Opinion Leaders and Social Influence, Opinion Leaders and Social Influence, Opinion Leaders and Social Influence, Opinion Leaders and Social Influence,
How are They Affecting the Adoption of New Products?
How are They Affecting the Adoption of New Products? How are They Affecting the Adoption of New Products?
How are They Affecting the Adoption of New Products?
A Simulation Study
By Peter van Eck
University of Groningen Faculty of Economics
Research Master Economics and Business August 2007
Student number: 1365878
Supervisors:
Dr. W. Jager and Dr. J. Kratzer
EBSCOhost page 1 of 1
Title: Opinion Leaders and Social Influence, How are They Affecting the Adoption of New Products? A Simulation Study
Author: Van Eck, Peter S.1 s1365878@student.rug.nl
Source: Students Journal of Marketing (SJM); August2007, Vol. 3 Issue 2, p3-11, 9p
Document Type: Article
Subject Terms: * Opinion Leaders
* Informational Influence and Normative Influence
* Strong Ties and Weak Ties
NAICS/Industry Codes: 541910 Marketing Research and Public Opinion Polling
Abstract: This study investigates the influence of opinion leader, interpersonal influence and strong and weak ties on the adoption process of new products. A simulation study is done, using two different network structures: a random network and a scale-free network . Especially the distinction between strong and weak ties is found to be important in both the random network and the scale-free network. The opinion leader is most influential in a scale-free network as is informational influence.
[ABSTRACT FROM AUTHOR]
Author Affiliates: 1Student Economics and Business (research) at the Faculty of Economics, University of Groningen
3
Students Journal of Marketing, Vol. III (August 2007), 3-11 INTRODUCTION
Mass media become less and less effective in reaching a large audience, because of the large availability of for example television channels, magazines etc.. On the other hand consumers become more sceptical about the commercial messages they see and hear, partly because they can share their experiences easily on the Internet.
Marketers have to deal with these developments and they do so by using word of mouth (WOM) as a marketing instrument.
WOM has many advantages in comparison with mass media, such as a higher effectiveness (Day, 1971; Still, Barnes and Kooyman, 1984) and lower costs, while reaching more people (Procter and Richards, 2002).
Furthermore people experience this informal communication (Westbrook, 1987) as highly credible (Fisher, Garret, Arnold and Ferris, 1999; Mangold and Miller, 1999; File, Judd and Prince, 1992).
A lot of research has been done with respect to WOM, but it is still difficult to predict whether and how WOM will develop. Many factors influence WOM and it is difficult to investigate these factors in empirical research, because they are strongly related and difficult to observe. An alternative way to investigate WOM is by doing a simulation study, in which all variables can be influence and ultimately the independent effects of the different factors can be determined. In this paper such a study will be used to investigate several factors that influence the spread of WOM in more detail.
Since WOM spreads through the personal networks of people, the structure of such a network obviously has influence on how WOM spreads. This study tries to replicate some results described in Delre, Jager, Bijmolt and Janssen (2007) and therefore uses a similar network structure: a random network based on a small-world network. The first experiment done in this study will also be done using a scale-free network. Besides the network structure, there are also other factors influencing the spread of WOM. Specific people in the network, called the
‘opinion leaders’ have been found to play an important in
* Peter S. van Eck (e-mail: p.s.van.eck@student.rug.nl) is a student Economics and Business (research) at the Faculty of Economics. The author wishes to thank Dr. W. Jager and Dr. J.
Kratzer for their feedback and Drs. S.A. Delre for his support!
the spread of WOM (e.g. Procter and Richards, 2002;
Berelson and Steiner, 1964). Two other important factors will also be discussed in this paper: the role of interpersonal influence (Deutsch and Gerrard, 1955) and the role of
‘strong ties’ and ‘weak ties’ (Granovetter, 1973).
