# Dynamics of Trust Reciprocation in Heterogenous MMOG Networks

Ayush Singhal, Karthik Subbian, Jaideep Srivastava  University of Minnesota,
Minneapolis, MN.
<EMAIL_ADDRESS>Tamara G. Kolda, Ali Pinar  Sandia
National Laboratories, Livermore, CA.
<EMAIL_ADDRESS>

###### Abstract

Understanding the dynamics of reciprocation is of great interest in sociology
and computational social science. The recent growth of Massively Multi-player
Online Games (MMOGs) has provided unprecedented access to large-scale data
which enables us to study such complex human behavior in a more systematic
manner. In this paper, we consider three different networks in the EverQuest2
game: chat, trade, and trust. The chat network has the highest level of
reciprocation (33%) because there are essentially no barriers to it. The trade
network has a lower rate of reciprocation (27%) because it has the obvious
barrier of requiring more goods or money for exchange; morever, there is no
clear benefit to returning a trade link except in terms of social connections.
The trust network has the lowest reciprocation (14%) because this equates to
sharing certain within-game assets such as weapons, and so there is a high
barrier for such connections because they require faith in the players that
are granted such high access. In general, we observe that reciprocation rate
is inversely related to the barrier level in these networks. We also note that
reciprocation has connections across the heterogeneous networks. Our
experiments indicate that players make use of the medium-barrier
reciprocations to strengthen a relationship. We hypothesize that lower-barrier
interactions are an important component to predicting higher-barrier ones. We
verify our hypothesis using predictive models for trust reciprocations using
features from trade interactions. Using the number of trades (both before and
after the initial trust link) boosts our ability to predict if the trust will
be reciprocated up to 11% with respect to the AUC. More generally, we see
strong correlations across the different networks and emphasize that network
dynamics, such as reciprocation, cannot be studied in isolation on just a
single type of connection.

##  I Introduction

The rapid growth in the amount and richness of online interactions, through
Massive Multi-player Online Games (MMOGs) such as
EverQuest111https://www.everquest2.com/ and World of
Warcraft222http://us.battle.net/wow/en/ are creating social interaction data
at an unprecedented scale. These MMOGs help computer scientists and
sociologists overcome the key difficulty in studying the social dynamics and
human behavior by providing an experimental platform for collecting data at
high resolution and for long periods. These virtual worlds provide a rich
environment for studying user interactions and have been used in several
recent experimental studies [1, 2, 3, 4].

Figure 1: Comparing reciprocation prediction accuracy via AUC. The figure
shows that adding hetergeneous network features (e.g. trade) boosts the
prediciton accuracy by 11%.

The ages of the players of these games vary from 13 to 60 and more than 50% of
the players are employed full-
time333http://www.nickyee.com/daedalus/gateway_demographics.html. They spend
an average of 22 hours per week and 60% of them reported playing 10 hours
continuously33footnotemark: 3. In these games, all user interactions, actions,
and communications are recorded in a log file. In this paper, we use one such
MMOG called Sony EverQuest II11footnotemark: 1, for analyzing the
reciprocation of trust relationship in heterogenous interaction networks,
including chat, trade, and trust relationships.

The dynamics of the reciprocation varies from network to network depending on
the level of barrier for reciprocation. The barrier for reciprocating a trust
relationship could be lack of resources or high risk involved. Needless to
say, these barriers affect the levels of reciprocation significantly in
different networks. For instance, in a chat network users have very low
barrier level for trusting each other as there is no commitment from either
side to participate in any involved relationship or potential loss. On the
other hand, in a trust network players grant access to each other’s housing
resources. The barrier level in the latter is very high. It is important to
understand questions related to reciprocation across different types of
interactions. For instance, do people reciprocate differently for trust
building activities compared to trust cancellations? As mentioned earlier,
understanding these questions in great detail is possible because of the MMOG
data.

The dynamics of complex network relationships cannot be studied in isolation
because low barrier interactions may play a critical role in building the high
barrier reciprocations. Understanding such dynamics offers several key
insights. For instance, our experiments verify that players use low barrier
interactions, like trade, before reciprocating trust. We verify our hypothesis
by building a predictive model for trust reciprocation; using features from
the trade network boosts the AUC by up to 11% as shown in Figure 1.

###  I-A Contributions

The goal of this paper is to understand the dynamics of reciprocation in the
context of trust. Following are the key contributions of this work:

  * •

We explore the relationship between reciprocation and different barriers for
reciprocation in several interaction networks. We establish that reciprocation
rate is inversely proportional to the barrier level.

  * •

We analyze the temporal aspect of reciprocation and show that the speed of
reciprocation is also inversely related to the barrier level.

  * •

Our analysis on trust building and cancellation shows that the trust building
reciprocations occur more often and more quickly.

  * •

Reciprocation cannot be studied in isolation, and hence we study the effects
of reciprocation in the presence of other interactions. We hypothesize that
players use low barrier interactions to establish initial trust, followed by a
high barrier reciprocation.

