03
(25.13)
301.5
(379.1)
76.81
(12.40)
1,520
(2,123)
Types of tickets
Proportion only buying
single-game tickets
Proportion only buying
package tickets
Proportion buying both
single-game and package tickets
0.491
(0.500)
0.328
(0.470)
0.140
(0.347)
0.0619
(0.241)
0.547
(0.498)
0.315
(0.465)
0.0667
(0.250)
0.342
(0.476)
0.400
(0.492)
Purchase channel
Proportion only buying
from box office
Proportion only buying
from internet
Proportion buying from
both box office and internet
0.266
(0.442)
0.396
(0.489)
0.104
(0.306)
0.374
(0.484)
0.340
(0.474)
0.286
(0.452)
0.167
(0.374)
0.167
(0.374)
0.667
(0.473)
Number of tickets purchased
Note: Standard deviations in parentheses. The single seller is defined as those with fewer
than 15 listings on StubHub in one season, while the broker is defined as those with more
than 110 listings.
12
Table 5 presents the summary statistics for all the listings by single sellers,
middle sellers, and brokers. There are 29,134 listings (25.4 percent of all the
listings) sold by the single sellers, and the number of brokers’ listings is
28,926 (25.2 percent). As to listing prices, the average price set by brokers
is higher than that set by single sellers. There are two factors affecting the
variation in listing prices. One is the quality of seats in different areas; the
other is the listing day before the game. Tickets from the single sellers and
the brokers are located in different areas, although the average face values
for their listings are similar in the table. The brokers usually focus on those
seats with higher markup, but single sellers have more uniform distribution
over different areas. In addition to the location of seats, the row quality
within the section is also different. Listings from brokers have higher row
quality with more front row seats.
Furthermore, listings with different starting dates have different listing
prices. Table 5 shows that around 66.2% of brokers’ listings are posted more
than one month prior to the game, but about 63.4% of single sellers’ listings
are posted within one month of the game. Latecomer sellers tend to have
lower prices than existing listing prices. Since brokers start the listing earlier,
their listings have longer listing periods, with more frequent price adjustment.
However, within a certain period, both types of sellers have a similar number
of price adjustments. Also, compared with the sold listings by the single
sellers, the brokers are likely to sell more listings with greater numbers of
seats in each listing.
To understand how the single sellers and the brokers price their tickets,
all of the characteristics related to the listing prices should be controlled in
the regression. For instance, the quality of listings by the brokers in the
same section is better than that of single sellers, and the row quality should
be considered the control variable as we compare their pricing strategies. In
this way, the difference between two types of sellers is based on the same
quality of tickets. I will discuss how to control those listing characteristics
to compare the pricing strategies for different types of sellers in the following
subsection.
13
Table 5: Listings by Single Sellers, Middle Sellers, and Brokers
Observations
Single Sellers
Middle Sellers
Brokers
29,134
56,354
28,926
Average Ticket Information
Average listing price ($)
Face value
Original purchase price
in the primary market
Number of seats
Starting date for listing
(days prior to game)
100 plus
30 to 100
14 to 30
0 to 14
Front row dummy
Row quality
Distance from seat
to home plate (feet)
Listing periods (days)
Number of price adjustments
for each listing
Sold out or not
Sold partly
56.51
(34.69)
39.49
(20.14)
32.51
(15.52)
2.984
(1.973)
66.11
(37.40)
44.26
(22.05)
36.22
(16.75)
2.938
(1.861)
72.19
(43.04)
39.44
(22.71)
33.23
(17.73)
4.004
(3.195)
0.126
(0.332)
0.239
(0.427)
0.199
(0.399)
0.435
(0.496)
0.0567
(0.231)
0.471
(0.297)
261.5
(83.30)
27.83
(37.84)
1.541
(2.179)
0.349
(0.477)
0.372
(0.483)
0.202
(0.402)
0.325
(0.468)
0.193
(0.394)
0.280
(0.449)
0.0949
(0.293)
0.561
(0.304)
239.4
(87.73)
38.62
(43.84)
2.038
(2.813)
0.423
(0.494)
0.447
(0.497)
0.263
(0.440)
0.399
(0.490)
0.202
(0.401)
0.137
(0.344)
0.151
(0.358)
0.604
(0.319)
261.9
(96.87)
46.57
(45.57)
2.112
(2.300)
0.442
(0.497)
0.504
(0.500)
Note: Standard deviations in parentheses. The single seller is defined as those with fewer
than 15 listings on StubHub in one season, while the broker is defined as those with more
than 110 listings.