Earlier research already used agent-based simulation studies to investigate WOM (e.g. Delre, et al., 2007). This type of study makes it possible to specify agent- characteristics on an individual level, thereby introducing heterogeneity in the model. The simulation model used in this study is based on the model used by Delre et al. (2007), but the model is extended with above mentioned factors.
The model is almost entirely based on literature and this study should therefore be seen as exploratory and can be used as an example of how to introduce several (complex) factors of WOM in a agent-based simulation study.
THE MODEL: SOME BACKGROUND INFORMATION Agent Based Modelling
Simulation studies have several advantages in comparison with empirical research. One of these advantages is that it is easy to run several simulations with slightly altered situations to investigate the difference.
Furthermore it is relatively easy to change parameters independent from each other, which is much more difficult in ‘real’ situations. The agent-based model is a specific type of simulation study, in which the ‘rules’ for agents can be defined on an individual basis. This makes it possible to introduce heterogeneity in the network: opinion leaders follow different rules than other agents, not every agent is equally sensitive for the interpersonal influence and not every agent has the same number of (weak and strong) ties.
Although it is preferable to base the agent rules on empirical data, for this exploratory study literature is used to define the agent rules. In marketing literature many studies are already done with respect to the factors included in this study and therefore it is possible to base the rules of the model on generally accepted ideas. The different characteristics of the model will now be discussed in more detail.
Network Type
In this study two different well-known network types are used: the random network (based on the small-world PETER S. VAN ECK*
This study investigates the influence of opinion leader, interpersonal influence and strong and weak ties on the adoption process of new products. A simulation study is done, using two different network structures: a random network and a scale-free network . Especially the distinction between strong and weak ties is found to be important in both the random network and the scale-free network.
The opinion leader is most influential in a scale-free network as is informational influence.
Opinion Leaders and Social Influence, How are They Affecting the Adoption of
New Products? A Simulation Study
4 STUDENTS JOURNAL OF MARKETING, AUGUST 2007
network) and the scale-free network. Since the random network is based on a small-world network, the random network will also be discussed here.
The small-world network has a very simple structure in which each agent is connected to its neighbours and to the neighbours of its neighbours (see figure 1). This type of network is modelled by Wilensky (2005a) and used as a
‘starting value’ for the random network described by Watt and Strogatz (1998). In the small-world network every agents is connected with any other agent within a maximum of ‘total-number-of-agents / 4’ steps (figure 1 one shows that agent 1 and 5 are connected through agent 3).
Therefore information spreads very fast in this type of network.
Figure 1
SMALL WORLD NETWORK
1
2 3 8
7
4 6
5
As mentioned, the random network as proposed by Watts and Strogatz (1998) uses the small-network as a starting value. However, the connections between the agents are ‘rewired’. For a certain percentage of links, one of the two agents of the link is replaced by another agent (e.g. agent 1 is connected with agent 2, but this relation is replaced by a relation between agent 1 and agent 6). The probability of ‘rewiring’ indicates the randomness in the network. In this random network the number of connections of a specific agent is unknown, as well as in how many steps information can flow from one agent to another.
However, the maximum number of steps can be expected to be lower than in the original small-world network, because certain agents act as ‘hubs’. Such a hub connects many agents in only a few steps, therefore information can spread even faster in this type of network.
The third type of network used in this study is the scale-free network. The scale-free network used in this study is called the Barabasi scale-free network (Wilensky, 2005b). Barabasi (2002) described a method to create a scale-free network: additional agents are connected to a network with a preference for a connection with a agent with more connections (hubs), which is often referred to as
‘preferential attachment’ (see figure 2 for an example). This type of network follows a power-law, in which many agents have only one connected and few agents have many connections (hubs). Since most hubs are connected to each
other in this network, the number of steps between to agents is relatively low.