  * •

We verify our hypothesis using predictive models to find reciprocation links
with behavioral features from low barrier networks. Several highly predictive
features in general link prediction, such as age homophily [5], are not as
effective as proposed heterogenous network features that boost the AUC by up
to 11%.

|  |
---|---|---
(a) Trust Network | (b) Trade Network | (c) Chat Network
Figure 2: Degree distributions of trust, trade and chat networks.

###  I-B Related Work

The notion of reciprocation is well studied in sociology, and, as defined by
Gouldner [6], it is the norm of reciprocation that people should help those
who help them. Indirectly, if you have helped someone then they have an
obligation to help you back. Following this notion, several studies analyze
the relationship between reciprocation and the human behavior in various
social networks, such as child care [7], social altruism [8], and online
communication [9]. Leider et al. [8] use reciprocation as a means to study
human behavior in social altruism in terms of favors and gifting. They
conclude, by several online field experiments, that there is a 52% increase in
directed altruism towards friends compared to random strangers. This number
further increases by another 24% when it leads to further prospects of
receiving return favors or gifts. Similar experiments were conducted by
interviewing families from different working groups to understand the child
care favors in social networks. Hansen [7] reveals that social location and
kinship improves reciprocation of interaction in these networks. In another
recent work [9], the Twitter reply network is analyzed to understand
reciprocation in relation to user happiness, where the measure of happiness is
computed using sentiment analysis of text content exchanged in Twitter
messages. This work concludes that reciprocal behavior in the Twitter reply
network shows high assortativity in terms of measured happiness of Twitter
users. In all these works, reciprocation is studied on hand picked user
samples or surveys [7, 8] or used to understand specific human behavioral
aspect such as happiness [9] or altruism [8].

There has been recent developments on developing graph models using
reciprocation as a model parameter. For instance, Zlatic and Stefancic [10]
develops a growing model for Wikipedia using three key parameters: reciprocal
edges, degree, and size of modeled network. They empirically evaluate that the
generated network closely matches the in- and out-degree distribution of the
actual Wikipedia. There are also several papers that discuss the relationship
between reciprocation and other network parameters such as degree
distribution. Durak et al. [11] propose a null model for directed graphs that
combines the reciprocal and the one-way edges to generate directed graphs that
match the in-, out-, and reciprocal-degree distributions. Ahmad et al. [12]
use theories of social exchange as a basis for building a generative model
GTPA for modeling temporally evolving directed networks.

There are other recent works, such as Gralaschelli and Loffredo [13] that use
statistical measures to conclude that the reciprocation of a network is never
at random and it is either reciprocal or anti-reciprocal. They define a
correlation coefficient in terms of the average and the actual reciprocation.
When the correlation coefficient is positive and nonzero, it is correlated,
and when negative, it is anti-correlated. Similarly, Zamora-Lopez et al. [14]
propose a method to compute the expected reciprocation of the network as a
function of in- and out-degree distributions and show empirically the expected
reciprocation closely matches the actual in several real-life networks.
reciprocation in weighted directed networks, especially in large scale mobile
communication networks, is discussed in [15, 16], . Akoglu et al. [15] propose
a novel triple power law (3PL) distribution that fits the reciprocation
behavior in several data sets and show interesting properties of this
distribution such as parsimony. The paper also concludes that reciprocation is
higher among users with more common neighbors and larger degree correlation.
Szell and Thurner [4] study the strength of positive and negative ties in
friend and enemy networks and propose approximate social laws relating
betweenness centrality and communication strength to the number of overlapping
links. In another work Szell et al. [17] show that negative interactions have
a lower reciprocation compared to the positive interactions.

Reciprocation has also been used for link prediction [18, 19, 5]. Cheng et al.
[18] study several attributes for predicting reciprocation in the Twitter
network, such as relative degree, absolute degree, and other link prediction
features. They use regression and decision tree classifiers to predict the
expected reciprocation and conclude that features that measure the relative
status of two nodes are the best predictors of reciprocation. Zlatic and
Stefancic [19] study how reciprocal edges influence other properties of
complex networks, such as degree distribution and correlations. They present a
statistical inference technique to estimate the number of reciprocal edges.

In summary, all these related works address the following class of problems:
modeling a generative process incorporating reciprocal edges, understanding
the effect of reciprocation on a particular human behavior, or using
reciprocation-based features in the task of link prediction. None of these
papers attempt to study multiple relational networks such as trade, chat, etc.
to understand the notion of reciprocation in trust relationship in
heterogeneous networks, especially on large-scale real-life networks such as
MMOGs. Also, these models do not use an evolving network scenario, where
understanding the behavior of reciprocation on the time dimension is extremely
important.

