The diffusion of innovations is an important topic for the consumer markets.
Early research focused on how innovations spread on the level of the whole
society. To get closer to the real world scenarios agent based models (ABM)
started focusing on individual-level agents. In our work we will translate an
existing ABM that investigates the role of opinion leaders in the process of
diffusion of innovations to a new, more expressive platform designed for agent
based modeling, GAMA. We will do it to show that taking advantage of new
features of the chosen platform should be encouraged when making models in the
field of social sciences in the future, because it can be beneficial for the
explanatory power of simulation results.
In our work we will translate an existing ABM that investigates the role of opinion leaders in the process of diffusion of innovations to a new, more expressive platform designed for agent based modeling.
We will do it to show that taking advantage of new features of the chosen platform should be encouraged when making models in the ﬁeld of social sciences in the future, because it can be beneﬁcial for the explanatory power of simulation results.
1 Introduction Diffusion refers to the process by which an innovation is adopted over time by members of a social system.
An innovation commonly refers to a new technology, but it can be understood more broadly as a spread of ideas and practices [Kiesling et al., 2012].
イノベーションは一般的には新しい技術を指すが、アイデアやプラクティスの拡散(kiesling et al., 2012)としてより広く理解することができる。
The question whether a certain innovation will diffuse in society successfully or not has always been of important nature at the market level and has gained interest of many researchers since a number of pioneering works appeared in the 1960s.
From the marketing perspective, it is of great importance to understand how information starting from mass media and traveling through word-of-mouth WoM affects adoption decisions of customers and consequently the diffusion of a new product [van Eck et al., 2011].
マーケティングの観点からは、マスメディアから始まり、口コミWoMを介して移動する情報が顧客の採用決定にどのように影響するかを理解することが非常に重要であり、その結果、新製品の拡散[van Eck et al., 2011]。
Mass media takes the role of an external inﬂuence to a society and WoM the role of an internal inﬂuence within the society.
Traditionally, models were based on macro level looking at the society as a whole.
Most such aggregate models stem from the model introduced by Bass , which takes the structure of a basic epidemic model where diffusion of innovation is seen as a contagious process driven by external and internal inﬂuences.
A study by van Eck  (further use: reference study) was picked as it not only models the diffusion of innovations, but additionally investigates the role of opinion leaders in the process, which is another interesting phenomenon.
van Eck氏(2011年)による研究(Further use:参照研究)は、イノベーションの拡散をモデル化するだけでなく、プロセスにおける意見リーダーの役割も調査するため、別の興味深い現象である。
Aside from agents being heterogeneous, they are further divided into two groups, namely the inﬂuentials or opinion leaders (OL) and followers or non-leaders (NL).
Goldenberg et al  determine inﬂuentials by three factors: connectivity, knowledge and personality characteristics.
Goldenberg et al は、コネクティビティ、ナレッジ、パーソナリティの3つの要素で影響力を判断します。
Opinion leaders are a type of inﬂuential customers that have all of the characteristics of the inﬂuentials represented as central positions in the network (which means high connectivity), market knowledge (not necessarily about a speciﬁc product but about markets in general) and innovative behaviour.
The reference study uses four critical assumptions about opinion leaders, which are later successfully checked by an empirical study: (1) OL have more contacts, (2) OL possess different characteristics, (3) OL exert different types of inﬂuence and (4) OL are among earlier adopters.
Two important characteristics of opinion leaders are their innovativeness and their interpersonal inﬂuence.
Regarding the degree of innovativeness, it means that opinion leaders have more experience and expertise with the product category than the other consumers and that they have been exposed to more information [Lyons and Henderson, 2005].
革新性の程度については、オピニオンリーダーが他の消費者よりも製品カテゴリに関する経験と専門知識を持ち、より多くの情報にさらされていることを意味します[Lyons and Henderson, 2005]。
Two main types of interpersonal inﬂuence exist:
• Informational inﬂuence is the tendency to accept information from others and believe it.
Opinion leaders inﬂuence other consumers by giving them advice about a product.
• Normative inﬂuence stems from the people’s tendency to follow a certain norm; to adopt a product in order to be approved by other consumers.
The focus of this study is to investigate the speed of information diffusion, the speed of product diffusion, and the maximum adoption percentage of the product.
The article is structured as follows: in Section 2 we describe the hypotheses that the reference study has set up and veriﬁed; Section 3 introduces the model with its agents, parameters, and social network; in Section 4 we present the experiments settings and discuss our simulation results; and in Section 5 we address the conclusions and suggestions for further work.
2 Hypotheses While investigating the role of opinion leaders in the innovation diffusion process, the impact of each of its three characteristics (innovative behaviour, normative inﬂuence, market knowledge) is looked at and thus more hypotheses are set up.
H3b: judging product quality, which results in a higher speed of product diffusion.”
”Opinion leaders are better at
3 Model In this chapter we describe in more detail how our model was built.
3 モデル この章では、モデルがどのように構築されたのかを詳しく説明します。
3.1 Network Bohlman et al.
3.1 Network Bohlman et al
 indicate that speciﬁc network topologies in agent based modeling strongly inﬂuence the process of innovation diffusion: they affect the likelihood that diffusion spreads and the speed of adoption.
many empirical researches and is conﬁrmed to imitate real world societies where some agents serve as hubs, meaning their number of connections greatly exceeds the average and they have central positions in the network.
