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Talk of the Network: A Complex Systems Look at the Underlying Process of Word-of-Mouth


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Though word-of-mouth (w-o-m) communications is a pervasive and intriguing phenomenon, little is known on its underlying process of personal communications. Moreover as marketers are getting more interested in harnessing the power of w-o-m, for e-business and other net related activities, the effects of the different communications types on macro level marketing is becoming critical. In particular we are interested in the breakdown of the personal communication between closer and stronger communications that are within an individual's own personal group (strong ties) and weaker and less personal communications that an individual makes with a wide set of other acquaintances and colleagues (weak ties). We use a technique borrowed from Complex Systems Analysis called stochastic cellular automata in order to generate data and analyze the results so that answers to our main research issues could be ascertained. The following summarizes the impact of strong and weak ties on the speed of acceptance of a new product: ••The influence of weak ties is at least as strong as the influence of strong ties. Despite the relative inferiority of the weak tie parameter in the model's assumptions, their effect approximates or exceeds that of strong ties, in all stages of the product life cycle. ••External marketing efforts (e.g., advertising) are effective. However, beyond a relatively early stage of the growth cycle of the new product, their efficacy quickly diminishes and strong and weak ties become the main forces propelling growth. The results clearly indicate that information dissemination is dominated by both weak and strong w-o-m, rather than by advertising. ••The effect of strong ties diminishes as personal network size decreases. Market attributes were also found to mediate the effects of weak and strong ties. When personal networks are small, weak ties were found to have a stronger impact on information dissemination than strong ties.
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Marketing Letters 12:3, 211±223, 2001
#2001 Kluwer Academic Publishers. Manufactured in The Netherlands.
Talk of the Network: A Complex Systems Look at the
Underlying Process of Word-of-Mouth
School of Business Administration, The Hebrew University of Jerusalem, Jersalem, Israel 91905
Davidson Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology,
Haifa, Israel 32000
Leon Recanati Graduate School of Business Administration, Tel Aviv University, Tel Aviv, Israel 69978.
*Corresponding author: e-mail:
Received November 2000; Revised February 2001; Accepted February 2001
Though word-of-mouth (w-o-m) communications is a pervasive and intriguing phenomenon, little is known on its
underlying process of personal communications. Moreover as marketers are getting more interested in harnessing
the power of w-o-m, for e-business and other net related activities, the effects of the different communications
types on macro level marketing is becoming critical. In particular we are interested in the breakdown of the
personal communication between closer and stronger communications that are within an individual's own
personal group (strong ties) and weaker and less personal communications that an individual makes with a wide
set of other acquaintances and colleagues (weak ties).
We use a technique borrowed from Complex Systems Analysis called stochastic cellular automata in order to
generate data and analyze the results so that answers to our main research issues could be ascertained. The
following summarizes the impact of strong and weak ties on the speed of acceptance of a new product:
The in¯uence of weak ties is at least as strong as the in¯uence of strong ties. Despite the relative inferiority of
the weak tie parameter in the model's assumptions, their effect approximates or exceeds that of strong ties, in
all stages of the product life cycle.
External marketing efforts (e.g., advertising) are effective. However, beyond a relatively early stage of the
growth cycle of the new product, their ef®cacy quickly diminishes and strong and weak ties become the main
forces propelling growth. The results clearly indicate that information dissemination is dominated by both
weak and strong w-o-m, rather than by advertising.
The effect of strong ties diminishes as personal network size decreases. Market attributes were also found to
mediate the effects of weak and strong ties. When personal networks are small, weak ties were found to have a
stronger impact on information dissemination than strong ties.
Key words: word-of-mouth, social networks, cellular automata, complex systems
Word-of-Mouth (w-o-m) communications is a pervasive and intriguing phenomenon. It
has been generally found that both satis®ed and dissatis®ed consumers tend to spread
positive and negative w-o-m, respectively, regarding products and services which they
purchase and use (Anderson 1998). The signi®cant role of w-o-m in the dissemination of
market information is supported by broad agreement among practitioners and academics.
A long list of academic scholarship, industry market research and anecdotal evidence
points to the signi®cant affect of w-o-m on consumer behavior and, consequently, on
sales (e.g., Eliashberg, Jonker, Sawhney and Wierenga 2000; Krider and Weinberg 1998;
Buttle 1998; Dabaher and Rust 1996; Reichheld 1996; Herr, Kardes and Kim 1991;
Mahajan, Muller and Kerin 1984). Evidence also indicates that consumers' decision
making is strongly in¯uenced by w-o-m. Over 40% of all Americans actively seek the
advice of family and friends when shopping for services such as doctors, lawyers and
auto mechanics (Walker 1995). W-o-m has also been found to constitute a major input to
the deliberations of potential consumers regarding the purchase of new products (Rogers
Recognition of the signi®cance of w-o-m, coupled with growing reservations regarding
the effectiveness of commonly used forms of marketing communications, such as
advertising (Rust and Varki 1996), may explain the repeated calls in the business press
for managers to attend to the power of w-o-m (Wilson 1994; Grif®n 1995; Silverman
1997). Today's managers are diverting increased efforts to the management of w-o-m.