##  II MMOG Data Sets

The Sony EverQuest (EQ) II game provides an online environment where multiple
players can log in and coordinate with each other to achieve a particular
mission. Note that players are free to invent, choose their mission and to
self-organize among groups of their own interest. The game provides several
mechanisms such as chat for instantaneously interaction. We were provided with
the game data set logs, and we extracted the information needed for our
experiments from these logs for various interactions. In this section, we
summarize each of these networks in terms of the number of nodes and edges,
the period of observation, and the direction of edges. Also, some networks
such as trust are rich in terms of edge attributes, we discuss them in more
detail.

###  II-A Trust Network

In EQ II, players form teams in order to complete the game tasks. As the
players are limited by the number of items they can carry at a time, players
buy houses as a temporary storage to retain their armory and other
accessories. Through the trust network, players share their house access with
other players. For this reason, we also refer to this network as the trust
network. We have 9 months of data from Jan-01-2006 to Sep-11-2006 with 63684
nodes and 140514 edges. Each node in the network is a player character in the
game, and each edge is a permission granted or removed by the character to
another character. Each edge has a time stamp when the access was granted or
removed. In addition, each edge also has a trust level: Trustee, Visitor,
Friend, None, and Remove. The Trustee access is the highest level of trust,
whereas Remove is the lowest level of trust the player can express towards
another player. The number of edges of the network by trust level is
summarized in Table I and each trust level is described as follows.

  * •

Trustee: Player can store, touch, move, add, and remove things, and has almost
same access as the owner.

  * •

Friend: Player can store, touch, and move things.

  * •

Visitor: Player can enter the house and view things.

  * •

None: Player can see the house externally but cannot enter it.

  * •

Remove: Permission granted to the player is revoked and the house is visible
only when the player is near-by.

TABLE I: Number of edges by each trust level.

Trust Level | Description | Count
---|---|---
4 | Trustee | 82498
3 | Friend | 30850
2 | Visitor | 10928
1 | None | 4336
0 | Remove | 11902

###  II-B Trade Network

In the EQ II trade network, players exchange goods for coins or goods. Players
trade multiple items and coins with other players by initiating a trade offer.
A typical offer includes items/coins offered, and items/coins needed in
exchange. The player offered can either accept or reject the trade request
instantaneously. If the request is accepted, then a trade link is established
between the seller (initiator) and the buyer (acceptor) in the trade network.
We analyzed such a trade network containing 295,055 nodes and 11,913,994 edges
over a period of 9 months from Jan-01-2006 and Sep-11-2006. The trust needed
to establish a trade relationship is much lower than housing, as the period of
interaction is short and the risk involved is nill.

TABLE II: Statistics of reciprocation in trade, chat and trust networks. The forward edge count also includes the count of multiple forward interaction between all pair of nodes. Network | All Forward | First | Second | Third | All Other | Total
---|---|---|---|---|---|---
Type (period) | Edges | Reciprocation | Reciprocation | Reciprocation | Reciprocation | Reciprocation
Chat (1 month) | 1840492 | 441039(23.9%) | 79412(4.3%) | 32128(1.7%) | 46969(2.6%) | 599548(32.6%)
Trade (9 months) | 520861 | 74137(14.23%) | 11850(2.3%) | 3766(0.72%) | 47056(9.0%) | 136809(26.3%)
Trust (9 months) | 62674 | 8452 (13.5%) | 351 (0.56%) | 0(0.0%) | 0(0.0%) | 8083 (14.0%)

###  II-C Chat Network

The chat network is a communication medium where players exchange instant
messages. This network is directed and the direction of an edge is from the
sender to the receiver. As the number of chat messages between two players is
quite high, and there is no associated session details, we assume all the chat
messages in a single day correspond to a single session. The number of nodes
in this network is 349,654, and the number of edges is 86,948,748, spanning
over a period of one month from Jul-29-2006 to Sep-10-2006.

###  II-D Network Profiles

We present the degree distribution of these networks in Figure 2. The
distributions were constructed using snapshots of different networks over the
entire observation period and we considered multiple interactions between a
pair of players for this plot. The distributions seem to follow the power law
with exponent of the power law ranging from 1 to 3. The exponent was
calculated using the slope of a least squares fit in the log-log plot. Now, we
look in to the much detail of these networks to understand how players
reciprocate in various networks in a snapshot and over time.

##  III Reciprocation in Different Networks

The reciprocation of a network is the ratio of forward edges (say from player
$a$ to $b$) that have a corresponding backward edge (from player $b$ to $a$),
i.e., the ratio of mutual interactions.

###  III-A Barriers of Reciprocation

Barriers of reciprocation can be broadly grouped in to risk and utility. The
risk factors include loosing an asset, in-game points, or in-game time; and
the utility includes, immediate gains in terms of points and assets and long
term future prospects. Each network has specific characteristics that lead to
low, medium or high barriers for reciprocation.