14
2.2
Price Dispersion
In this subsection, I specify a linear model to discuss the price dispersion for
all the listings:
pijt = Xijt γ + uijt ,
(1)
where pijt is the listing prices for seller i in section j at period t, and Xijt
includes four sets of variables: quality of seats in the field, characteristics of
listings, game effects, and time effects. First, the quality of seats consists of
the distance from seats to home plate for different sections, row quality, area
effect, and area effect×row quality. Listings with higher quality have higher
prices in the market. Second, I control the number of seats in each listing and
the starting date prior to the game. Most of the listings in the sample have
two or four seats in one listing. Listings with more than five seats could be
sold separately into several two-seat transactions or could be sold together as
one transaction; therefore, those listings with more seats have higher value.
Besides the number of seats in each listing, the starting date can affect the
starting listing price. Sellers are likely to list lower prices when they come
into the market late.
Third, instead of using opponent dummies, I use all the game dummies
to represent the effect of each game. In this way, I don’t need to control
the game day information, such as afternoon game or day of the week for
game day. The last factor I control in the regression is the timing. Dummies
for each day before the game and the day of the week effect for listing are
included because sellers might have different strategies to adjust their listing
prices on different days of the week. Table 6 shows the linear regression
results for interpreting price dispersion.
Columns (1)-(4) in Table 6 are the results for the whole sample. On
average, the effect of distance on prices is around -$15.5 for every 100 feet
from home plate. Compared with the listings with two seats, the listings
with only one seat have lower value, but the listings with over two seats have
higher value. In addition, listing prices with starting date 0-2 days before
the game are $10.34 less than those posted over 100 days prior to the game.
R-squared in column 4 shows that around 67.1% of the variation for price
dispersion could be interpreted by the model. Column (5) shows similar
15
Table 6: Price Dispersion for Listings
Price
Distance from seat to home plate
log(Price)
Price Relative
to Face Value
(1)
(2)
(3)
(4)
(5)
(6)
(7)
-0.147***
[0.000957]
-0.155***
[0.000947]
-0.155***
[0.000947]
-0.156***
[0.000940]
-0.136***
[0.000971]
-0.00194***
[1.44e-05]
-0.00280***
[2.94e-05]
-7.231***
[0.127]
7.635***
[0.0931]
5.688***
[0.0627]
12.06***
[0.0978]
-7.226***
[0.127]
7.632***
[0.0931]
5.687***
[0.0627]
12.05***
[0.0978]
-7.369***
[0.127]
7.192***
[0.0918]
5.834***
[0.0620]
12.26***
[0.0969]
-8.025***
[0.120]
8.139***
[0.105]
4.698***
[0.0640]
10.85***
[0.101]
-0.171***
[0.00219]
0.128***
[0.00143]
0.0655***
[0.000902]
0.192***
[0.00153]
-0.242***
[0.00341]
0.209***
[0.00285]
0.113***
[0.00172]
0.374***
[0.00320]
-10.78***
[0.188]
-10.19***
[0.136]
-9.550***
[0.115]
-8.981***
[0.111]
-7.455***
[0.0867]
-2.423***
[0.0878]
195.7***
[0.650]
-0.155***
[0.00310]
-0.151***
[0.00202]
-0.142***
[0.00166]
-0.136***
[0.00158]
-0.111***
[0.00132]
-0.0328***
[0.00132]
5.656***
[0.00476]
-0.270***
[0.00472]
-0.269***
[0.00348]
-0.260***
[0.00301]
-0.251***
[0.00291]
-0.207***
[0.00245]
-0.0719***
[0.00248]
3.271***
[0.0113]
754,679
0.653
Yes
Yes
Yes
754,679
0.727
Yes
Yes
Yes
754,679
0.438
Yes
Yes
Yes
Relative to number of seats = 2
Number of seats = 1
Number of seats = 3
Number of seats = 4
Number of seats ≥ 5
Relative to starting date 100+
days prior to game
