Download Group Membership and Diffusion in Virtual Worlds

Group Membership and Diffusion in Virtual Worlds
David A. Huffaker, Chun-Yuen Teng, Matthew P. Simmons, Liuling Gong, Lada A. Adamic
School of Information, University of Michigan, Ann Arbor, MI
Email: [email protected], (chunyuen,mpsimmon,llgong,ladamic)@umich.edu
Abstract—Virtual goods continue to emerge in online communities, offering scholars an opportunity to understand how social
networks can facilitate the diffusion of innovations. We examine
the social ties for over one million user-to-user virtual goods
transfers in Second Life, a popular 3D virtual world, and the
unique role that groups play in the diffusion of virtual goods.
The results show that individuals – especially early adopters –
are more likely to adopt a virtual good when they belong to
the same groups as previous adopters. We also find that groups
exhibit bursty adoption, in which many individuals adopt in short
succession. In addition, we show that adoption activity within a
group depends on the group’s size and interactivity. Our work
provides insights into theories of social influence and homophily.
I. I NTRODUCTION
Virtual goods continue to become incorporated into social
network services, gaming platforms and virtual worlds, allowing users to enhance their online experiences or customize
their online identities. These virtual items can be purchased
for a small payment or for free, and often manifest as
commodities (e.g., fashion, brand name or celebrity gear) or
game accessories (e.g., a World of Warcraft shield or a wagon
in Zynga’s Farmville) [1], [2]. Virtual goods represent a way
to measure information being transmitted over social networks
and provide broader insights into our understanding of social
influence and diffusion.
While previous research in communication studies has
demonstrated the important role that social ties play in the
spread of information [3], little empirical work has been able
to test these propositions on a large-scale. More recent research
on diffusion has highlighted the intricate and intertwined roles
of social influence (i.e., a friend or opinion leader impacts
one’s propensity to adopt an idea or innovation) and homophily
(i.e., sharing similar interests with others increase one’s exposure to new innovations and propensity to adopt) [4], but it
is unclear which variables best measure these complex social
behaviors.
This research examines the role of social influence and homophily in large-scale virtual goods adoption with a particular
focus on the role that groups play in the process of diffusion. It
is motivated by the following research questions: What social
factors increase the likelihood that a user will adopt a virtual
good? What role does group membership play in the adoption
of virtual goods, and to what extent do group characteristics
impact adoption?
To answer these questions, we examine how virtual goods
spread along social networks using a unique data set of online
interactions in a popular 3D immersive virtual world called
Second Life (SL). SL allows users to create and distribute
virtual goods, and uses an in-game currency that can be
purchased with real money. Because 95% of the content in
SL is actually created by the users, and because an astounding
number of paid and zero-cost transactions occur in SL [5], it
remains an ideal venue for studying why some virtual goods
are adopted by users while others fail to diffuse. Second Life
also allows us to examine the unique role of groups in the
process of diffusion. Users can join up to 25 formal groups
based on common interests or identities. SL users can send
messages to other group members, hold events and meetings,
and share information about products and locations inside the
virtual world.
II. T HEORETICAL F RAMEWORK
Two popular theoretical frameworks have been used to
explain diffusion: (a) theories of social influence ; and (b)
theories of homophily. Theories of social influence suggest
that exposure to influential individuals increases the likelihood
of adopting similar beliefs or attitudes [6]. Friends, peers,
family, or more distant leaders, cultural figures or celebrities
all have the potential to impact another person’s attitudes
or behaviors. Examples in recent research include evidence
that obese friends or partners can increase one’s own weight
gain [7] or that local social networks can influence others
to quit smoking [8]. Research in online settings also show
support for theories of social influence: digital information
tends to spread within the same social circles [9]; adoption
rates increase as friends begin adopting an item [10], [11];
neighbors provide social reinforcement of a particular health
behavior [12].
Theories of homophily posit that individuals seek out others
who follow the same interests and self-categorization (e.g.,
auto restoration hobbyists, punk rockers), or belong to the
same formal or informal groups (e.g., ethnicity, IT workers) [6]. Homophily not only increases exposure to ideas
or innovations as one coalesces with the group, but group
members are more likely to adopt because they already have
a propensity towards the attitude, behavior or idea. In other
words, it is not that hanging with the wrong crowd will
increase bad behavior, but that individuals with a propensity
for bad behavior might gravitate toward the wrong crowd [13].