Recent anecdotal evidence con®rms an upward trend in the use of referral reward
programs, in which customers are compensated for ``spreading the word'' about a product,
and inducing product consumption by their acquaintances (Biyalagorsky, Gerstner and
Libai 2001). Diverse marketers, including museums (DeMasters 2000), book publishers
(Cohen 1999) and movie producers (McCarthy 1999) have launched w-o-m campaigns
with reported success.
Furthermore, the mounting use of the Internet, enabling surfers to communicate quickly
with relative ease, has established the contemporary version of this phenomenon, known as
``Internet w-o-m'' or ``word of mouse'', as an important marketing communication
channel. In what is sometimes labeled as ``viral marketing'', companies are currently
investing considerable efforts to trigger a word of mouse process and accelerate its
distribution (Schwartz 1998; Oberndorf 2000).
However, the current interest in w-o-m management has yet to succeed in transforming
managers' entrenched perceptions of the w-o-m phenomenon as a ``black box''. Main-
taining explicit or implicit beliefs that the personal in¯uence process is beyond their
control (Silverman 1997), managers hope, at the most, to ``manage'' rather than ``direct''
w-o-m effects. Unfortunately, as most academic research and writing on w-o-m in areas
such as marketing or communications has concentrated on the individual or personal
network level (e.g., Herr, Kardes, and Kim 1991; Gilly, et al. 1998; Brown and Reingen
1987), academic marketing research offers little to mitigate managers' sense of inef®cacy.
Unlike other areas of marketing communications, such as advertising, sales promotion or
sales force (e.g., Boulding, Lee and Staelin 1994; Jeddidi, Mela and Gupta 1999), in which
signi®cant attention has been given to assessing aggregate effects on sales, little is known
about how w-o-m aggregates to impact sales levels.
One cause of this gap in knowledge relates to the underlying complexity of the w-o-m
process. The spread of information in a given social system may be described as ``an
adaptive complex system'', i.e., a system that consists of a large number of individual
entities which interact with each other (in what is sometimes an indiscernible manner),
ultimately generating large-scale, collective visible behavior. Although the individual
interactions may be simple in many such adaptive systems, the large scale of the system
at work allows the emergence of patterns which are hard to predict, hard to track
empirically, and are often almost impossible to analyze analytically (Waldorp, 1992).
Various disciplines, such as physics, biology and ecology, have developed theories and
methods to investigate the evolution of complex systems. In the social sciences, which
recognize the inherent complexity of many social systems such as markets and organiza-
tions, attention has recently been drawn to the analysis of complex systems, speci®cally in
the ®elds of economic analysis (see Rosser 1999) and organizational management (e.g.,
Anderson 1999). However, this trend is still in its infancy, and research activity has yet to
invest in the question of how micro-level w-o-m activity governs macro-level effects.
Here, we offer a technique for linking w-o-m micro- and macro-phenomena, employing
stochastic cellular automata, a tool for complex system analysis. Cellular automata models
are simulations of aggregate consequences, based on local interactions between individual
members of a population. In the case of w-o-m, these local interactions are diverse types of
interpersonal interactions. In the speci®c model presented here, we concentrate on the
emergence of macro-effects from micro-effects, based on one of the fundamental theories
of communications, known as the ``strength of weak ties'' (Granovetter 1973).
1. Weak and Strong Ties
The theory of ``the strength of weak ties'' (Granovetter 1973) offers one of the most
important conceptual explanations of the process by which micro-level interactions affect
macro-level phenomena. Granovetter claimed that individuals are often in¯uenced by
others with whom they have tenuous or even random relationships. These in¯uences are
labeled ``weak ties'', to distinguish them from the more stable, frequent and intimate
``strong tie'' interactions that characterize individuals' personal networks. Although
weaker in absolute impact on the individual level, the signi®cance of weak ties lies in
their potential to unlock and expose interpersonal networks to external in¯uences
(individuals in distant networks), thus paving the path for the spread of information
throughout society.
Since its publication, Granovetter's theory has been the object of repeated inquiry, albeit
primarily in contexts not directly related to marketing research, such as job searches or
migration patterns (e.g., Bian, 1997; Wilson, 1998). Adopting a consumer research
orientation, Brown and Reingen (1987) generally found support for the focus on the
two types of w-o-m ties proposed by Granovetter. They found that although strong ties
were more likely to be activated and perceived as in¯uential in consumers' decisions, weak
ties were more likely than strong ties to facilitate w-o-m referral ¯ows. Duhan et al. (1997)
also found support for these two distinct paths of in¯uence, noting that factors such as
consumers' previous knowledge or perceived task dif®culty affect consumers' information
reception from different sources. Other empirical work found that when ties are strong,
w-o-m receivers are more likely to actively look for information and that the w-o-m
information will have a signi®cant in¯uence on the receiver's purchase decision (Bansal
and Voyer 2000). However, Rogers (1995) suggests that even given the stronger informa-
tion ¯ow within strong ties, weak ties play a crucial role in the spread of information by
word-of-mouth on the aggregate level, especially about innovations.