Figure 2 SCALE-FREE NETWORK
9 1 5 8 2
6 4
3 7
Opinion Leaders
The important role of opinion leaders is already described by many researchers (e.g. Procter and Richards, 2002; Berelson and Steiner, 1964: 550). With respect to the spread of WOM, opinion leaders have several important characteristics: in comparison with other people in their network they have more experience with the product, acquire more information about the product and are more involved with the product (King and Summers, 1970;
Rogers and Cartano, 1962; Goldsmith and Flynn, 1994).
Furthermore, opinion leader are more innovative than their
‘followers’ (Rogers, 1983; Hansen and Hansen, 2005).
Opinion leaders also tend to have a central position in a network (Berelson and Steiner, 1964; Valente, 1996;
Czepiel, 1974).
Informational and Normative Influence
In relation with WOM two different types of interpersonal influence are often mentioned: informational influence and normative influence (Deutsch and Gerrard, 1955). Both types of influence represent a different type of information flowing through the network. Normative influence, defined as the tendency to conform to the expectations of others (Burnkrant and Cousineau, 1975), especially refers to social pressure. In a product adoption process, this type of influence is therefore especially affected by the number of other people close to the person that adopted the product already.
Informational influence, defined as the tendency to accept information from others as evidence about reality (Deutsch and Gerrard, 1955), is more related to who tells something. In relation with the opinion leaders, it could be expected that people tend to believe the opinion leaders more than someone else. Although it does not necessarily matter how many people give the information, if more people give the same information it is more likely that someone accepts this information as the truth.
Opinion Leaders and Social Influence, How are They Affecting the Adoption of New Products? 5 A Simulation Study
The different types of influence can be important in different situations. Visible information about a product can be transferred trough normative influence, while for other information informational influence is more appropriate.
Therefore intangible goods will be more sensitive to informational influence, while highly visible goods are more sensitive for normative influence.
In earlier research some evidence is found that opinion leaders have more informational influence than the people who follow them, although they do not necessarily know more about the products than the others (Van Eck, 2006).
On the other hand, their sensitivity to normative influence is about the same (Van Eck, 2006). This means that opinion leaders are actively spreading information if the have the information. However, the normative influence is as strong as it is for other people in the network!
Strong and Weak Links
People are not equally strongly connected to everyone they are connected with. Granovetter (1973) made a distinction between two types of relations between people:
‘strong ties’ and ‘weak ties’. Strong ties refer to the relation with (for example) friends and family and facilitate social pressure (Goldenberg, Libai and Muller, 2001), which is mostly related with normative influence. Weak ties, representing the relation with (for example) acquaintances and colleagues, are very important for the spread of WOM (Staber, 2004). This is especially because weak links often connect different networks and therefore allow the spread of information from one network to another network.
According to Rogers and Cartano (1962), opinion leaders have many strong ties with people in their environment. Therefore the social pressure within one cluster of the network will be high. However, as mentioned by Granovetter (1973) weak ties are necessary to spread information to other parts of the network.
THE MODEL: TECHNICAL SPECIFICATION The model used in this study is based on a model developed by Delre et al. (2007). Whether an agent adopts the product depends on the utility (Uij) the agent gets from adopting and the utility-threshold (Uij,MIN) of this agent. So the agent will adopt the product if:
MIN ij
ij U
U ≥ ,
In the utility-function a distinction is made between individual preference (yij) and social influence (xij). The importance of these parts of the utility-function is weighted using βij, which results in the following utility-function:
ij ij ij
ij
ij x y
U =β +(1−β )
In the original model the individual preference is based on the product quality (qj) and the quality-threshold ( pij). If the product-quality is higher than the threshold
yij will be 1, otherwise 0. The model is extended by introducing informational influence. The agents does not
believe information about the product quality by definition:
the source has (/ sources have) to be reliable enough.
Therefore the agent has a certain reliability-threshold (rtij) and every agent has a ‘reliability value’ (rij), indicating how reliable this agent is as a source of information about the product quality. The observed reliability (orij) is therefore defined as:
∑=
= A
a aj
ij r
or
1
,
in which A is the number of neighbours that already adopted the product.