Recent online studies lend support for theories of homophily
and diffusion: a study of mobile app adoption finds that
homophily explains more than half of diffusion [14]; a study
of email product recommendations finds that the most popular
items represent niche interests, suggesting that there is a low
GROUP B
GROUP A
GROUP C
which small groups can rely on strong connections of a few
individuals while large groups require continuous changes in
membership [19]. Our secondary contribution is to provide
more insight into the relationship between group-level social
structure and diffusion.
III. M ETHODOLOGY
A. Data
Fig. 1. Conceptual model of how diffusion spreads via social influence and
homophily. The origin of the virtual good (in black) influences the adoption
of several friends, one of whom is able to spread the asset further because of
shared interest among fellow group members.
probability of crossing over to individuals who do not share
that particular interest [15].
These theories are not independent. Scholars argue that homophily selection results in correlated attitudes and behaviors,
making it difficult to determine a causal relationship between
social influence and diffusion [4]. Some even argue that social
influence and homophily are so highly intercorrelated that
they can not be distinguished from one another [16]. This
is not unique to offline settings; a study of social influence
in Wikipedia shows that users become rapidly similar after
their first online communications, and this keeps increasing
over time, making it difficult to tease social influence and
homophily apart [17].
This research intends to provide further insights into the
ways in which we can disentangle social influence and homophily in online interactions. In Second Life, users can
distribute virtual goods to one another, communicate through
a chat system, add each other to a friend list, or join up to
25 formal groups based on interest or self-categorization. This
allows us to study the various types of interaction that users
engage in, and measure the extent to which diffusion is related
to friendship or shared group membership. We argue that
while social ties impact adoption, being a member of a group
increases the diffusion of virtual goods. This is illustrated in
Figure 1: the node in black shares a virtual good to several
friends, but the asset continues to diffuse because nodes in
gray are in groups based on shared interests. This even allows
the asset to spread across multiple groups with a potential
boundary. Since Group C is focused on a completely different
topic, the asset does not penetrate.
We also argue that not all groups share the same communication patterns or structural signatures, and it is likely that
some attributes such as the size and communication patterns
should impact diffusion as well. For example, participation
equality and dynamism, group size and diversity, maturity
and cohesiveness all contribute to seeking and sharing information [18]. The structural signatures necessary for the
health and stability of large and small groups also differ, in
Our data includes all virtual goods adoptions that took place
in SL between November and December 2008 for two types
of assets, provided the user still held the asset at the time
of data collection. The first, landmarks, are bookmarks that
avatars can use to visit a specific location within the virtual
world. There may be multiple landmarks with different annotations that correspond to identical coordinates, facilitating the
tracking of diffusion of information about a location through
different initial landmark instances. The second kind of asset
is a gesture, which allows the avatar to execute a sequence
of motions, or to emit a particular sound. Landmarks and
gestures were selected because they are two types of nondivisible virtual goods that can easily be traced.
In addition, we have weekly snapshots of the social network
(buddy) graph for SL users, as well as weekly updates on their
group affiliations for the same Nov.-Dec. 2008 time period. We
also have data on fee transactions that have been described in
previous studies [5], [10], [20], but which here are used only
to determine whether a user is active in SL during the period
in question. Data on individual users includes information
on their experience and activity level: when they joined SL,
how many days they were active and how much revenue they
generated.
B. Sample
Our goal is to be able to predict which users will adopt
which asset, given certain types of information such as the
number of their friends who had previously adopted a particular asset, or the number of groups the user shares with previous
adopters of the asset. At first it may seem difficult to determine
which of hundreds of thousands of users will adopt one of
the millions of assets. However, the problem becomes much
more scoped once we know that a user’s friend has adopted
an asset. In previous work, we showed that a large portion of
asset transfers occurs between users who are friends in SL,
and users are more likely to adopt after their friends do, even
if they do not obtain the asset from the friend directly [10].