While it is clear that weak and strong ties may be conceptualized as two distinct paths of
information dissemination, we know little about their macro-effects. For example, we lack
any comparative data on the respective rates of dissemination of these two mechanisms,
nor do we know how they interact with other marketing efforts such as advertising. Given
the increased efforts to ``manage'' w-o-m, improving our understanding of how these two
major paths of w-o-m affect information dissemination should be of great interest to
In our present study, we employ stochastic cellular automata to investigate the following
1. Which of the effects - strong ties, weak ties or marketing efforts - has more in¯uence on
the aggregate growth of information dissemination?
On the one hand, information is expected to pass more readily through strong ties, due
to their larger frequency of activation and perceived reliability. However, weak ties are
essential for initializing the information ¯ows in distinct networks. What is the time-
dependent relationship between these two forces?
2. How do personal network size and quantity of weak ties affect the in¯uence of strong
and weak ties on the aggregate growth of information dissemination?
How do factors such as the number of weak ties contacts and network size (number of
individuals in a typical personal network) mediate the consequential effects of weak and
strong ties?
3. How does advertising interact with strong or weak ties to affect the aggregate growth
of information dissemination?
Which of the two types of w-o-m paths will be more highly impacted by the presence of
marketing support such as advertising?
2. Cellular Automata
Cellular automata is a complex systems modeling technique, which simulates aggregate
consequences based on local interactions between individual members of a population.
Individual members in the model may represent plants and animals in ecosystems, vehicles
in traf®c, people in crowds or autonomous units in a physical system. The models typically
consist of a framework in which interactions occur between various types of individuals. In
stochastic cellular automata model, each individual's behavior is dictated by a prede®ned
scheme of response probabilities and is a function of the state of other individuals with
whom he interacts (see, for example, Holland 1995). The solution of such models consists
of tracking the changing state of each individual over time. Thus, cellular automata is
distinct from alternative modeling techniques that use individual attributes to calculate
average population attributes and then simulate changes in the ``average'' population. For
recent applications of complex systems models to marketing problems see Krider and
Weinberg (1997), Goldenberg et al. (2000) and Goldenberg, Libai and Muller (2001).
Figure 1 depicts the cellular automata model graphically. The model consists of a ®nite
number of virtual individuals in a given simulated social system, each of whom is able to
receive information during consecutive, discrete periods. Social interactions in the system
are of two types: proximal contacts among members of the same network and weak ties
interactions with individuals belonging to different networks. We de®ne two states
of individuals: ``informed'' ± those who have received the relevant information and are
informed of the phenomenon ± and ``uninformed'' ± those individuals who have not
received the information. The model makes use of the following additional assumptions:
1. Interpersonal contacts (b) are de®ned as the probability of an uninformed individual to
be affected by an informed individual, in one period, i.e., change his=her state from
``uninformed'' to ``informed''. Subscripts sand w, respectively, differentiate interactions
in which the source of the information belongs to the individual's network or to a
different network. Re¯ecting theory and previous research (e.g., Brown and Reingen
1987) b
is larger than b
. Thus, the probability of an individual to be affected by other
individuals in his own network is greater than the probability of changing his state from
uninformed to informed as a result of contacts with other, weak ties individuals.
2. Each individual ``belongs'' to a single personal network. Each network consists of
individuals who are connected by strong ties (b
). In each period, individuals also
conduct a ®nite number of weak ties interactions with individuals outside their personal
networks ( b
Figure 1. Market with Personal Networks. Strong Ties (bs) are Depicted with Solid Lines while Weak Ties (bw)
are Depicted with Dotted Lines.
3. Uninformed individuals also have a one period probability, a, of becoming informed
through their exposure to other marketing efforts, such as advertising. Following the
w-o-m literature (e.g., Buttle, 1998), the probability of being affected by advertising
exposure is assumed to be smaller than the effect of a w-o-m contact. Although the
present model incorporates advertising, other mass media sources of marketing
information are hypothesized to have a similar effect.
In the ®rst stage of the analysis, we de®ne the range of the individual level parameters to be
analyzed by a computer program (written in C for this study). The program both generates
individual level data and aggregates these results to plot macro-level adoption curves. In the
second stage of analysis, individual level and aggregate level data are fed into a statistical
program (SAS) to perform the necessary statistical analyses to identify main effects.
We divide the entire market equally into personal networks, in which each individual
can belong to one network. In addition, in each period every individual conducts random
meetings with other individuals external to his personal network.
Thus if in period t, an individual is connected to minformed others belonging to his or
her personal network and jinformed others who are random contacts represented by weak
ties, the probability of the individual becoming informed in period t, is given by:
The following step-by-step outline describes the cellular automata algorithm:
Period 0: This is the initial condition where all individuals are uninformed (receiving the
value of 0)
Period 1: The probabilities for each individual (given by equation 1) are realized. Clearly
only advertising is at work in this period as word-of-mouth needs informed
individuals to start the process. A random number U is drawn from a uniform
distribution in the range [0,1]. If U <p(t) then the individual moves from non-
informed to informed (receiving the value of 1). The individual stays non-
informed otherwise.
Period 2: The informed individuals begin the w-o-m process by deploying their strong
ties within their own personal network, and weak ties to other networks.
Probabilities are realized as in step 1, and the random number is drawn so that
when U <p(t) the individual moves from non-informed to informed.
Period n: This process is repeated until 95% of the total market (3000 individuals)
becomes informed.
3. Method
All combinations of the parameters were considered in a full factorial design experiment.