The agents only accepts the information about the product quality if orijis higher than rtij. Until this moment the agent will assume the product quality (qj) is 0, therefore resulting in yij =0.
The ‘social pressure’ part of the utility-function is defined as normative influence. This part of the model is also extended, now introducing weak and strong ties. This introduces five new parameters in the model: the percentage of ‘adopting weak-linked neighbours’ (aiij), a threshold with respect to this percentage (iij), the percentage of ‘adopting strong-linked neighbours’ (anij), a threshold with respect to this percentage (nij) and a weight (χij) that indicates which of the ties is most important for the agent.
The total social pressure is therefore defined as:
ij ij ij
ij
ij ai an
xp = χ +(1−χ )
The total threshold with respect to social pressure is:
ij ij ij
ij
ij i n
xt =χ +(1−χ )
With respect to the social pressure in the utility- function the following can be said:
< ⇒
≥ ⇒
= 0
1
ij ij
ij ij
ij xp xt
xt x xp
As a result of these equations, the social pressure (xij) can only be 1 if either enough ‘weak-linked neighbours’ or ‘strong-linked neighbours’ (or both) are connected with the agent.
The Network Structure
The weak/strong ties are randomly distributed in the network, as well as the opinion leaders. Based on the
6 STUDENTS JOURNAL OF MARKETING, AUGUST 2007
literature it is possible to give relatively strict rules about which relation is represented by a weak tie and which is represented by a strong tie. It is also known that the opinion leader often has a central position in the network. However, because of the simple network structures, it is difficult or even impossible to include these rules in the model. The scale-free network is the only network with clear ‘central positions’ (the hubs) and clusters (a hub and its neighbours) that can be linked with a weak tie. The random network does have some agents with more connections than other agents, but the differences between the agents are not great enough to make a clear distinction between ‘central positions’ and other positions in the network.
The opinion leader has a special position in the network: according to earlier research this agent has more informational influence than the other agents. In the model the opinion leader has three important characteristics that make this informational influence possible: it is the only agent that can spread information without adopting the product, the agents is more open to information (the threshold for reliability is 50% of that of a normal agent) and the opinion leader is by definition observed as reliable (rij =1).
THE RESULTS
‘The First Experiment’: The S-Curve
For all the parameter setting see also Appendix 1.
One of the graphs show in Delre et al. (2007) is an S- curve, produced using the model with specific settings. A replication of this experiment proved to be very difficult.
The first problem is the large number of agents that was used in the original study: 3000. The model used in this study couldn’t initialise a network with so many agents in a reasonable time. In the end only 150 agents were used in the analysis. This also resulted in another problem: in the simulation study by Delre et al. (2007) 0.1% of the agents are informed about the product in the initialisation phase, which results in (on average) 3 informed agents. Since only 150 agents are used this would mean that in most situations nobody will be informed about the product, therefore leading to no market penetration at all! The experiment therefore had to be adjusted on this point: 1 agents is randomly selected as an adopter of the product (0.7% of the population). A final difference can be found in the network structure. Delre et al. (2007) used a small-network and added random links, while in the network used in this study some links are changed randomly. However, both networks should have the same properties (Newman, 2002; Newman and Watts, 1999).
As an social threshold (xtij) Delre et al (2007) use 0.3, which means that at least 30% of the neighbour agents have to adopt the product before an agents feels any social pressure. They describe that this threshold can differ between 0.2 and 0.4. The threshold used in this experiment is 0.2, because higher settings do not lead to high market penetrations. On average all agents have four links, which means that only one neighbour adopting the product already results in social pressure.
The weight between social influence and personal preference (βij) can also vary, in this case between 0.75 and 0.9. In this experiment this weight is 0.85, which means
that 85% of the total utility (Uij) is based on social influence, while only 15% is based on personal preference.
Therefore someone with an utility-threshold (Uij,MIN) lower than 0.85 can adopt a product based on social influence, without liking the product.