We chose our first sample accordingly by examining only
adopters and non-adopters who both have at least one adopting
friend. This allows us control for a user’s knowing someone
who adopted while examining our variables of interest described below. In other words, for each asset we select one
adopter who had a friend subsequently adopted the same asset,
and then record that adopting friend and as well as one friend
who did not adopt. We omit assets where no pair of adopters
are friends. In terms of asset adoptions, we see 1,092,094
adoptions, which represent 546,047 unique assets that were
exchanged among 235,467 unique users.
1.00
0.20
0.10
0.05
P(X>=x)
0.50
gesture
landmark
1
5
10
50
100
500 1000
# of adopters per asset
Fig. 2. The distribution of number of adopters for two types of virtual goods.
As a control, we also construct a sample where neither
adopters nor non-adopters share an adopting friend. For this,
we select one adopter per asset, and to balance the sample,
we select one non-adopter who actively transacted during the
time that the asset was being adopted. This excludes users
who may have been non-adopters due to inactivity. However,
because there is no record of adopting users subsequently
discarding the item. predictive accuracy is compromised by
lack of complete information about all adoptions.
For our examination of group characteristics conducive to
diffusion, we analyze the network characteristics of 61,722
unique groups. We limit our analysis to groups with ten (10)
or more members, and for virtual goods with at least five (5)
adopters.
From Figure 2, we can see that while a few assets enjoy
widespread popularity, most were adopted by just a few individuals. The distribution of gestures displays a step function
because avatars by default have a certain number of gestures
that tend to remain unless discarded from inventory. It is also
interesting to note that adopters tend to occupy a distance of
two degrees in the buddy graph from the first adopter.
C. Variables of Interest
Our dependent variables focus on the likelihood of adoption,
as well as total adoptions within a group. Our independent
variable selection captures many unique social behaviors including relationships with friends, groups and other adopters.
We also control for how long users have been in SL, their previous adoption behavior, and the adoption rates of the groups
they inhabit. Because SL users can join up to 25 different
groups, we develop an aggregated measure of group similarity
between adopters and non-adopters. We also present a variety
of social network variables used to measure characteristics of
these groups.
Asset Adoption. This dichotomous outcome variable represents whether a unique asset has been adopted by a particular
user.
Number of Days in SL: Total number of days a user has
spent logged into Second Life.
Number of Previous Adoptions: Total number of other
virtual assets that the user has adopted in the past.
Adopt Time: Ratio of the adopter’s position in the adoption
chain (i.e., first adopter, second adopter, nth adopter) divided
by the total number of adopters of the asset. For example, t =
0.1 means that the user was among 1/10th of users to adopt.
Number of Previously Adopting Friends: Total number of
friends that previously adopted the same virtual asset. Friends
are users the user has added to their buddy list.
Distance to First Adopter: Length of the shortest path
from the first adopter of an asset in SL to any other adoptions
that occur afterwards. The first adopter is also likely to be the
creator.
Number of Friends Shared with Previous Adopter: In the
sample where the paired adopter and non-adopter both share
the same adopting friend, this is a proxy for the strength of
tie with the adopting friend.
Number of Groups: Total number of SL groups a user
belongs to during the sampling frame.
Group Similarity: Cosine similarity between the group
membership of an adopter and the groups of previous adopters.
|Gi · Gj |
(1)
� Gi �� Gj �
We assign the following weight Wk to each group k:
Wk = log[(total # users)/(# users in group k)]. When comparing one user against all previous adopters, we take the
average pairwise similarity between that user and all previous
adopters.
Crowding Factor: Percentage of adopters in each of the
user’s groups. It is calculated as:
Si,j =
Crowdingf actor =
�
k
Wk
# adopters in Group k
# users in Group k
(2)
Burstiness: Binary variable specifying whether a burst event
is detected in the asset adoption time series.
Group Adoptions: Total number of assets adopted by all
users in the group. The asset can be exchanged with any other
user in SL.
Group Transfers: Total number of assets transferred between group members.
Number of Group Members, N: Total number of users
that have joined or were already members of a group during
the one-month period.
Number of Edges E: Total Number of connections between
group members in the social graph or through transactions.
Average Degree: E/N.
Clustering Coefficient: The number of closed triads as a
proportion of all connected triples. It represents how cliquish
social ties are within a group.
Largest Connected Component (LCC): The LCC is the
largest subset of the network by which one can reach any node
from any other node within the subset by traversing edges.