0-2 days prior to game
16
Constant
190.9***
[0.606]
190.8***
[0.601]
191.7***
[0.604]
-10.34***
[0.191]
-9.484***
[0.135]
-8.957***
[0.114]
-8.020***
[0.108]
-6.542***
[0.0853]
-0.523***
[0.0856]
200.6***
[0.607]
Observations
R-squared
Area effect, Area effect×row
Day prior to game, game effect
Day of the week effect
880,723
0.652
Yes
Yes
No
880,723
0.664
Yes
Yes
No
880,723
0.664
Yes
Yes
Yes
880,723
0.671
Yes
Yes
Yes
3-5 days prior to game
6-9 days prior to game
10-13 days prior to game
14-30 days prior to game
30-100 days prior to game
Note: Robust standard errors in brackets; *** p < 0.01, ** p < 0.05, * p < 0.1. Columns (5), (6), and (7) use the sample with
information of sellers.
45
Listing Prices (Dollars)
50
55
60
65
Figure 2: Estimated Listing Price Path for Single Sellers and Brokers
15
10
5
0
Days Prior to Game
Single sellers
Brokers
Note: Dotted lines represent 95 percent confidence intervals. Each plotted value is the
value of the time dummies estimated from the regression model plus the average listing
price for brokers in the last day before the game. The dependent variable in the estimated
regression is the listing price in dollars. On the last day, prices by single sellers is around 5
dollars higher than those decided by brokers; however, in the earlier day, prices by brokers
is around 2 dollars higher than those by single sellers.
results when I focus on those listings with the information of sellers. Instead
of measuring the price level, column (6) shows the regression with dependent
variable, log(price). All the signs are the same, and the coefficients could
be interpreted as the percentage change. The dependent variable in the last
column is the price relative to face value. Only 43.8% of the total variation
could be explained by the model. The reason why those variables Xijt cannot
fully capture the variation of prices relative to face value is that the prices
relative to face value could represent the markup of each ticket, which should
depend on how the franchise underprices or overprices the tickets.
To analyze the pricing strategies between the single sellers and the brokers, I extend the model in column (5) in Table 6 to add the dummies for
17
different types of the sellers and interactions between sellers’ dummies and
the day before the game. The result is shown in Figure 2. Controlled by all
the potential factors to affect the listing prices, prices set by the brokers are
higher than those set by the single sellers in the early days before the game,
but this situation reverses in the last few days.
In the last few days before the game, higher prices set by the single
sellers could be interpreted as the remaining value, because the single sellers
might be able to attend the game. However, the remaining value for the
single sellers on the last day should also affect the pricing level in the early
days before the game, but the listing prices set by the single sellers are not
consistently higher than those set by the brokers in the early period.
In the next section, I will present a theoretical model with referencedependent preference to a provide possible explanation for these pricing
strategies. The single sellers have fewer tickets to sell, and they usually
buy single-game tickets in the primary market. The original purchase prices
might become reference points for them when setting listing prices in the
secondary market. However, the brokers have more experience selling tickets, and they also buy lots of package tickets from the primary market at
bundled prices. The original purchase prices have less chance to affect their
pricing strategies in the secondary market.