These settings ultimately lead to an S-curve as shown in figure 3. It is not surprising that the model reaches a steady state in only 25 steps (in comparison with about 150 steps in Delre et al., 2007), because of the smaller number of agents.
Figure 3 S-CURVE SETTING 1
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
1 5 9 13 17 21 25 29 33 37 41 45 49
time
market penetration
Setting1
For this experiment three different ‘settings’ are used:
- Setting 1 refers to the ‘original model’: no opinion leaders, no ‘reliability factor’ and no difference between weak and strong links.
- Setting 2 introduces the ‘reliability factor’ and therefore makes the information-stream in the network more uncertain (not every agent immediately believes information about the product from a neighbour agent).
- Setting 3 includes opinion leaders, with the earlier mentioned characteristics.
- Setting 4 includes both opinion leaders and the
‘reliability factor’
- Setting 5 includes a distinction between strong and weak links (5% of the links are weak links).
This does not include opinion leaders or the
‘reliability factor’
The resulting S-curves are shown in figure 4: most settings produce very similar results. However this is not really surprising, because most adjustments of the model are strongly related to the personal preference (informational influence) side of the model. For example, opinion leaders are strong in spreading information, but they act as every other agent with respect to social influence. In the current settings the model especially focuses on the social pressure (normative influence): 85%
of the utility of an agent is based on social influence!
Only setting 5 (strong and weak links) has influence on the ‘social influence’ as it is described in the model, which immediately results in a lower market penetration.
That this is not a surprising result can be demonstrated with the following example:
Opinion Leaders and Social Influence, How are They Affecting the Adoption of New Products? 7 A Simulation Study
The threshold for both weak links (aiij) and strong links (anij) is 0.2 (which is equal to the social threshold
xtij in setting 1). Consider the weight of weak links (χij)
is 0.5, which means that both types of links have the same importance for the agent. This results in a total-threshold of social influence of (xtij = 0.5 x 0.2 + 0.5 x 0.2 =) 0.2, which is the same as for setting 1. Furthermore the agent has 5 neighbours: the agent is connected strongly with 4 neighbours and weakly with 1 neighbour. One strong- linked neighbour has adopted the product. The strong-link ratio (nij) is therefore 0.25 and the weak-link ratio (iij) 0.
The total social pressure (xpij) is therefore (0.5 x 0.25 + 0.5 x 0 =) 0.125. The agent does not adopt, because the social threshold is higher than the social pressure! In setting 1 the pressure would have been 0.2 (1/5), which would have lead to an adoption. Agents with multiple types of links therefore can stop the diffusion from continuing.
To investigate the influence of the other settings in more detail the experiment is repeated, now using a scale- free network. All setting are the same, except for the fact that 100 runs are used for every setting instead of 20 (the diffusion in a scale-free network is much more dependent on who is the first adopter and therefore is more unstable) and only 15 time-steps are used (the model reaches a steady state earlier).
Also with respect to opinion leaders a change has been made: in the former part of the experiment 30% of the agents are randomly assigned as opinion leaders. In the scale-free network the opinion leaders are ‘fixed’ on ‘hub positions’, because literature shows that opinion leaders
have a central position in the network (Berelson and Steiner, 1964; Valente, 1996; Czepiel, 1974) and in a scale- free network it is easy to make a distinction between a central position and another position in the network. In this part of the experiment setting 3 and setting 4 as described above are therefore referred to as ‘Setting 3 fixed’ and
‘Setting 4 fixed’.
As can be seen in figure 5, all setting result in a very low market penetration. Given the fact that the model with the current settings still focuses on social pressure, this is not surprising. For all hubs in the scale-free network the threshold for social pressure (0.2) is very high, because they have many links. If hubs do not adopt the product, there is almost no diffusion at all. However, there are differences between the different settings. Compared with Setting 1, introducing the ‘reliability factor’ actually makes it even more difficult for the information to spread. Even if a neighbour adopts the product, there still is a chance that the agent does not believe information about the product quality.