The trust network yields direct access to a player’s house. This is the
highest level of barrier as the other person can enter, add, and remove assets
from a player’s house. In the case of trade network, coin and items are
exchanged between the players on a pre-specified contract, so the barrier is
having sufficient items or coins for trade. The resulting risk involved is
nill with immediate utility for both players. Such networks fall in to medium
barrier category. In the chat network players are at no risk and there is
minimal cost to reciprocation, so these networks fall in to the low barrier
group. For the purposes of this paper, we limit ourselves to one example for
each group for our analysis.

###  III-B Multiple reciprocations

There can be several overlapping forward and backward arcs between each pair
of players. For the purpose of measuring the reciprocation and response time,
we first partition the timeline into several partitions. We consider the start
time of first forward edge and the corresponding end time of the first
response as the first partition. Similarly, the second forward arc and its
response marks the end of the second partition and so on. This notion of
partitions of the timeline is illustrated in Figure 3. The figure shows the
forward arcs above the timeline arrow (dashed line) and backward arcs
(reciprocations) below the timeline arrow. For remainder of this paper, unless
specified, we always refer to the overall reciprocation rate. In Table II we
show multiple reciprocation rate for two different networks.

Figure 3: The timeline showing the first, second, and third partitions used
for computing the response times for first, second, and third interactions.

(a) Trust

(b) Chat

(c) Trade

Figure 4: The response time distribution for the three networks. The average
response time for trust network is the highest among chat, trade and trust.

###  III-C Reciprocation in Trust Network

The trust network is a high barrier reciprocation network as players have to
trust each other in terms of granting house access. It consists of several
levels of access permission: Trustee, Friend, Visitor, None, and Remove. As we
see in Table I, the percentage of edges that belong to the Trustee category
accounts for more than 50% and some categories, like None, are rarely used.
Also the dominant transition is from other permissions to Trustee and most of
these permissions remain in Trustee state until the end of the observation
period. For these reasons, we assume that there are only two major permission
categories in the trust network: Trust and Not-Trust. The Trust level
corresponds to being a Trustee. We collapse the lower trust levels, (Freind,
Visitor, None, and Remove), to a single Not-Trust level. As the lower level
permissions are equivalent to having no relationship at all, we consider
absence of an edge as the Not-Trust state. In essence, we focus only on the
Trustee level of access and all the other links are as equivalent to having no
access at all.

In the trust network, 14.0% of the forward trust (8803 one-way) links receive
a trust response (reciprocation) back and their response time distribution is
shown Figure 4a. We study the response time between the reciprocations and see
how quickly and in what volume these reciprocations happen using the response
time distribution. We analyze the entire graph edge wise for this purpose. If
an edge occurs from node $i$ to $j$ at time $t_{1}$, then we will account for
the start time of that edge as $t_{1}$. If the reciprocation occurs from node
$j$ to $i$ at time $t_{2}$ then the response time is computed as
$t_{2}-t_{1}$. All the forward edges from $i$ to $j$ between $t_{1}$ to
$t_{2}$ are subsumed by the first forward edge, until a reciprocation response
is received by $i$ from $j$. We then use this data to draw the distribution of
response times. The x-axis denotes the time to reciprocate and y-axis
corresponds to the number of reciprocations. We find that the response time
distribution follows a power law, with a mean response time of 27 days.

We also measured the number of player who waited indefinitely for a response
back from the other player until the end of observation period. Surprisingly,
68.54% of players waited indefinitely, while the remaining 8.16% of players
switched from Trust to Not-Trust state as they did not receive a Trust
response. This indicates that around 69% of players in the trust network show
patience.

The users, in the trust network, can move from Trust to Not-Trust state and at
a later date they can again establish a new Trust relationship. As this
network has an unique feature of canceling the edges, we wish to study the
reciprocation of granting trust, followed by cancellation. We measure the
number players who initiate a revocation of housing permission and the number
players who reciprocated by a similar action. From the 8803 reciprocated links
1062 (12.1%) of them initiated a reduction of housing access to their peer
player and 207 players out of 1062 (19.4%) reciprocated back with a revocation
response. About 80% of the players who received a cancel request never
responded back and ignored the request. This again confirms that when a
reciprocation relationship has high barriers, an established mutual trust is
quite stable to cancellation from one-side. Also, the players seem to respond
to trust requests with a mean response time of 27 days compared to a
cancellation request of 32 days. This suggests that the players pay more
attention to granting requests compared to canceling requests, as establishing
trust is a more preferred social activity than losing it.

###  III-D Reciprocation in Chat,Trade and Trust Networks

In this section, we study the reciprocation behavior in chat and trade as
independent homogenous networks. Then, in the next section, we analyze the
interactions of chat and trade relationships in affecting the reciprocation of
trust network. The chat and trade networks have simple edge types with no
attributes except time stamps.