Each of the ®ve input variable parameter s was manipulated on seven levels, to produce overall
16,808 information dissemination process simulations. Each process was terminated
when 95% of the population attained informed status. Parameter ranges were set as follows:
1. Size of each individual's personal network 5±29
2. Number of each individual's weak ties contacts 5±29
3. Effect of weak ties (b
) 0.005±0.015
4. Effect of strong ties (b
) 0.01±0.07
5. Effect of advertising (a) 0.0005±0.01
Note that since weak and strong ties effects represent probabilities, their absolute value
range determines the magnitude of a ``period'', which is less of an interest to us. Our interest
lies with the relative values of the parameters analyzed. Consistent with previous literature
as speci®ed above, we set the advertising effect to be in a range that is lower than the range
of the w-o-m effects. In addition, the weak ties probabilities are set to be lower than the
strong ties probabilities. Networks size range were set to re¯ect a reasonable range of
personal contacts, and while the ranges of weak ties and strong ties contacts are the same,
through the simulation we can analyze the effect of different combinations of their sizes.
After generating all possible outcomes of the above manipulations, a number of analyses
were conducted to explore the relationship between weak and strong ties and the rate of
information dissemination. One possible aggregate level measure, All Informed, is the
number of periods elapsing before 95% of the population becomes informed. However,
cellular automata modeling enables us to extend our examination and discover more
complex, perhaps non-linear, effects, by observing the succession of changes occurring
over the life-span of the process. More speci®cally, to understand how the respectiveimpacts,
weak and strong ties, evolve over the different stages of the process, we look at Early
Informed, Middle Informed and Late Informed - variables re¯ecting the number of periods
elapsing before 0±16%, 16±50 % and 50±95% of the market become informed. We denote
the time from the onset of the process until 16% of the market has attained ``informed''status
as T
and so forth. Three OLS regressions, designed to relate aggregate level measures
to micro-level parameter values, were conducted, with Early Informed, Middle Informed and
Late Informed respectively as the dependent variables, and the network and in¯uence
parameters outlined above as the dependent variables. Regression results presenting the
effects of the different communication parameters are given in Table 1. We also examined the
impact of the interactions between the size of personal networks, the number of weak ties and
advertising, on the one hand, and weak and strong ties on the other. This was done by running
an OLS regression for each factor value and the other four parameters as independent
variables, with All Informed as the dependent variable. Results are given in Figures 2±4.
4. Results
The following main results raised some interesting observations:
Result 1: The in¯uence of weak ties on the speed of information dissemination is at
least as strong as the in¯uence of strong ties.
Despite the relative inferiority of the weak tie parameter in the model's assumptions
(strong ties re¯ect a greater probability for an individual-level transformation), their effect
approximates or exceeds that of strong ties, in all three process stages (see Table 1). These
results challenge the emphasis placed, in most of the research on w-o-m, on strong ties
as the important means of information dissemination (Brown and Reingen, 1987) and
provide quantitative support for Granovetter's theory (1973) in this regard. However,
recalling our conceptualization of the market as a complex system, these results should not
cause us excessive surprise. Like most complex systems, interactions and non-linear
effects may be present beneath the surface.
While this ®nding is intriguing at all stages of the information growth process, the
increasing importance of the effect of weak ties during the middle stage (T
suggests that their signi®cance stems from their unique effect on growth, rather than from
their prevalence. De®ne ``activated networks'' as networks containing at least one informed
individual. Closely tracking the dynamics of the process reveals that the initially large
proportion of uninformed individuals in activated networks gradually decreases as more
individuals become informed in each network. Since the impact of strong ties is related to
the ratio of uninformed to informed individuals in each network, as more individuals
become informed, the potential effect of strong ties is gradually exhausted. When all
members of activated networks become informed, the effect of strong ties is contingent
upon on the activation of new networks, a task performed by the weak ties. The increasing
slope of the effect of the weak ties between the ®rst and middle stages thus re¯ects the fact
that the successive activation of new networks through weak ties enables the continuation
of the process.
Result 2: Beyond a relatively early stage of the process, the effect of external marketing
efforts (e.g., advertising) quickly diminishes and strong and weak ties become
the main forces propelling the process.
The results clearly indicate that information dissemination is dominated by both w-o-m
paths, rather than by advertising. This con®rms ®ndings from the diffusion of innovation
literature, which pointed to w-o-m as the main factor driving the speed of innovation
diffusion (Rogers 1995; Mahajan, Muller and Srivastava 1990).
Moreover, the results in Table 1 also provide quantitative support for Rogers' (1995)
argument that, while advertising may be important in the initial stages of information
Tab le 1. A Comparison of the Effects of Weak and Strong Ties on the Speed of Information Dissemination (The
Dependent Variable is the Number of Periods Comprising Each Process Stage, the OLS Parameters are
Strong ties effect 70.25 70.33 70.37
Weak ties effect 70.26 70.40 70.38
Advertising effect 70.61 70.11 70.04
Adjusted R
0.66 0.60 0.63
All variables are signi®cant at p 0.0001 level.
dissemination, the main mechanism driving innovation diffusion after product takeoff is
Our ®ndings show how the major role of marketing efforts in the initial stage of the
process (their impact is twice as powerful as that of either the strong or weak ties)
diminishes after 16% of the market becomes informed. When information dissemination
reaches the halfway mark (i.e., 50% of all individuals are informed), the impact of
marketing efforts diminishes further, to one-third and one-quarter of the impact of strong
ties and weak ties, respectively. Although in the initial stage, strong and weak tie effects
were almost equal in potency, weak ties have a larger effect than strong ties, relative to the
advertising effect, in the second stage of the process.