Change in Size: Positive or negative change in group membership between November and December 2008, normalized
by the size by the group membership in November.
Number of Active Users: Users in the group who actively
communicated or traded during the one-month period.
The groups in this sample demonstrate a large amount of
variability in the above characteristics. While 36% of groups
have at least 10 members, the top 1% of groups have 500
or more members. There is a high rate of overall adoptions
by group members (M = 1531.89), as well as within-group
transfers (M = 856). There is a high degree of clustering
(M = .29), a medium average degree (M = 5.6), and a large
connected component (M = .51). These groups also show high
variability in their membership turnover, ranging from losing
two members in a month to gaining 4,000 members.
IV. R ESULTS
A. Predicting Virtual Goods Adoption
In order to predict adoption, we include attributes of the
individual users, their interactions with other adopters, and
adoption activity within the groups to which they belong. We
rely on two data sets to build our models. In the first test data
set, we select two users for each asset who have a friend that
has previously adopted it. One user adopts the asset after the
friend, and the other user does not. This allows us to utilize a
logistic model where asset adoption serves as a binary outcome
variable.
As shown in Table I, all the variables in the logistic
regression are significant. We note that because our sample
is very large, some of the variables — while significant —
do not explain much of the variance. In order to examine
the individual impact of each variable on the model, we
rely on cross-validation measures [21]. Cross-validation (CV)
randomly selects ten “folds” in the data, removes each fold and
re-fits the regression model repeatedly, in order to estimate
how well the predictive model performs. Values above 0.5
suggest that the variable(s) is predicting better than a random
guess, i.e., that everyone in our balanced data set would have
50% chance of adopting.
The model shows that group similarity (CV = 0.63) and
crowding factor (0.61) are the most predictive individual
variables in determining if an adopter’s friends will adopt.
The group similarity measure shows that the more groups that
a potential adopter shares with those who previously adopted,
the higher the likelihood of adoption (Odds Ratio = 1.26). The
crowding factor also reveals that the more adoption activity
found in a users’ groups, the more prone its members are to
adopt (Odds Ratio = 1.11).
The next three most predictive variables represent one’s
propensity to adopt virtual goods in general, how embedded
an individual is in a particular social circle with the previous
adopter, and the social distance from the first adopter. The
number of friends that are shared with the previous adopter,
a proxy for tie strength, shows a positive impact on adoption
(Odds Ratio = 1.40). The more items a user has adopted in
the past, the more likely she is to adopt in the future (Odds
Ratio = 1.62). The further removed a user is from the first
adopter, who is also potentially the creator, the less likely
that the former will adopt an asset (Odds Ratio = .93). The
length of individual users have been in SL does not affect their
likelihood of adoption (Odds Ratio = .99).
The number of adopting friends tells us whether the user
had more than just one friend who adopted before him. In
the full model, having additional friends who have adopted
corresponds to a lower likelihood of adopting (Odds Ratio
= .64). However, in a simple logistic regression the number
of adopting friends is a positive predictor. One interpretation
is that both the adopter and non-adopter in the test set have
potentially been exposed to the asset through the shared friend
who adopted. Once we account for the user’s potential interest
in the asset through the group similarity variable, the number
of adopting friends actually signals that this user has resisted
adoption through multiple potential exposures. Hence he is
less likely to eventually adopt.
We then apply the same analysis to the second data set,
where the sampled adopter and non-adopter do not share
a common adopting friend. We find qualitatively consistent
results with one important exception. As shown in Table II,
the number of adopting friends variable has a much higher
CV accuracy in the second sample (0.73 vs. the earlier 0.53),
which is expected since the previous sample had guaranteed at
least one adopting friend, but this one does not. The variables
capturing the connection between groups and adoption also
have a higher individual predictive ability, and the combined
model achieves a CV accuracy of 0.86.
We also measured specifically how much prediction improved when group variables are included. In our first sampled
dataset, we find that the full model including group similarity
and crowding factor shows roughly 5.5% greater accuracy
(CV = 0.68) than the full model without group similarity (CV
= 0.63). In our second sampled dataset, the accuracy of the
full model with group similarity and crowding factor is still
higher (CV = .86) than the model without group similarity and
crowding factor (CV = 0.83).