3
Theoretical Model
In this section, I present a dynamic pricing model in which sellers have a
reference-dependent preference. For a given event g, there are T periods,
indexed by t={1,2,...T}, for the sellers to sell their tickets, and the game
starts after the period T . The sellers might come into the market at different
times, but during each period in which the number of sellers is large, the
market power for each seller is relatively small. Because of the heterogeneity
of tickets, each seller can decide his or her own prices in each period to
maximize expected profits. If a ticket is not sold in period t, the seller can
decide the price again in period t + 1. In the model, each seller is assumed
to have only one ticket when entering the market, and there is no switching
cost for sellers to adjust the prices every day. To ignore the index g, the
18
maximization problem for seller i in section j at time t could be written as
Vijt = max ui (pijt )Φjt (pijt ) + (1 − Φjt (pijt ))Et (Vijt+1 ), t = 1, 2, ..., T,
pijt
(2)
where Φjt (.) is the probability of sale in section j at time t, and Et (Vijt+1 ) is
the expected value of the ticket at time t + 1. Because the quantity provided
by each seller is relatively small in the market, the probability of sale Φjt (.)
is assumed to be exogenous for each seller, which can be estimated based on
all the listings in the market.
Different sellers in the same section might decide different prices based on
difference in expected value of the tickets. In the last period T , the expected
value could be explained as the remaining value of the ticket after the game
starts. For those sellers who can attend the game even if they cannot resell
their tickets, the remaining value should be positive. However, for those
sellers with many tickets in one game, they might only have zero remaining
value for most of the tickets.
The first-order condition for the profits maximization problem is
u′i (pijt )Φjt (pijt ) +
∂Φjt (pijt )
(ui (pijt ) − Et (Vijt+1 )) = 0, t = 1, 2, ..., T.
∂pijt
(3)
For a risk-neutral seller without gain-loss utility, the utility is defined as
ui (pijt ) = pijt . Then the first-order condition can be rewritten as
Φjt (pijt )
pijt = − ∂Φjt (pijt ) + Et (Vijt+1 ), t = 1, 2, ..., T.
(4)
∂pijt
The intuition for equation (4) is that the optimal price in the current period
is equal to the next period expected value plus the markup, which depends
on the current period demand elasticity. This result is the same as the
traditional dynamic pricing model.
However, if the risk-neutral seller has gain-loss utility based on the exogenous reference point, RPi , the utility can be specified as
ui (pijt ) = pijt + ηG(pijt |RPi ),
19
(5)
where G(pijt |RPi ) is the gain-loss utility, and η > 0 is the parameter to indicate how the gain-loss utility is relative to the consumption utility. G(pijt |RPi )
can be defined as
(
pijt − RPi
if pijt ≥ RPi
G(pijt |RPi ) =
,
(6)
(−λ)(RPi − pijt ) if pijt < RPi
where λ > 0 is the loss-aversion parameter.
Depending on the reference-dependent preference, we have the following
three cases:
• p∗ijt ≥ RPi : the optimal price should satisfy the first-order condition:
p∗ijt
Φjt (p∗ijt )
= − ∂Φjt (p∗
ijt )
+
∂pijt
1
η
RPi +
Et (Vijt+1 ) , t = 1, 2, ..., T.
1+η
1+η
(7)
• p∗ijt < RPi : the optimal price should satisfy the first-order condition:
p∗ijt
Φjt (p∗ijt )
= − ∂Φjt (p∗
ijt )
∂pijt
+
ηλ
1
RPi +
Et (Vijt+1 ) , t = 1, 2, ..., T.
1 + ηλ
1 + ηλ
(8)
• p∗ijt = RPi if the previous two cases are not satisfied.
In equation (4), the expected value Et (Vijt+1 ) can be interpreted as opportunity cost. Similarly, from equations (7) and (8), the last two terms,
ηλ
η
1
1
RPi + 1+η
Et (Vijt+1 ) and 1+ηλ
RPi + 1+ηλ
Et (Vijt+1 ), can also be interpreted
1+η
as ”adjusted” opportunity cost based on the gain-loss utility.