Result 3: The effect of strong ties on the speed of information dissemination diminishes
as personal network size decreases.
Market attributes were also found to mediate the effects of weak and strong ties, as this
and the following results show. When personal networks are small, weak ties were found to
have a stronger impact on information dissemination than strong ties. A non-linear
relationship between weak ties and network size was indicated (see Figure 2).
Result 4: As the number of weak ties contacts increases, the effect of strong ties
decreases while the effect of weak ties increases (see Figure 3).
Result 5: As the level of advertising increases, the effects of both strong and weak ties
are marginally impacted, in inverse directions: the effect of strong ties
increases while the effect of weak ties decreases (see Figure 4).
Figure 2. The Effects of Strong and Weak Ties on Speed of Information Dissemination as a Function of Personal
Network Size.
5. Discussion and Implications
In the present study, we demonstrated how complex systems analysis (stochastic cellular
automata in our case) contributes to our understanding of the aggregate level effect of
Figure 3. The Effects of Strong and Weak Ties on Speed of Information Dissemination as a Function of the
Number of Weak Ties Contacts.
Figure 4. The Effects of Strong and Weak Ties on the Speed of Information Dissemination as a Function of
weak and strong social ties, in terms of the spread of information through word-of-mouth.
First, as Table 1 demonstrates, for the range of parameters examined here, weak ties have
an in¯uence on information dissemination, which is at least equal to that of strong ties.
Second, both types of social effects have a stronger in¯uence on information dissemination
than the effect of advertising.
As shown in Figures 2±4, the relative effects of strong and weak ties may depend on
other factors, such as personal network size, number of weak ties interpersonal interactions
characterizing a social system, and advertising. When network size is small, or weak ties
contacts are numerous, or advertising effect is weak, weak ties may have a greater impact
on the rate of information dissemination than strong ties.
These results have important managerial implications. Managers attempting to in¯uence
w-o-m spread should distinguish between the two kinds of social interactions that
contribute to both positive and negative w-o-m communications. For example, in certain
situations managers may want to distinguish referral rewards for referrals of close friends
and family members from rewards for referring others. When personal networks are large,
weak ties contacts among inter-network individuals are few, or the advertising effect is
strong, fostering inter-network ties may be one of the few options available to marketers.
Moreover, as ®ndings from the diffusion of innovations literature suggest, w-o-m and
advertising effects may differ among different market segments (Rogers and Kincaid,
1981; Rogers, 1995). Marketers are advised to develop market research, which would
provide estimates of these factors for different segments and products.
While this study adds to our knowledge by exploring the aggregate level effect of weak
and strong w-o-m ties, we recognize its limited scope, especially considering the wide
range of analyses enabled by cellular automata methods for the exploration of phenomena
such as w-o-m. This technique, due to its unique features and especially the ability to
model a wide variety of market situations, is suited to model many marketing phenomena
that have been traditionally under-researched. We believe it is especially suited to analyze
interpersonal based processes such as the growth of new products and other w-o-m based
social phenomena that have been only partially explored due to the complexity inherent in
these processes. Where diffusion of innovations modelers are often restricted by simplify-
ing assumptions, cellular automata enables us to deeply explore real life phenomena that
are not analytically tractable. It is especially suited to model individual level heterogeneous
behavior where the aggregation is done by the program itself without having to resort to
simplifying assumptions needed for the aggregation.
For example, such methods may be used to explore web-based information dissemina-
tion or the consequences of diverse ``viral marketing'' approaches using w-o-m channels
such as ``chat rooms'', websites of various sizes containing links to other sites, large-scale
information transmission though e-mail lists and web-based referral reward programs.
Other non-web examples include an analysis of time-based changes of marketing mix and
consumer behavior variables for new product growth (e.g., price, advertising, repeat
purchase, market potential), the optimal marketing in the presence of network externalities
or the optimal marketing to early and mainstream markets for high-tech products.
Considering the options complex system methods such as cellular automata open for
researchers, it is clear that this is just a short list for promising future research.
The authors would like to thank Moshe Givon, John Hogan, David Mazursky, Charles
Weinberg and two anonymous reviewers for their insightful comments and suggestions.
This research was supported by The Israel Science Foundation founded by the Israel
Academy of Sciences and Humanities and by grants from the K-mart International Center
of Marketing and Retailing, and Davidson Center at the Hebrew University and the Israeli
Institute for Business Research ar Tel Aviv University.
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... For example, government effort was found to be critical in encouraging the adoption of sustainable technology in the Malaysian SMEs sector [138]. Effects of an external influence (via advertising or mass media) have already been studied extensively [22,[139][140][141][142]. It has been argued that advertising mostly contributes to the spread of initial awareness about the innovation, rather than to its adoption [22]. ...