We summarize the total reciprocation for each network type in Table II. As the
chat network is a low barrier network, it has the highest amount of
reciprocation with 32.6% of forward edges reciprocated. The low barrier in
this network is due to the instant nature of the communication and minimal
risk involved in making a chat reciprocation. On contrary, in the medium
barrier trade network the reciprocation rate is 26.3%, lower than chat but
more than the trust network. There several reasons why a player may not
reciprocate in this network, it could be either lack of resources or a need
for doing so. Further, we wish to analyze the response time distributions of
these networks to understand some key questions, such as, does all
reciprocations occur within a certain number of days or are they spread
uniformly over a longer period of time?

Figure 4b shows the response time distribution, which roughly follows a power
law. There is an outlier region around 45 days. We investigated this region
and found that these are first time users who are not familiar with the
system. We note that such users are extremely rare in the dataset (less than
0.01%). The figure also shows that most of the users in the low barrier, chat
network reciprocate within the same day or at most the next day. This is
evident since the mean first response time in the chat network is less than
one day (0.317). In the chat network there is a sharp truncation [20] after 7
days, as the significance of a message beyond a week becomes completely
irrelevant to the context of the game.

For the trade network, we show the response time distribution in Figure 4c;
the distribution has a heavy tail and seems to follow a power law. The slope
of this distribution is not as steep as for the chat network, implying the
trade reciprocation is not as quick as in chat. As the barrier for
reciprocation in the trade network is more than chat, the average response
time in trade is 43X slower at around 13 days.

##  IV Reciprocation in Heterogeneous networks

We will now overlay the trust, chat, and trade networks to analyze the
interactions among heterogeneous edges. As the chat data is available only for
a month, we restrict the other data sets also to this one month period. Every
pair of players in this network have several edges between them with time
stamps for each edge denoting when the edge occurred. For the trust network we
consider the TRUST and NOT-TRUST edges. The focus of this section is to answer
questions, such as: How many times does a trust granting from player $a$ to
$b$ result in a trust reciprocation from $b$ to $a$? Does a player $b$ prefer
to reciprocate with trade or some other low barrier interaction such as chat
before granting a high barrier relationship such as trust to player $a$. The
first interaction, as noted earlier in Figure 4b, captures all the
characteristics of the additional interactions, hence we consider only the
first interaction for this experiment. For each forward edge type, we count
the number of first reciprocation between pairs of players in the consolidated
network. In the case of tie reciprocations across multiple edge types we
include all the tied edges while counting. We have summarized the
reciprocations for each forward interaction type in Table III.

TABLE III: The reciprocation counts for first interaction (first forward request and first reply) in a heterogeneous MMOG network for a period of one month. The forward edge count includes only the first forward edge between any pair of nodes. The reciprocation captures the first type of response (chat, trade or trust) to the forward edge. Forward | First Forward | Chat | Trade | Trust
---|---|---|---|---
Type | Edges | Reciprocation | Reciprocation | Reciprocation
Chat | 1645623 | 435758 | 1187 | 105
Trade | 74428 | 7953 | 11402 | 335
Trust | 10502 | 907 | 1016 | 722

As we see from Table III, the players who perform chat predominantly make a
reciprocation using the chat link (26.48%). The main reason for this is that a
chat relationship is a low barrier relationship, which can be established
between two players instantly and does not require high degree of trust. For
this reason, players do not hesitate to reciprocate a chat response as the
amount of cost involved is insignificant and the utilities are never worse
off. This observation justifies the theory of rational selfishness [21],
whereby it is in the best interest of the player to reciprocate to a chat
request to maximize his/her utilities. The same observation is made for the
trade relationship, which is also a low barrier relationship (but higher than
chat). Here also we find that trade responses are the predominant type of
responses for a trade relationship. This is in line with bargaining theory
[22] where bilateral parties who often negotiate a successful deal tend offer
favors to each other again. However,this is not the same in the case of a
trust forward edge type as it is a high barrier relationship and a more time
consuming activity. So people are very careful before reciprocating for such
activities and reciprocations are first initialized through low barrier
activities before reciprocating with a high barrier relationship, such as
trust. The reciprocations for trust forward edge is predominantly through chat
(8.63%) or trade (9.67%).

We now analyze the dependency between trust interactions against trade and
chat interactions. Recall that trade is often a high barrier relationship
whereas chat and trade are instantaneous and hence have a low barrier. The aim
of this experiment is to quantify how chat and trade, low barrier
relationships, influence reciprocation in a high barriermrelationship.

For any two nodes $a$ and $b$ in the trust network, we start our analysis from
the time when a forward TRUST edge from $a$ to $b$ is established. For such a
forward edge there can either be a TRUST reply to complete the TRUST
relationship or no TRUST reply (incomplete TRUST relationship). The TRUST
relationship is determined as incomplete if there is no trust response from
$b$ to $a$ within the average trust response time which is 4.6 days in this
case. In other words, we truncate the response time for the incomplete
reciprocations by the mean response time (4.6 days) and use only the period
before this mean response time for further analysis. There can also be several
other responses (low barrier interactions) from $b$ to $a$ before $b$ replies
with a TRUST link. Understanding these other relationships, such as chat and
trade, before a TRUST reply is formed from $b$ to $a$ is crucial to decipher
the nature of socialization required for a healthy mutual trust relationship.