Figure 3 shows the simulation result. Based on the gain-loss utility, the
seller tends to price lower under the domain of gains when the expected price
is higher than the reference point. On the other hand, the seller is likely to
price higher under the domain of losses if the reference point is higher than
the expected value.
20
30
40
Listing Prices
50
60
70
80
Figure 3: Simulation Results
10
8
6
4
Days Prior to Game
With RP=70
2
0
Without RP
Note: The simulation result is based on the probability of sale Φ(1.5 − 0.05p), gain-loss
parameter η = 0.8, and loss-aversion parameter λ = 2.25, where Φ(.) is normal cumulative
distribution function.
4
Estimation and Results
In this section, I specify a model to estimate the probability of sale for each
section. Based on the estimated probability of sale, the adjusted opportunity
costs could be recovered by equations (7) and (8). Then I will show evidence
of how the single sellers price toward the original purchase prices.
4.1
Model Specification
In order to obtain the probability of sale for each section in each period, I
specify a probit model as follows:
s∗ijt = β0 − αpijt + Xijt β + uijt,
(9)
pijt = Xijt Π1 + Zijt Π2 + vijt ,
(10)
21
where sijt = 1{s∗ijt ≥ 0} represents the sale of listings, and Xijt includes
the listing characteristics and competition variables to control the demand
equation. However, prices set by sellers might be correlated with some unobserved demand shock uijt , so equation (10) is needed to specify a cost-based
shock to solve the endogeneity problem. The error terms uijt and vijt are
jointly distributed according to a joint normal distribution:
!!
!
!
uijt
0
1 ρσv
,
(11)
∼N
,
vijt
0
ρσv σv2
where ρ is the parameter to specify this endogeneity problem. If ρ = 0, there
is no endogeneity problem. The demand estimation only needs to rely on the
traditional probit model. However, if ρ 6= 0, the endogeneity problem arises.
I use the control function approach to first estimate equation (10), and then
the estimated error term from the first stage is included into equation (9) to
estimate the probit model.
In order to flexibly estimate the demand equation, I estimate the coefficients on listing prices separately in two periods: 1-7 days prior to the
game and 7-14 days prior to the game, so the 1-7 days prior to the game
dummy×listing prices should be included in equation (9). Furthermore, the
variables Zijt in equation (10) should also include the interactions between
instrumental variables and the period dummy variable.
Besides the endogenous listing prices variable in equation (9), the variables Xijt include two sets of variables: quality-based characteristics for
listings and competition variables for demand estimation. Quality-based
characteristics include the distance from seats to home plate, row quality,
area dummies, row quality×area dummies, game dummies, days prior to the
game, and number of tickets in one listing. Those variables related to the
quality of tickets not only can affect how the sellers decide the prices but also
can influence the demand of consumers.
The competition variables in Xijt should be controlled because they are
correlated with the sellers’ decision on listing prices. I control the dummy to
indicate whether there exists competing listings,7 the number of competing
7
The definition of competing listings is those listings in the same event, in the same
section, on the same date, and with the same number of tickets.
22
listings, mean and lowest prices for competing listings, and the proportion of
listings with higher row quality.
To solve the endogeneity problem, the instrumental variables in equation
(10) should be correlated with the listing prices but not correlated with
unobserved demand shock in uijt . I use two sets of instruments: types of
sellers and timing of listing. Different types of sellers might have different
opportunity costs which affect the pricing decision. I use the different types
of tickets they have and the number of listings they post in one season as the
cost-based shift instruments, which should not be correlated with unobserved
demand shock. The other set of instruments is the starting date for listings.
Sellers with different opportunity costs would decide to post their listings on
different days; however, it is better to assume that those timing decisions are
not correlated with unobserved demand shock.