... It has been argued that advertising mostly contributes to the spread of initial awareness about the innovation, rather than to its adoption [22]. Goldenberg et al. [141] concluded that the effect of external influences is strong at early stages of the diffusion process and decreases in time. Here we assumed that all individuals were already aware of the new technology and the effort of the external authority was directed towards exploiting individual tendencies to comply with propaganda [143,144] by modifying both the behaviour and ...
... This would allow us to study the effect of interactions between different socio-psychological and topological factors on the diffusion process. This will also allow us to model explicitly the effects of opinion leaders [141,[173][174][175][176] and to examine the effectiveness of different more comprehensive targeting intervention strategies, e.g. targeting opinion leaders, different small groups of individuals located in different places of a network, or a small number of large groups [177]. ...
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Technological innovations drive the evolution of human societies. The success of innovations depends not only on their actual benefits but also on how potential adopters perceive them and how their beliefs are affected by their social and cultural environment. To deepen our understanding of socio-psychological processes affecting the new technology spread, we model the joint dynamics of three interlinked processes: individual learning and mastering the new technology, changes in individual attitudes towards it, and changes in individual adoption decisions. We assume that the new technology can potentially lead to a higher benefit but achieving it requires learning. We posit that individual decision-making process as well as their attitudes are affected by cognitive dissonance and conformity with peers and an external authority. Individuals vary in different psychological characteristics and in their attitudes. We investigate both transient dynamics and long-term equilibria observed in our model. We show that early adopters are usually individuals who are characterized by low cognitive dissonance and low conformity with peers but are sensitive to the effort of an external authority promoting the innovation. We examine the effectiveness of five different intervention strategies aiming to promote the diffusion of a new technology: training individuals, providing subsidies for early adopters, increasing the visibility of peer actions, simplifying the exchange of opinions between people, and increasing the effort of an external authority. We also discuss the effects of culture on the spread of innovations. Finally, we demonstrate that neglecting the cognitive forces and the dynamic nature of individual attitudes can lead to wrong conclusions about adoption of innovations. Our results can be useful in developing more efficient policies aiming to promote the spread of new technologies in different societies, cultures and countries.
... There are two main research lines on models of information diffusion in networks [42], namely the explanatory and the predictive models. The first line of research includes modeling inspired in epidemics, while the second includes propagation models such as the cascade [20] or the linear threshold models [23]. This research is of utmost importance to areas like marketing, advertising, epidemiology, and social media analysis [79]. ...
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Understanding at microscopic level the generation of contents in an online social network (OSN) is highly desirable for an improved management of the OSN and the prevention of undesirable phenomena, such as online harassment. Content generation, i.e., the decision to post a contributed content in the OSN, can be modeled by neurophysiological approaches on the basis of unbiased semantic analysis of the contents already published in the OSN. This paper proposes a neuro-semantic model composed of (1) an extended leaky competing accumulator (ELCA) as the neural architecture implementing the user concurrent decision process to generate content in a conversation thread of a virtual community of practice, and (2) a semantic modeling based on the topic analysis carried out by a latent Dirichlet allocation (LDA) of both users and conversation threads. We use the similarity between the user and thread semantic representations to built up the model of the interest of the user in the thread contents as the stimulus to contribute content in the thread. The semantic interest of users in discussion threads are the external inputs for the ELCA, i.e., the external value assigned to each choice.. We demonstrate the approach on a dataset extracted from a real life web forum devoted to fans of tinkering with musical instruments and related devices. The neuro-semantic model achieves high performance predicting the content posting decisions (average F score 0.61) improving greatly over well known machine learning approaches, namely random forest and support vector machines (average F scores 0.19 and 0.21).
... It is challenging to predict dynamic behavior at the meta-level of a network, even if we know how individual nodes respond to stimuli and how they are linked. Network science offers several notable graph-based predictive diffusion models [22], such as the classic linear threshold LT [20,21], the independent cascade IC [23], the classic voter model [24], the Axelrod model [25] and the Sznajd model [26]. These models use fixed thresholds to trigger opinion changes or thresholds that evolve according to simple probabilistic processes that are not driven by the internal state of social agents [22]. ...
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Inferring the diffusion mechanisms in complex networks is of outstanding interest since it enables better prediction and control over information dissemination, rumors, innovation, and even infectious outbreaks. Designing strategies for influence maximization in real-world networks is an ongoing scientific challenge. Current approaches commonly imply an optimal selection of spreaders used to diffuse and indoctrinate neighboring peers, often overlooking realistic limitations of time, space, and budget. Thus, finding trade-offs between a minimal number of influential nodes and maximizing opinion coverage is a relevant scientific problem. Therefore, we study the relationship between specific parameters that influence the effectiveness of opinion diffusion, such as the underlying topology, the number of active spreaders, the periodicity of spreader activity, and the injection strategy. We introduce an original benchmarking methodology by integrating time and cost into an augmented linear threshold model and measure indoctrination expense as a trade-off between the cost of maintaining spreaders’ active and real-time opinion coverage. Simulations show that indoctrination expense increases polynomially with the number of spreaders and linearly with the activity periodicity. In addition, keeping spreaders continuously active instead of periodically activating them can increase expenses by 69–84% in our simulation scenarios. Lastly, we outline a set of general rules for cost-effective opinion injection strategies.