From Table IV we can infer that complete and incomplete TRUST rows differ from
each other in terms of chat and trade responses. We can see that the responses
are exactly in an opposite order in the two rows. For the complete TRUST we
observe that there were 743 forwards edges that were responded back with
TRUST. However, before the TRUST is completed between $a$ and $b$, we see that
there are 408 trade responses from $b$ to $a$. These trade responses account
for nearly 63% of the total responses. We have only 243 chat responses from
$b$ to $a$ , which is comparatively smaller than the trade responses.
Surprisingly, the amount of low barrier responses for the incomplete TRUST
gets completely reversed. There are 9145 forward TRUST edges which do not get
a TRUST reply back and remain one sided. For these TRUST requests from $a$ to
$b$, we find that the chat responses from $b$ to $a$ are now 6962
(approximately 75% of the total responses) while the trade responses are
significantly lower (as low as 25 %).

This experiment confirms that a TRUST relationship between $a$ and $b$ is more
likely to complete if there are more trade responses than chat responses from
$b$. This interesting result can be used to infer the future TRUST
relationships based on some low barrier relationships such as chat and trade.

TABLE IV: The effect of low barrier relationships on high barrier relationship
(TRUST). This tables shows the connection between chat and trade reciprocation
counts and completion or incompletion of trust reciprocation.

TRUST | Forward | Chat | Trade
---|---|---|---
Type | Edges | Responses | Responses
Complete | 743 | 243 (37%) | 408 (63%)
Incomplete | 9145 | 6962 (75%) | 2331 (25%)

##  V Predicting trust reciprocation

In this section we evaluate how well can we predict a high barrier
relationship, such as a trust, using information about the medium barrier
relationships between the nodes. The empirical analysis in the previous
section showed that the success (completion) of high barrier trust
relationship depends on some medium barrier relationship like trade. We use
this as our motivation to quantify how well the medium barrier relationship
can help to predict high barrier relationship completion. However, we use the
entire 9 months of data in order to make any conclusions for the trust
reciprocation prediction. The chat relationship has to be excluded from this
experiment because of its limited availability for a single month. But we add
several other features to make the experiment more interesting.

For the trust network data for 9 months, there are a total of 61006 trust
requests (forwards edges). The trust links that are reciprocated is 8252
whereas 52574 forwards edges remained incomplete. For the forward requests, we
ignored the requests that started in the last (9th) month because it is hard
to determine whether the requests were completed. Thus the number of trust
requests are slightly lesser than those mentioned in earlier sections. So the
completed trust link (reciprocated) forms one class and the incomplete trust
links (unreciprocated) forms the second class. Now that we have two classes,
we construct several features in order to build a prediction model. The
following features will be used to build prediction models.

Features from high barrier relationship(trust): This set of features are built
using the structural properties of the trust network. These features
characterize the position of players (nodes) in the trust network. For the
reciprocation links $(A,B)$ we consider two structural features. The first
structural feature describes the connectivity of $A$ to other nodes in a trust
network. The second structural feature is the connectivity of $B$ with other
nodes in the trust network. For convenience, we refer these features as
“trust” features.

Features from medium barrier relationship(trade): This feature set consists of
features from three sub-categories namely, structural, past-behavioral and
future-behavioral. For a link $(A,B)$ the structural feature corresponds to
the degree of $A$ and degree of $B$ in the trade network. The past-behavioral
features for a link $(A,B)$ correspond to the count of the trade interaction
of the type $A$ to $B$ and $B$ to $A$ before the trust request from $A$ to $B$
started. This feature takes into account the trade behavior between $A$ and
$B$ before any trust interaction started between them. The future-behavioral
features takes into account the behavior of trade interaction between $A$ and
$B$ once the trust request is sent from $A$ to $B$. Here we use a time window
$K$ (in days) starting from the time when trust request was initiated from $A$
to $B$. We count the number of trade interactions in this time window $K$.

Features from player demography(homophily): In this feature set we take into
account the two types of homophilies. The first type of homophily is gender
homophily. The gender homophily between $A$ and $B$ is 1 if $A$ and $B$ has
the same gender, and 0 otherwise.

The second demographic feature is the experience homophily between $A$ and
$B$. It is computed as $X(A,B)=X(A)-X(B)$, where, $X(A)$ is the experience
level of $A$.

As mentioned earlier, the aim of this experiment is to quantitatively compare
the impact of using different features (described above). In the previous
section we hypothesized that the success of trust reciprocation (completion)
can be determined by the amount of medium barrier interactions between player
$A$ and $B$. Thus to validate this hypothesis, we conduct several experiments
using different set of features.