Opinion leaders on the other hand cancel out this effect duo to their characteristics (high reliability and being capable of spreading information without adopting the product). This makes the market penetration slightly higher than in Setting 1.
The Second Experiment ‘Seeding the Product’ (Throwing Gravel)
Delre et al. (2007) do another experiment, in which a certain percentage of the agents adopts the product in the first step of the simulation. As in the experiment above, only 150 agents are used in the simulation. The other Figure 4
S-CURVE SETTING 1, 2, 3, 4 AND 5 (RANDOM NETWORK)
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52
time
market penetration
Setting1 Setting2 Setting3 Setting4 Setting5
8 STUDENTS JOURNAL OF MARKETING, AUGUST 2007
settings are the same as in Delre et al. (2007): the weight for social influence (βij) is 0.9 and the threshold for social influence (xtij) is 0.35. The experiment is done using Settings 1-5 for 1%, 5%, 10% and 15% adopters in the first step. Surprisingly this experiment has different results than in Delre et al. (2007) (considering setting 1). Delre et al.
(2007) found about 90% market penetration for the 15%
setting, while in this study only about 70% market penetration is found. This difference is possibly caused by the number of agents used or the difference in network structure.
When we compare the results of the other settings, we can see that some difference do exist between the settings (see figure 6).
When only 1 percent of the agents adopts the product in the first step, not much differences occur. An one-way ANOVA test shows that the differences between those results are indeed not significant (F = 0.207; p-value >
0.05). This is not surprising, because on average 1.5 agents will adopt the product. With a social threshold of 0.35 the chance is very small that enough agents adopt the product to increase the social pressure, no matter what setting is used: the social pressure not to adopt is just to high in all cases.
If 5 percent of the agents adopt there are still not many differences. There is no significant difference between the settings (F = 2.445; p-value > 0.05). Though, setting 5 results in a lower penetration, which (again) indicates that the combination of strong and weak links makes it more difficult to reach a high market penetration.
For the ’10 percent’ results, this effect of strong and weak links diminishes. A possible explanation is that the
chance is now higher that an agent with both types of connections adopts the product in the first step. The product spreads more easily through the weak links, because the weak-link ratio (iij) is almost always 1 if one of the two agents connected with this link has adopted the product (since only 5% of the links are weak links not many agents will have two weak links). This cancels out the negative influence of this weak link as described in the former experiment. The differences for the ’10 percent’ results appear to be significant (F = 2.621; p-value < 0.05).
An LSD test is done to find out which settings differ significantly (the variance is homogeneous at a 5%
significance level). This test shows that (at a 5%
significance level) Setting 2 differs significantly from Setting 1 and Setting 3. The ‘reliability factor’ makes it difficult for the product to spread in comparison with the original model (Setting 1) and with the model including opinion leaders. This can be explained by the information stream in the network: the ‘reliability factor’ makes it more difficult for information to spread (agents don’t believe each other by definition), while opinion leaders support a better information stream (spreading information, even without adopting the product). Apparently product information can still be important under certain conditions, even if the social pressure is the main driver for the spread of a product!
If 15% of the agents adopt the product, the market penetration does not differ significantly between the different settings (F = 1.493; p-value > 0.05). In this case to many agents already adopted the product to see any difference in how many agents will ultimately adopt the product: agents will adopt the product one way or another.
Figure 5
S-CURVE SETTING 1, 2, 3, 4 AND 5 (SCALE-FREE)
0 0,005 0,01 0,015 0,02 0,025 0,03 0,035 0,04 0,045 0,05
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Setting1 Setting2 Setting3Fixed Setting4Fixed
Opinion Leaders and Social Influence, How are They Affecting the Adoption of New Products? 9 A Simulation Study
CONCLUSION
It is difficult to interpret the results straightforward: it proved to be impossible to replicate the results from the earlier research by Delre et al. (2007). However, keeping this uncertainty in mind, some conclusions can be drawn.