... The simplest of the dynamic cascade models, IC was first mentioned by Goldenber et al. [36], and then was used by Kempe et al. [7]. The model supposes that every vertex is either active or inactive, and activation occurs in discrete time-steps (i.e., an inactive neighbor can be activated by each of its active neighbors), which can be described as follows. ...
For the purpose of maximizing the spread of influence caused by a certain small number k of nodes in a social network, we are asked to find a k-subset of nodes (i.e., a seed set) with the best capacity to influence the nodes not in it. This problem of influence maximization (IM) has wide application, belongs to subset problems, and is NP-hard. To solve it, we should theoretically examine all seed sets and evaluate their influence spreads, which is time-consuming. Therefore, metaheuristic strategies are generally employed to gain a good seed set within a reasonable time. We observe that many algorithms for the IM problem only adopt a uniform mechanism in the whole solution search process, which lacks a response measure when the algorithm becomes trapped in a local optimum. To address this issue, we propose a phased hybrid evaluation-enhanced (PHEE) approach for IM, which utilizes two distinct search strategies to enhance the search of optimal solutions: a randomized range division evolutionary (RandRDE) algorithm to improve the solution quality, and a fast convergence strategy. Our approach is evaluated on 10 real-world social networks of different sizes and types. Experimental results demonstrate that our algorithm is efficient and obtains the best influence spread for all the datasets compared with three state-of-the-art algorithms, outperforms the time consuming CELF algorithm on four datasets, and performs worse than CELF on only two networks.
... In social networks, and in Twitter in particular, different sources of information diffusion coexist. In fact, information may come and is propagated directly from the users within the platform following the word-of-mouth effect [37], as well as from other sources that are external to social networks (e.g. television and radio) [38]. ...
In the last few years, Online Social Networks (OSNs) attracted the interest of a large number of researchers, thanks to their central role in the society. Through the analysis of OSNs, many social phenomena have been studied, such as the viral diffusion of information amongst people. What is still unclear is the relation between micro-level structural properties of OSNs (i.e. the properties of the personal networks of the users, also known as ego networks) and the emergence of such phenomena. A better knowledge of this relation could be essential for the creation of services for the Future Internet, such as highly personalised advertisements fitted on users' needs and characteristics. In this paper, we contribute to bridge this gap by analysing the ego networks of a large sample of Facebook and Twitter users. Our results indicate that micro-level structural properties of OSNs are interestingly similar to those found in social networks formed offline. In particular, online ego networks show the same structure found offline, with social contacts arranged in layers with compatible size and composition. From the analysis of Twitter ego networks, we have been able to find a direct impact of tie strength and ego network circles on the diffusion of information in the network. Specifically, there is a high correlation between the frequency of direct contact between users and her friends in Twitter (a proxy for tie strength), and the frequency of retweets made by the users from tweets generated by their friends. We analysed the correlation for each ego network layer identified in Twitter, discovering their role in the diffusion of information.
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Influence maximization (IM) is a challenging combinatorial optimization problem on (social) networks given a diffusion model and limited choice for initial seed nodes. In a recent paper by Keskin and Güler (Turkish J of Electrical Eng & Comput Sci 26:3383–3396, 2018) an integer programming formalization of IM using the so-called deterministic linear threshold diffusion model was proposed. In fact, it is a special 0-1 linear program in which the objective is to maximize influence while minimizing the diffusion time. In this paper, by rigorous analysis, we show that the proposed algorithm can get stuck in locally optimal solution or cannot even start on certain input graphs. The identified problems are resolved by introducing further constraints which then leads to a correct algorithmic solution. Benchmarking results are shown to demonstrate the efficiency of the proposed method.
Due to the continuous emergence of various social and trade networks, network influence analysis has aroused great interest of the researchers. Based on different influence propagation models, many new models and methods for influence maximization on networks have been proposed. As an extension and expansion of the traditional influence maximization problem, influence blocking maximization has become a hotspot of research, and has been widely applied in many areas such as physics, computer science and epidemiology. In recent years, various methods for influence blocking maximization problem have been reported. However, we still lack a comprehensive review to systematically analyze the methodological and theoretical advances in influence blocking maximization problem from the aspects of social networks influence analysis. This review aims to fill this gap by providing a comprehensive survey and analysis of the theory and applications of influence blocking maximization. Not only it advances the theoretical understanding of the influence maximization problem, but will be a point of reference for future researches.
One important task in the study of information cascade is to predict the future recipients of a message given its past spreading trajectory. While the network structure serves as the backbone of the spreading, an accurate prediction can hardly be made without the knowledge of the dynamics on the network. The temporal information in the spreading sequence captures many hidden features, but predictions based on sequence alone have their limitations. Recent efforts start to explore the possibility of combining both the network structure and the temporal feature. Here, we propose a new end-to-end prediction method CasSeqGCN in which the structure and temporal feature are simultaneously taken into account. A cascade is divided into multiple snapshots which record the network topology and the state of nodes. The graph convolutional network (GCN) is used to learn the representation of a snapshot. A novel aggregation method based on dynamic routing is proposed to aggregate node representation and the long short-term memory (LSTM) model is used to extract temporal information. CasSeqGCN predicts the future cascade size more accurately compared with other state-of-art baseline methods. The ablation study demonstrates that the improvement mainly comes from the design of the input and the GCN layer. We explicitly design an experiment to show the quality of the cascade representation learned by our approach is better than other methods. Our work proposes a new approach to combine the structural and temporal features, which not only gives a useful baseline model for future studies of cascade prediction, but also brings new insights on a wide collection of problems related with dynamics on and of the network.