TABLE V: Table comparing reciprocation prediction accuracy using different
feature sets. Here K denotes the time window starting from the time when an
initial trust link was established between two nodes.

|  |  | Average | Average |
---|---|---|---|---|---
Classifier | CWA | AUC | Precision | Recall | F-measure
only trust | 0.515 | 0.659 | 0.800 | 0.863 | 0.806
trust+trade(K=0) | 0.526 | 0.637 | 0.825 | 0.866 | 0.816
trust+homophily | 0.519 | 0.604 | 0.788 | 0.849 | 0.808
trust+trade(K=0)+homophily | 0.527 | 0.636 | 0.826 | 0.866 | 0.817
trust+trade(K=20) | 0.588 | 0.714 | 0.871 | 0.885 | 0.851

(a) Class weighted accuracy

(b) $F_{1}$ measure

(c) Precision

(d) Recall

Figure 5: Comparing class weighted accuracy, $F_{1}$ measure, precision, and
recall for trust reciprocation prediction. Here K is the size of time window
from the formation of intial trust link between the nodes. The prediction
accuracy increases by incorporating trade interactions after the intial trust
link was formed. This figure shows that trade features are more significant
once a initial trust link is established between two nodes.

Table V compares the trust reciprocation accuracy for various feature sets.
The addition of trade features boosts the performance of the predictive model
over the case when no trade features are used. All the feature values for this
experiment are computed using the values before the trust request was
initialted between $A$ and $B$. Thus we do not take into account the impact of
future time window (K) in this experiment. The class weighted accuracy (CWA)
is highest in case when all the features are used. However, the difference
between the CWA using trust and homophily and all features is not very
significant. This trend can be observed over all the accuracy measures.
However column 2 of the table shows that the AUC measures are higher when
using only trust features and AUC drops slightly as we include the trade
features.

Since this table by itself is not sufficient to draw concrete conclusions, we
extend this experiment to include the variation of future time window size (K)
for all features and monitor its impact in term of accuracy of the prediction
model. Figure 5 shows the results of this experiment. As mentioned earlier, we
study the impact of varying the time windows size (from 0 to 25 days) for all
the features. In the previous experiment, we considered the features values
without any time window (K=0). As shown in Figure 5 and Figure 1, using trade
as an additional feature in the prediction model outperforms the model which
uses only trust or trust and homophily only. The performance of the model with
trade features with trust and/or homophily) increase as we increase the size
of the time windows from 0 to 25. We also find that addition of homophily
features do not have a significant impact in predicting reciprocation in trust
network. This is an interesting finding for trust reciprocation prediction
because it is a general notion that homophily is significant in predicting
trust links [23]. A possible explanation of this observation is that the
reciprocation phenomenon is significantly different from a normal trust
formation phenomenon. As we know, in reciprocation there is already a one
sided relationship established and a reciprocation might depend on entirely
other dynamics such as trade interactions.

In Figure 1, the AUC for the prediction model with trade features actually
increase as we increase the time window size (K). Thus this experiment
confirms that using trade features boosts the performance of the prediction
model for predicting trust reciprocations. One of the reasons why performance
of prediction model keeps on increasing as the time window (K) is increased is
due to the fact that players start doing other activities such as trade once a
player has initiated a trust request. So the trade activity increases after
the trust is initiated by any player and the trust activity pattern helps to
discriminate whether a trust reciprocation will happen or not.

In conclusion, the experimental results confirms our hypothesis that trust
reciprocation is significantly improved by incorporating features from other
heterogeneous networks such as trade over. We also found that using homophily
features does not necessarily improve the accuracy in trust reciprocation
prediction. This makes trust reciprocation a all together different phenomenon
from trust link formation.

##  VI Conclusion

Understanding reciprocation in networks is important in several fields from
computational social science to sociology. In this paper, we have extensively
studied various social factors affecting reciprocation in three different
interaction networks from Sony EverQuest II MMOG. These networks vary in trust
levels, interaction type and sparsity and give a broad perspective of how
players reciprocate across a variety of networks. We established the
connection between the trust level required to establish a connection
inversely affects the number of reciprocations. We also, using response time
analysis, show that people are slow in building mutual high trust
relationships compared to low trust ones. We also show that in high trust
networks player patience plays a key role in reciprocation. We extend our
analysis from single-type networks to heterogeneous networks, where we confirm
that high degree of socialization is crucial for reciprocation in high trust
relationships.

## Acknowledgments

This work was funded by the GRAPHS Program at DARPA. Sandia National
Laboratories is a multi-program laboratory managed and operated by Sandia
Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the
U.S. Department of Energy s National Nuclear Security Administration under
contract DE-AC04-94AL85000.