4.2
Results
Table 7 presents the regression on all the instruments and interactions between the instruments and period dummy. I also include all the characteristics Xijt in this equation. The overall F-statistic for all the instrumental
variables is greater than 10, which indicate that there is no weak instrument
problem in the first stage.
Table 8 shows the estimates of demand. Column 1 presents the traditional
probit model with exogenous listing prices; Column 2 shows the IV probit
model estimated by control function approach. If the unobserved demand
shock is ignored, the coefficients on listing prices from the probit model have
slightly positive bias. Furthermore, the mean elasticities calculated by the
IV probit model are around -0.679 and -0.660 for 7-14 days and 1-7 days
prior to the game respectively.
Assume that all the listing prices are optimal. The opportunity costs can
be recovered based on equations (7) and (8). Opportunity costs are defined
23
Table 7: Regression on Instruments
Variables
Listing Prices
Types of seller variables:
Sellers buying single-game tickets
× 1-7 days prior to game
Sellers buying package tickets
× 1-7 days prior to game
Number of listings
× 1-7 days prior to game
Starting date for listings (Days prior to game)
100 days plus
× 1-7 days prior to game
30-100 days
× 1-7 days prior to game
10-30 days
× 1-7 days prior to game
7-10 days
× 1-7 days prior to game
4-7 days
Observations
F-statistic on all the instruments
p-value
0.475***
(0.0459)
-0.208***
(0.0632)
0.233***
(0.0606)
-0.198***
(0.0766)
0.00211***
(7.46e-05)
-5.99e-05
(9.63e-05)
7.745***
(0.0665)
3.419***
(0.141)
5.230***
(0.0540)
2.429***
(0.133)
-0.714***
(0.0905)
2.207***
(0.133)
-1.436***
(0.0788)
0.548**
(0.214)
-1.986***
(0.0793)
2,304,574
3871.13
0.000
Note: Standard errors in parentheses; *** p < 0.01, ** p < 0.05, * p < 0.1.
24
Table 8: Demand Estimation
Variables
Listing price coefficients
×1-7 days prior to game
Distance from seat to home plate (feet)
Relative to number of seats = 2
Number of seats = 1
Number of seats = 3
Number of seats = 4
Number of seats ≥ 1
Competition coefficients:
Dummy variable for competing listings
Number of competing listings, log(N+1)
Mean price for competing listings
Lowest price for competing listings
Proportion of higher row quality seats
Probit Model
IV Probit Model
-0.0289***
[0.0002]
-0.0036***
[0.0001]
-0.0043***
[0.0001]
-0.0316***
[0.0005]
-0.0035***
[0.0001]
-0.0044***
[0.0001]
-0.4261***
[0.0145]
0.1732***
[0.0070]
0.1195***
[0.0045]
0.2191***
[0.0052]
-0.4529***
[0.0156]
0.1829***
[0.0072]
0.1249***
[0.0046]
0.2356***
[0.0064]
-0.2737***
[0.0088]
-0.1894***
[0.0045]
0.0048***
[0.0002]
0.0002
[0.0002]
-0.1300***
[0.0057]
-0.3045***
[0.0108]
-0.1942***
[0.0047]
0.0053***
[0.0002]
0.0002
[0.0002]
-0.1391***
[0.0058]
0.0012**
[0.0005]
4.1710***
[0.0795]
2304574
-332937.755
Coefficients on estimation error from first stage
Constant
3.8153***
[0.0301]
2304574
-334335.073
Observations
Log-likelihood
Note: Standard errors in brackets; *** p < 0.01, ** p < 0.05, * p < 0.1.