TABLE I
VARIABLES PREDICTING WHETHER FRIENDS OF AN ADOPTER WILL ADOPT
# Days in SL
# Adopting Friends
# of Groups
Distance from 1st Adopter
# other Adopted Assets
# Friends with Prev Adopter
Crowding Factor
Group Similarity
Combined model
Estimate
-0.01
-0.44
-0.52
-0.07
0.48
0.34
0.10
0.23
Std. Error
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
z value
-10.13
-140.46
-239.48
-17.72
438.47
316.52
225.86
341.87
CV acc.
0.50
0.53
0.53
0.56
0.58
0.58
0.61
0.63
0.68
In sum, the results suggest that group similarity and crowding factor have a strong impact on the likelihood of adoption.
To better illustrate this, we plotted the fitted regressions for
both group similarity and crowding factor, as well as the
number of adopting friends. As Figure 3 shows, the impact
of the number of adopting friends has a flatter slope than
TABLE II
VARIABLES PREDICTING ADOPTION OF A VIRTUAL GOOD WHERE
ADOPTERS AND NON - ADOPTERS DO NOT NECESSARILY SHARE AN
ADOPTING FRIEND
# Days in SL
# of Groups
# Adopting Friends
# Other Adopted Assets
Distance from 1st Adopter
Crowding Factor
Group Similarity
Combined model
Estimate
0.01
-0.40
3.11
1.04
-8.39
0.21
0.94
Std. Error
0.00
0.00
0.02
0.00
0.04
0.01
0.00
z value
6.04
-113.94
169.93
424.24
-238.68
27.64
341.61
CV acc.
0.50
0.66
0.73
0.74
0.75
0.77
0.78
0.86
in the “middle”.
Predicting whether someone adopts an asset might further
depend on the overall popularity of that asset. Therefore, we
classify the assets by the number of adopters into popular
(i.e. more than 100 adopters), less popular (between 6 and
12 adopters), and least popular assets (fewer than 6 adopters).
As can be seen in Table III, when we try to predict which
of two friends of an adopter will themselves adopt, it is
the early adopters who are easiest to predict. However, it is
the late adopters who can most easily be differentiated from
a non-adopter who does not necessarily have an adopting
friend. We believe there are two contributing factors. The first
is that groups may be more instrumental in early adoption.
However, having an adopting friend is also an important factor
in adoption. Therefore, in the case where we control for having
an adopting friend, it is the early adopters who are more
predictable using information on group affiliation. By contrast,
late adopters are more likely to have had a previously adopting
friend, and are therefore more predictable when compared to
non-adopters who do not have adopting friends.
We also observe for both sampling methods that adoption
of the least popular assets is most predictable. It is the niche
items that are most easily predicted by information on whether
one’s friends and groups are adopting.
TABLE III
C ROSS - VALIDATION ACCURACY FOR PREDICTING ADOPTION BROKEN
DOWN BY ADOPTION TIME AND ASSET POPULARITY. F DESIGNATES THAT
BOTH THE SAMPLED ADOPTER AND NON - ADOPTER SHARE A FRIEND WHO
PREVIOUSLY ADOPTED ; NF DESIGNATES THAT THE SAMPLED ADOPTER
AND NON - ADOPTER DO NOT NECESSARILY SHARE AN ADOPTING FRIEND .
Fig. 3. Probability of adoption based on group similarity, crowding factor
and number of adopting friends among adopters and non-adopters who
have a friend who previously adopted the virtual good. All predictors were
standardized to the same scale.
the impact of these two group-related variables. In the next
section, we examine how these patterns differ among early
and late adopters.