## References

  * [1] D. Lazer, A. Pentland, L. Adamic, S. Aral, A.-L. Barab si, D. Brewer, N. Christakis, N. Contractor, J. Fowler, M. Gutmann, T. Jebara, G. King, M. Macy, D. Roy, and M. V. Alstyne, “Computational social science,” vol. 323, no. 5915, pp. 721–723, 2009.
  * [2] N. Yee, “Motivations for play in online games,” _Cyberpsychology and Behavior_ , vol. 9, no. 6, pp. 772–775, 2006.
  * [3] E. Castronova, _Synthetic Worlds : The Business and Culture of Online Games_. University Of Chicago Press, 2005.
  * [4] M. Szell and S. Thurner, “Measuring social dynamics in a massive multiplayer online game,” _Social Networks_ , vol. 32, no. 4, pp. 313–329, 2010.
  * [5] M. A. Ahmad, Z. Borbora, J. Srivastava, and N. S. Contractor, “Link prediction across multiple social networks,” in _ICDM Workshops_ , 2010, pp. 911–918.
  * [6] A. W. Gouldner, “The norms of reciprocity: A preliminary statement,” _American Sociological Review_ , vol. 25, no. 2, pp. 161–178, 1960.
  * [7] K. V. Hansen, “The asking rules of reciprocity in networks of care for children,” _Qualitative Sociology_ , vol. 27, no. 4, pp. 421–437, 2004.
  * [8] S. Leider, M. M. M bius, T. Rosenblat, and Q.-A. Do, “Directed altruism and enforced reciprocity in social networks,” _The Quarterly Journal of Economics_ , vol. 124, no. 4, pp. 1815–1851, 2009.
  * [9] C. A. Bliss, I. M. Kloumann, K. D. Harris, C. M. Danforth, and P. S. Dodds, “Twitter reciprocal reply networks exhibit assortativity with respect to happiness,” _Journal of Computational Science_ , vol. 3, no. 5, pp. 388–397, 2012.
  * [10] V. Zlatić and H. Štefančić, “Model of wikipedia growth based on information exchange via reciprocal arcs,” _EPL (Europhysics Letters)_ , vol. 93, no. 5, p. 58005, 2011.
  * [11] N. Durak, T. G. Kolda, A. Pinar, and C. Seshadhri, “A scalable null model for directed graphs matching all degree distributions: In, out, and reciprocal,” in _Proc. IEEE 2nd Workshop on Network Science_ , 2013.
  * [12] M. A. Ahmad, D. A. Huffaker, J. Wang, J. W. Treem, M. S. Poole, and J. Srivastava, “GTPA: A generative model for online mentor-apprentice networks,” in _AAAI_ , 2010.
  * [13] D. Garlaschelli and M. I. Loffredo, “Patterns of Link Reciprocity in Directed Networks,” _Phys. Rev. Lett._ , vol. 93, p. 268701, 2004.
  * [14] G. Zamora-Lopez, V. Zlatic, C. Zhou, H. StefanCic, and J. Kurths, “Reciprocity of networks with degree correlations and arbitrary degree sequences,” _Phys. Rev. E_ , vol. 77, p. 016106, 2008.
  * [15] L. Akoglu, P. V. de Melo, and C. Faloutsos, “Quantifying reciprocity in large weighted communication networks,” in _Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD)_ , 2012, pp. 85–96.
  * [16] C. Wang, A. Strathman, O. Lizardo, D. Hachen, Z. Toroczkai, and N. V. Chawla, “Weighted reciprocity in human communication networks,” _arXiv preprint arXiv:1108.2822_ , 2011.
  * [17] M. Szell, R. Lambiotte, and S. Thurner, “Multirelational organization of large-scale social networks in an online world,” _Proc. National Academy of Sciences_ , vol. 107, no. 31, pp. 13 636–13 641, 2010.
  * [18] J. Cheng, D. M. Romero, B. Meeder, and J. M. Kleinberg, “Predicting reciprocity in social networks,” in _IEEE SocialComm/PASSAT_ , 2011, pp. 49–56.
  * [19] V. Zlatic and H. Stefancic, “Influence of reciprocal edges on degree distribution and degree correlations,” _Physical Review E_ , vol. 80, no. 1, p. 016117, 2009.
  * [20] L. A. N. Amaral, A. Scala, M. Barthélémy, and H. E. Stanley, “Classes of small-world networks,” _Proc. National Academy of Sciences_ , vol. 97, no. 21, pp. 11 149–11 152, 2000.
  * [21] K. Baier, _Egoism in A Companion to Ethics_. Blackwell: Oxford, 1990.
  * [22] C. Rhodes, “Reciprocity in trade: the utility of a bargaining strategy,” _International Organization_ , vol. 43, no. 2, pp. 273–299, 1989.
  * [23] M. Ahmad, I. Ahmed, J. Srivastava, and M. Poole, “Trust me, i’m an expert: Trust, homophily and expertise in mmos,” in _IEEE SocialComm/PASSAT_ , 2011, pp. 882–887.