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The extremely short life cycle and the rapid decay in revenues after opening coupled with the rapid and frequent introduction of new competitive products makes the timing of new product introductions in the motion picture industry critical, particularly during the high-revenue Christmas and summer seasons. Each studio wants to capture as much of the season as possible by opening early in the season. At the same time, each wants to avoid head-to-head competition. The authors model competition between two motion pictures in a share attraction framework and conduct an equilibrium analysis of the product introduction timing game in a finite season. The following three different equilibrium configurations emerge: (1) a single equilibrium with both movies opening simultaneously at the beginning of the season, (2) a single equilibrium with one movie opening at the beginning of the season and one delaying, and (3) dual equilibria, with either movie delaying opening. A key factor is the product life cycle, which can be captured well with a two-parameter exponential decline. The authors relate the life-cycle parameters to these possibilities with the general result that the weaker movie may be forced to delay opening. These results are related to case studies of the opening of recently released movies. A statistical analysis of the 1990 summer season in North America provides support for the conclusions and suggests that current release timing decisions can be improved. The authors discuss the rationale of "avoiding the competition" in the general context of product introduction timing.
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Five network principles are elaborated from literature on Mexican immigrants and from research that I conducted on immigration from a rancho in Jalisco state to a variety of destinations within the United States. These principles are, first, that networks are multilocal, encompassing a number of geographical destinations. The importance of destinations, however, may change over time. Second, time anchoring points at any given geographical location are the work sites where immigrants find employment. Thus, labor market conditions structure where immigrants go and where they stay. Third, new geographical locations are often accessed through the 'strength of weak ties,' leading to geographic dispersion. Over time, some weak ties may be converted to strong ties though marriage or compadrazgo. Fourth, both dense networks and diffuse, weak-tie, or acquaintance networks constitute 'social capital' for their members. Fifth, given the geographical dispersion at the work site and/or work type clustering found among immigrants from any particular source community, the latter can best be explained by job recruitment primarily through dense network members, especially close relatives.
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Marketing practitioners and theorists routinely cite the power of the personal referral on customer behaviour. However, relatively few companies have tried to harness the power of word of mouth (WOM). Scholars have been pondering WOM over 2400 years, although modern marketing research into WOM started only relatively recently, in the post-war 1940s. WOM can be characterized by valence, focus, timing, solicitation and degree of management intervention. Most recent WOM research has been conducted from a customer-to-customer perspective, even though WOM is found in other contexts such as influence, employee and recruitment markets. Marketing research into WOM has attempted to answer two questions. What are the antecedents of WOM? What are the consequences of WOM? This paper integrates that research into a contingency model and attempts to identify researchable gaps in our knowledge.
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Although interpersonal word-of-mouth communication, by definition, takes place between two people, rarely has the phenomenon of word of mouth been studied using both members of the dyad. Building on the literature, this article offers a model of active interpersonal information search that is tested by using a method in which information seeker and source perceptions were obtained. Source characteristics were important determinants of interpersonal influence, but seeker characteristics also played an important role. Interestingly, it proved useful to distinguish between demographic and attitudinal homophily of seeker and source as the former was inversely and the latter directly related to interpersonal influence.
Complex organizations exhibit surprising, nonlinear behavior. Although organization scientists have studied complex organizations for many years, a developing set of conceptual and computational tools makes possible new approaches to modeling nonlinear interactions within and between organizations. Complex adaptive system models represent a genuinely new way of simplifying the complex. They are characterized by four key elements: agents with schemata, self-organizing networks sustained by importing energy, coevolution to the edge of chaos, and system evolution based on recombination. New types of models that incorporate these elements will push organization science forward by merging empirical observation with computational agent-based simulation. Applying complex adaptive systems models to strategic management leads to an emphasis on building systems that can rapidly evolve effective adaptive solutions. Strategic direction of complex organizations consists of establishing and modifying environments within which effective, improvised, self-organized solutions can evolve. Managers influence strategic behavior by altering the fitness landscape for local agents and reconfiguring the organizational architecture within which agents adapt. [ABSTRACT FROM AUTHOR] Copyright of Organization Science is the property of INFORMS: Institute for Operations Research and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
The spatial dimension of competition among retail outlets is well researched and typically captured with spatial interaction models. A stream of theoretical research has studied the consequences of incorporating various types of dynamics into these models. We build on this research by incorporating a behavioral decision process based on bounded rationality, and by allowing for unexpected adversity in the environment in the form of exogenous shocks. Given these characteristics - spatial competition, boundedly rational decision making, and environmental adversity - we study the long-run dynamics of a model retail industry. The model reaches a stochastic steady state which is "poised," in the sense that a shock may - or may not - trigger a wave of innovation which sweeps the entire system. Detailed investigation of this steady state shows that it has the characteristics of a general type of organization, known as self-organized criticality, that has been described in both theoretical biology and statistical physics.
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