B. Differentiating Early vs. Late Adoption and Item Popularity
Groups may differ in their ability to explain early as
opposed to late adoption. If groups serve as active distributors
of information about an item, they may be instrumental in
dispersing early word of a new available item, or they may
give late-comers an opportunity to catch up with what they
had missed. On the other hand, even if groups are simply a
proxy for user interests, it may be that early adopters tend
to share more characteristics with one another relative to
late adopters [14]. To understand this further, we separate all
adoptions into early, middle, and late. Given differing time
spans over which different assets are adopted, we normalize
the time span from the first to last adoption event. Early
adoptions occur in the first 1/5 of the time interval, late
adoptions in the last 1/4, and the rest are labeled as being
Adoption time
EarlyF
M iddleF
LateF
EarlyN F
M iddleN F
LateN F
Popular
0.758
0.682
0.667
0.820
0.852
0.892
Less popular
0.736
0.714
0.671
0.828
0.862
0.880
Least popular
0.787
0.726
0.682
0.841
0.873
0.900
C. Exploring Asset Adoption Through Group Coverage
The regressions in the previous sections show a correspondence between sharing groups with adopters and being likely
to adopt. This effect did not merely reflect overall engagement
with the virtual world and its groups, since the number of
groups to which a user belongs is not a significantly predictive
variable. Rather, adopters of the same assets are likely to
share the same specific groups. To illustrate this further, we
computed a minimum number of groups required to “cover”
all users who adopt an asset and who are also members of at
least one group.
Omitting users who are not members of any group reduces
the per-asset adoption count by less than 1% for 91% of assets.
We then find a minimal subset of groups where the members
of those groups cover all adopters of the asset, according to the
greedy algorithm developed in [5]. We then create a baseline
by calculating the number of groups it would take to cover any
random set of users who adopted any asset of a given size.
adopters of same asset
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with ≥ 1000 adopters, 2,754 medium assets with between
500 and 1000 adopters, and 5,082 small assets with < 500
adopters. Figure 5 shows that the minimum required number
of groups to cover adopters is smaller for those assets which
are adopted in bursts. This implies that bursts of adoption
tend to occur within groups. This further suggests that groups
are either a rapid medium for the diffusion of information, or
that they in other ways correspond to pockets of susceptible
individuals in the social graph through which information can
spread rapidly.
10000
10000
0.12
random set of adopters
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0.02
% of group contributed to coverage for largest group
Data Source
Number of users adopting asset (grouped only)
dataset
D. Group Membership and Adoption Bursts
An asset adoption time series gives the adoption frequency
of an asset over a large time scale. A burst in the time
series suggests an abnormal behavior in the series where an
unexpectedly large number of events, e.g. adoptions, occur
within some time window. One might expect friends and
members of the same group to adopt during a narrower time
window than all adopters of an asset. We therefore ask whether
those individuals involved in the bursts are more likely to be
linked through friendship or group ties.
Here we select two methods of identifying such bursts. The
first, a fixed window burst detection, looks simply at whether
a high proportion of all adoptions occurs within a short, 7day time window. We identify those assets where 90% of
adoptions occur within a week, those where a maximum of
between 20% and 90% of adoptions occurred within any single
7-day period, and assets with no such period of concentrated
adoption. This definition can be applied regardless of the total
number of adoptions, although assets with fewer adoptions are
more likely to have a majority of those adoptions occur within
a short time window.
The second method, elastic window burst detection using
a wavelet technique [22], must have a sufficient number of
observations for a burst to be detected. We randomly sampled
one fifth, or 11,398 such assets adopted at least 250 times,
among which 6809 assets (or about 60%) contained a burst
event. The assets are then classified into three categories
according their total number of adopters, i.e., 3,562 large assets
1000
90% burst
No burst
Random set of adopters
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As can be seen in Figure 5, it takes on average a smaller
number of groups to cover users who are adopting the same
asset than to cover users who are adopting assets in general.
This pattern, consistent with our regression results, suggests
that the individuals who choose to adopt an asset are more
likely to share the same groups. Furthermore, as Figure 4
shows, adopters can comprise a small but significant portion
of an individual group’s membership. As expected, randomly
chosen users do not comprise a significant portion of any
group.
Number of groups required to cover
20% burst
Fig. 4. For each asset, we select the group that contains the most adopters of
that asset. We then show what fraction of the group is comprised by the asset’s
adopters. We compare this against equally sized random sets of adopters.
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● ●
● ●
50−150 150−400 400−1.1k 1.1k−3k
3k−8k
8k+
Number of users who adopted asset (group members only)
Fig. 5. The number of groups required to cover all adopters of a particular
asset, provided they are members of least one group. The number of groups
required to cover the adopters of an asset is smaller than the number that
would be required to cover a randomly assembled group of the same size.