25
as
Oppijt =
p∗ijt
+
Φjt (p∗ijt )
∂Φjt (p∗ijt )
∂pijt
1
η
RPi +
Et (Vijt+1 ) under the domain of gains
1+η
1+η
ηλ
1
=
RPi +
Et (Vijt+1 ) under the domain of losses
1 + ηλ
1 + ηλ
=
∂Φjt (p∗ )
According to the estimates from Table 8, Φjt (p∗ijt ) and ∂pijtijt can be
calculated for each listing in each period. Estimated opportunity costs for the
single sellers and the brokers are shown in Figure 4. Most of the opportunity
costs are positive, and the brokers have overall higher opportunity costs. One
possible interpretation is the selection effect, because the brokers hold the
tickets with higher value to resell. To examine the story of reference point,
the null hypothesis should be H0 : η = 0. However, it is impossible both
to have the variation on RPi and to control all the possible characteristics
which would affect Et (Vijt+1 ), because RPi is constant over time. The only
variation on RPi within the same quality should rely on different sellers, so
it is impossible to estimate η for the single sellers or for the brokers.
Instead of running the regression to obtain η, the other possible way to
show evidence of the reference point is to compare the difference between the
opportunity costs and the original purchase prices. If there is no referencedependent preference, the opportunity costs should be independent from the
original purchase price. If the sellers decide the listing prices based on the
reference points, the opportunity costs should be affected by the reference
points. Then the opportunity costs are likely to be close to the original
purchase prices under a reference-dependent framework.
Because all the listings might have different original purchase prices, I
subtract the original purchase prices from the opportunity costs. Figures 5
and 6 show the density function for positive and negative differences respectively. From Figure 5, the single sellers have more negative difference values
close to zero. In addition, the single sellers also have more positive difference
values close to zero in Figure 6. This shows that the opportunity costs for
the single sellers are affected by the original purchase prices in the primary
26
0
.005
Density
.01
.015
.02
.025
Figure 4: Estimated Opportunity Costs for Single Sellers and Brokers
0
50
100
150
Opportunity Cost
Single sellers
Brokers
.05
.1
Density
.15
.2
.25
Figure 5: Difference between Opportunity Costs and Original Purchase
Prices (Negative)
−6
−4
−2
Difference between Opportunity Cost and Original Price
Single sellers
27
Brokers
0
market. If there is no effect from the reference points for the single sellers, we
do expect that the single sellers will also have smaller negative difference values in Figure 5. Therefore, compared with the brokers’ decisions, the pricing
behavior for the single sellers is indeed affected by the reference points, and
the possible reference points are the original purchase prices in the primary
market.8
0
.005
.01
Density
.015
.02
.025
Figure 6: Difference between Opportunity Costs and Original Purchase
Prices (Positive)
0
50
100
Difference between Opportunity Cost and Original Price
Single sellers
5
150
Brokers
Conclusion
In this research, I use both listing and transaction data on StubHub to study
how different types of sellers decide their listing prices. Based on the number
of listings in the whole season, sellers can be defined as two types: single
8
Instead of using the original purchase prices, I can obtain the same result by using
the face values. This means that primary market prices do become the reference points
affecting the single sellers’ pricing behavior.
28
sellers and brokers. The singles sellers only sell a few tickets in one year, but
the brokers sell many tickets in many listings in the whole year. The result
shows that prices set by brokers are higher than those set by single sellers
further in advance of the game, but this relationship is inverted in the last
few days prior to the game.
To interpret this phenomenon, I propose a pricing model based on the
reference-dependent preferences of sellers. The sellers tend to price close
to their reference points, and the natural reference points for sellers in the
secondary market are the original purchase prices in the primary market.
Based on the model’s prediction, the sellers with the original prices as the
reference points should price lower to ensure a gain in the early days, but price
higher to prevent the losses in the last few days. I also specify an econometric
model to obtain the opportunity costs for different types of sellers. The result
shows that the opportunity costs for the single sellers are affected by their
original purchase prices.
References
Barberis, N., and W. Xiong (2009): “What Drives the Disposition Effect? An Analysis of a Long-Standing Preference-Based Explanation,”
Journal of Finance, 64(2), 751–784.