With respect to the first experiment, it is clear that strong links and weak links can have a huge impact on the final market penetration of the product. Including these links can therefore change the results of the model and that makes clear that if people don’t evaluate the social pressure of all the people they know as equally heavy, the inclusion of different types of links is essential for the model.
Furthermore the role of opinion leaders can be important if the network structure is scale-free (which is the case with for example the internet). In a random network without clear centre positions the role of the opinion leader might be far less important according to the results of this study.
The role of the ‘reliability factor’ can also be observed strongest in the scale-free network, because in this type of network it is easier a single agent to blocks further diffusion. In a random network information spreads so easily that uncertainty with respect to this information is almost doesn’t exist.
The second experiment shows that even in a random network there are conditions in which the role of opinion leaders is quite important, especially if the information- stream has influence on the ultimate market penetration of the product.
DISCUSSION
Although this study already present some interest results, a lot of research is still needed. In the first place it is very important to use empirical data to determine which values the parameters actually should have. The percentage of weak links and the percentage of opinion leaders can strongly influence the results of the simulation, but there is not enough literature that indicates which values these parameters should have. The role of opinion leaders should also be studied in more detail. In this study the role of the opinion leader is mainly based on informational influence (spreading information), while this type of agent might also have a strong influence on the social pressure in the group.
Furthermore the threshold of the agents should be based on empirical data, as well as the possible relation between different thresholds (especially the relation between the threshold for strong links and the threshold for weak links).
Without empirical data it will be impossible to build a realistic simulation that comes closer to representing the
‘real world’.
The process described in the current model with the
‘reliability factor’ must also be investigated in more detail.
The role of ‘reliability’ and the position of the opinion leader in this process has not been investigated. Perhaps it is better to use Elaboration Likelihood Models (Petty and Cacioppo, 1986) and/or Social Judgement Theory (Sherif and Hovland, 1961) to model this process in more detail.
The structure of the network should also be investigated in more detail: the study already shows that there are great differences between random networks and scale-free networks. The scale-free network is very interest Figure 6
RESULTS OF THROWING GRAVEL
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
1 percent 5 percent 10 percent 15 percent
percentage of seeds
Setting1 Setting2 Setting3 Setting4 Setting5
10 STUDENTS JOURNAL OF MARKETING, AUGUST 2007
to investigate in more detail, because it seems to be much more difficult to randomly spread information in this kind of network! Perhaps it is even possible to combine the different types of networks. Another option is to use a real- world network (based on empirical research) and use this structure to run the simulation. These results could than be compared with experiments from the empirical study.
APPENDIX 1: PARAMETER SETTINGS
Name Parameter Values Assumption
Simulation runs
20 (SW);
100 (SF)
SW: same as Delre et al. (2007)
SF: much more unstable results, therefore more runs are needed to come to more stable results Time steps of
simulation runs
50 (SW);
15 (SF)
Steady state is reached within this period
Number of
agents N 150
Rewiring
probability 0.01 Same as Delre et al.
(2007) Minimum level
of satisfaction Uij,MIN Uniform distribution [0, 1]
Same as Delre et al.
(2007) Personal
preference pij Uniform distribution [0, 1]
Same as Delre et al.
(2007)
Quality of
product qj 0.5
Chance that someone likes the product is 50% (Delre et al., 2007)
Social thresholds
xtij,
iij,nij
Normal distribution around value mentioned in text (SD
= 0.01)
Same as Delre et al.
(2007)
Reliability
(threshold) rtij,rij Uniform distribution [0, 1]
Weight of
social influence βij
Normal distribution around value mentioned in text (SD
= 0.01)
Same as Delre et al.
(2007)
Weight of
weak links χij Uniform distribution [0, 1]
Weak-links
percentage 0.05
Percentage of
opinion leaders 0.30
In line with Katz and Lazarsfeld (1965:
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