In addition to being more likely to share groups, adopters
of bursty assets are more likely to be friends. We quantify
this by constructing equivalent networks using a configuration
model proposed by Chung and Lu [23].The model keeps the
degree of each node fixed, but randomly matches the endpoints
of the edges. One can then calculate, given the number of
friends each adopter has, the number of connections one
would expect between adopters. Table IV shows that friendship
connections are more common relative to what is expected
for assets being adopted in bursts than for those who don’t
exhibit bursty adoption. Furthermore, users who adopt in close
succession, i.e., those who are part of the same burst event,
are more likely to be friends (see Table V). Moreover, it is
notable that those who end up holding smaller (i.e. less-widely
adopted assets) are more likely to be friends. They may have
been brought together by a unique interest, or influenced one
another directly. This illustrates that social variables are more
important for diffusion in the niche.
E. Group Characteristics that Increase Adoption
So far we have provided several pieces of evidence that
groups play an important role in the diffusion of virtual
goods. Yet groups tend to vary in their size, attrition rates
and interconnectedness. A second goal in our analysis is
to determine what characteristics of groups, if any, impact
diffusion. In order to examine this, we performed a linear
regression of the total virtual goods transfers among members
within a group, as well as a linear regression of the total
TABLE IV
M ULTIPLE COMPARISON OF THE ACTUAL - TO - EXPECTED RATIOS OF
CONNECTIONS BETWEEN ALL - ADOPTERS FOR BURST- ASSETS AND FOR
NON - BURST- ASSETS
Mean
Large Assets
Medium Assets
Small Assets
Non-burst
Burst
Non-burst
Burst
Non-burst
Burst-assets
7.0040
6.4031
14.2801
19.3747
23.0261
32.4454
99% Conf. int
mean diff.
[-1.6326, 0.4308]
[1.7275, 8.4618]
[1.8695, 16.9693]
TABLE V
M ULTIPLE COMPARISON OF THE ACTUAL - TO - EXPECTED RATIOS OF
CONNECTIONS BETWEEN ALL - ADOPTERS AND BETWEEN
BURST- ADOPTERS FOR BURST- ASSETS
Mean
Large Assets
Medium Assets
Small Assets
All-adopters
Burst-adopters
All-adopters
Burst-adopters
All-adopters
Burst-adopters
6.4031
13.2359
19.3747
54.0735
32.4454
123.3453
99% Conf. int
mean diff.
[3.5348, 10.1310]
[15.4171, 53.9804]
Fig. 6. Network visualizations of transaction ties (in black) and social ties
(in gray) for lowest (top) and highest (bottom) frequency of adoption for a
random sample of groups with 20 members.
TABLE VI
VARIABLES PREDICTING TOTAL WITHIN - GROUP TRANSFERS
[35.5050, 146.2946]
adoptions by group members from anywhere in Second Life.
As shown in Table VI, we find several group-level attributes to
be correlated with the transfer of virtual goods within groups.
In particular, the number of group members (β = −.06)
is slightly negatively correlated with total transfers. A simple
explanation could be that large groups are more easily joined
and therefore might be composed of users who are not as
active in SL. However, we fail to find a correlation between
the size of a group and the percentage of its members who
are active, as judged by last login. We also do not find that
changes in the size of groups impact the volume of transfers.
The number of active users (β = .11) does show a strong
positive relationship with transfers. This shows that it is the
active group size that matters.
Although the total number of social ties between members
follows the trend of total number of members in being
negatively correlated with transfers (β = −.04), the average
in-group degree per member, measuring how connected each
member is within the group, is positively related with transfers
(β = .17). Further measures of social connectedness, such as
the clustering coefficient (β = .21) and the strongly connected
components (β = .24) are also positively correlated with
transfers. This suggests that groups that show signatures of
social interactions are more likely responsible for the spread
of assets.This is illustrated in Figure 6, in which low adopting
groups (top row) show very few links between members,
especially with regard to social ties (in gray).
When we examine all adoptions that are made by group
members, some of the group characteristics show a different
relationship. First, as shown in Table VII, change in group size
has a small but significant impact on total adoptions (β = .05).