Baucells, M., M. Weber, and F. Welfens (2011): “Reference-Point
Formation and Updating,” Management Science, 57(3), 506–519.
Bell, D. R., and J. M. Lattin (2000): “Looking for Loss Aversion in
Scanner Panel Data: The Confounding Effect of Price Response Heterogeneity,” Marketing Science, 19(2), 185–200.
Bitran, G. R., and S. V. Mondschein (1997): “Periodic Pricing of
Seasonal Products in Retailing,” Management Science, 43(1), 64–79.
Crawford, B. V. P., and J. Meng (2011): “New York City Cab Drivers’
Labor Supply Revisited: Reference-Dependent Preferences with RationalExpectations Targets for Hours and Income,” American Economic Review,
101(5), 1912–1932.
29
Deneckere, R., and J. Peck (2012): “Dynamic Competition With Random Demand and Costless Search: A Theory of Price Posting,” Econometrica, 80(3), 1185–1247.
Escobari, D. (2012): “Dynamic Pricing, Advance Sales and Aggregate
Demand Learning in Airlines,” Journal of Industrial Economics, 60(4),
697–724.
Gallego, G., and G. Van Ryzin (1994): “Optimal Dynamic Pricing of
Inventories with Stochastic Demand over Finite Horizons,” Management
Science, 40(8), 999–1020.
Genesove, D., and C. Mayer (2001): “Loss Aversion and Seller Behavior: Evidence from the Housing Market,” Quarterly Journal of Economics,
116(4), 1233–1260.
Kahneman, D., and A. Tversky (1979): “Prospect Theory: An Analysis
of Decision Under Risk,” Econometrica, 47(2), 263–291.
Kőszegi, B., and M. Rabin (2006): “A Model of Reference-Dependent
Preferences,” Quarterly Journal of Economics, 121(4), 1133–1165.
(2007): “Reference-Dependent Risk Attitudes,” American Economic Review, 97(4), 1047–1073.
(2009): “Reference-Dependent Consumption Plans,” American
Economic Review, 99(3), 909–936.
Levin, Y., J. McGill, and M. Nediak (2009): “Dynamic Pricing in the
Presence of Strategic Consumers and Oligopolistic Competition,” Management Science, 55(1), 32–46.
Lin, K. Y., and S. Y. Sibdari (2009): “Dynamic Price Competition with
Discrete Customer Choices,” European Journal of Operational Research,
197(3), 969–980.
Netessine, S., and R. A. Shumsky (2005): “Revenue Management
Games: Horizontal and Vertical Competition,” Management Science,
51(5), 813–831.
30
Perakis, G., and A. Sood (2006): “Competitive Multi-period Pricing for
Perishable Products: A Robust Optimization Approach,” Mathematical
Programming, 107(1-2), 295–335.
Popescu, I., and Y. Wu (2007): “Dynamic Pricing Strategies with Reference Effects,” Operations Research, 55(May 2015), 413–429.
Soysal, G. P., and L. Krishnamurthi (2012): “Demand Dynamics in
the Seasonal Goods Industry: An Empirical Analysis,” Marketing Science,
31(2), 293–316.
Sweeting, A. (2012): “Dynamic Pricing Behavior in Perishable Goods
Markets: Evidence from Secondary Markets for Major League Baseball
Tickets,” Journal of Political Economy, 120(6), 1133–1172.
Tversky, A., and D. Kahneman (1991): “Loss Aversion in Riskless
Choice: A Reference-Dependent Model,” Quarterly Journal of Economics,
106(4), 1039–1061.
Xu, X., and W. J. Hopp (2006): “A Monopolistic and Oligopolistic Stochastic Flow Revenue Management Model,” Operations Research,
54(6), 1098–1109.
Zhao, W., and Y.-S. Zheng (2000): “Optimal Dynamic Pricing for Perishable Assets with Nonhomogeneous Demand,” Management Science, 46(3),
375–388.
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