This suggests that as groups grow and membership changes,
there are new opportunities for adoption. For example, a new
(Intercept)
Num of Members
Num of Edges
Clustering Coefficient
Average Degree
LCC
Change in Size
Num of Active Users
Estimate
-1.902
-0.002
-0.000
12.275
0.326
8.924
-0.002
0.008
Std. Error
0.122
0.000
0.000
0.234
0.011
0.189
0.008
0.001
t value
-15.601
-10.106
-8.477
52.549
30.835
47.224
-0.252
16.432
Pr(>|t|)
0.000
0.000
0.000
0.000
0.000
0.000
0.801
0.000
member of the group may come with new ideas or innovations,
which are attractive to members who have been exposed to
the same items for a period of time. However, there may
be some internal boundaries: the results show that average
degree has a negative impact on adoption (β = −.22), that
as the interconnectedness of group members increases, the
less likely new innovations are to be adopted. For example,
members may be accustomed to certain types of virtual goods
and uninterested in investing time or money in new ones, or
certain cultural practices or norms may be in place that lend
themselves to some types of innovation but not to others.
TABLE VII
VARIABLES PREDICTING TOTAL ADOPTIONS FROM GROUP MEMBERS
(Intercept)
Num of Members
Num of Edges
Clustering Coefficient
Average Degree
LCC
Change in Size
Num of Active Users
Estimate
5.048
-0.006
-0.000
9.860
-0.547
26.434
0.133
0.016
Std. Error
0.162
0.000
0.000
0.310
0.014
0.251
0.011
0.001
t value
31.206
-27.383
-2.430
31.809
-38.994
105.413
12.063
23.807
Pr(>|t|)
0.000
0.000
0.015
0.000
0.000
0.000
0.000
0.000
V. C ONCLUSION
We explored the role of group membership and structure
in the adoption of virtual goods in a large-scale online community. Prior work had focused primarily on the influence of
single social ties, or at most the entirety of an individual’s ego
network. By contrast, we examine the role of larger social
collectives, namely groups, and demonstrate that they are
useful in discerning whether a given individual will eventually
adopt an asset. We show that when an individual belongs to
many of the same groups as other adopters, and conversely,
when that individual’s groups are populated by adopters, then
the individual is more likely to adopt. These findings are
particularly germane for assets that are adopted by a small
number of users. Individual groups are also more likely to
play a role in bursty adoption, when many individuals adopt
in rapid succession, and for adoptions that occur shortly after
the asset is first created.
From these findings we can infer that groups represent niche
interests, and that assets may be more likely to diffuse initially
through a small group. Groups might also facilitate rapid
diffusion of an asset during a short time period, through oneto-many announcements, events, or other ways in which group
members interact. We gain further insight that group structure
is conducive to diffusion. Smaller groups tend to show higher
overall adoption activity, as well as within-group transfers.
Denser, more interconnected groups, are related to exchanges
within the group, but not in terms of virtual goods adoption
among group members and the rest of the community.
There are clear limitations to our approach. Group activity is
reflective of both social ties and shared interests, two variables
that contribute to adoption, highlighting the complex interplay
and potentially confounding nature of social influence and
homophily [4], [16]. While we have demonstrated the utility of
factoring in information about group membership to predicting
adoption events, controlling for variables such as the number
of friends in one’s social circle who adopted, the present data
analysis does not allow us to distinguish how much of the
explanatory power of group membership is due to groups
reflecting interests that would make an individual susceptible
to adoption, and how much is due to activities within a group
promoting adoption. We think this is an interesting avenue for
future work.
In conclusion, we have demonstrated the important role that
groups and group membership play in the diffusion process,
and provided evidence that the adoption of virtual goods in
Second Life is more likely to occur when users share similar
groups. We also show that the communication behaviors and
network structure of these groups are tied to the number of
adoptions that occurs among group members. These findings
provide further support that individual influence is not the
sole factor in the diffusion process and that considering larger
social collectives such as formal groups can better explain the
likelihood of adopting an innovation.
ACKNOWLEDGMENT
We thank Linden Lab for sharing Second Life data. This
work was supported by the Intelligence Community (IC) Postdoctoral Research Fellowship Program, NSF IIS-0746646, and
MURI award FA9550-08-1-0265 from the Air Force Office of
Scientific Research. We also thank Robert Horowitz.
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