The utility function consists of a weighted sum of the individual preference and the social inﬂuence.
First represents informational inﬂuence and describes the agent’s opinion on the product quality, and second represents normative inﬂuence and takes into account the number of neighbouring agents that have already adopted the product.
On the contrary, high weight value means that the agent is very socially susceptible [van Eck et al., 2011].
逆に、高い重み付けは、エージェントが非常に社会的に感受性が高いことを意味する[van Eck et al., 2011]。
3.3 Parameters The model contains several parameters, which describe the inﬂuence of opinion leaders in various market settings [van Eck et al., 2011].
3.3パラメータ モデルは、様々な市場設定における意見リーダーの影響を説明するいくつかのパラメータを含む[van Eck et al., 2011]。
Some parameters are ﬁxed for all experiments and others vary experimentally.
The group of ﬁxed parameters and their values, derived from the model by Delre et al.
, are presented in Table 1.
The product quality is set to 0.5, meaning that if the agents base their decisions
Variable Product quality Mass media coefﬁcient Number of agents
可変製品品質 マスメディア係数 エージェントの数。
Parameter q m m
パラメータ q メム
nb agents Value 0.5 0.01 500
Table 1: Settings for global parameters, that were ﬁxed in current experiments
Variable Max utility threshold of OL Average normative inﬂuence, OL Standard deviation for normative inﬂuence, OL Average normative inﬂuence, NL Standard deviation for normative inﬂuence, NL OL judges product better
one percent of population is reached in each step).
The varied parameters are changed one at a time per experiment to test the separate hypotheses.
The parameters and their values, derived from empirical study conducted by reference study are presented in Table 2.
First a base experiment with these values was run so that later hypotheses could be tested realistically.
The innovativeness of opinion leaders is implemented as smaller possible values of it’s utility threshold with regard to that of the followers (the utility threshold of the followers has a uniform distribution in the range U(0, 1.0), for OL it’s in the range U(0, 0.8)), which makes them approximately 20% more likely to adopt the product.
意見リーダーの革新性は、フォロワーのそれに対する実用しきい値の可能な値(フォロワーの実用しきい値がu(0, 1.0)の範囲で均一に分布している、ol it's in the range u(0, 0.8))よりも小さく実装されているため、製品を採用する確率はおよそ20%高い。
The difference is not big as OL are trying to avoid being too innovative, because if they adopted a product that turned out to be unsuccessful, they would loose followers.
As observed in the empirical study, the weight of normative inﬂuence of opinion leaders holds a lower value (βOL = 0.51) than that of the followers (βN L = 0.6) as they care less about the social pressure.
実証研究で観察されたように、世論指導者の規範的影響の重みは、社会的圧力をあまり気にせず、従者(βn l = 0.6)よりも低い(βol = 0.51)。
The weights of normative and informative inﬂuences sum up to 1, so the weight of informative inﬂuence is 1 - β.
規範的および情報的影響の重みは 1 にまとめられるので、情報的影響の重みは 1 - β となる。
The model can be run either with opinion leaders in the network or without them.
This was important to be able to see whether the diffusion of the innovation indeed spreads faster in the networks where innovative opinion leaders are present.
4.1 Experiment settings A model was created for each separate hypothesis.
4.1 実験設定 各仮説毎にモデルを作成する。
The values of the varied parameters used for each model are shown in Table 3.
Each model was run in a separate experiment that consisted of 25 time steps, which was enough for the maximum adoption percentage to be reached.
To collect results for statistics each experiment was run with the same settings 60 times.
We realize that 60 is a low number of repetitions for completely adequate statistics, but we faced a problem of the GAMA platform freezing due to too big memory consumption while trying to run it in batch mode, where more than one experiment is run one after another automatically.
Thus, we were reduced to having to run each experiment manually which proved to be quite time consuming so we limited the number of runs to 60 and might do more tests to calibrate the results if needed in the future.
Each time step further consisted of three phases: mass media, WoM and adoption.
In the beginning of the experiment no agents are aware of the product or have adopted it.
Then mass media informs a predeﬁned percentage (in our case 1%) of the population about it.
In this step, the better market knowledge of the opinion leaders is implemented as such: because opinion leaders are able to make good product judgment they will have learned of a real product quality from mass media and their quality judgment will become equal to it (q = 0.5, Table 1).
It claims that in networks that include opinion leaders, higher speed of both the information and product diffusion as well as greater adoption percentage are achieved, than in the networks without them.
The same case happens for the speed of product diffusion, in the model with OL it takes 2.80 steps compared to 5.78 steps in the model without the OL, which means that the product diffuses faster in the model with OL.
Table 4 shows the obtained averaged results from the reference study and from our model for each of the hypotheses models.
Each hypothesis was run in a different experiment on it’s own model, for which the values are presented in the Table 3, except for the hypothesis H2a which the reference study validated by empirical study.
When comparing the results we can see that even though values are a bit different, their proportions stay the same, meaning that our model was successfully validated against the reference NetLogo model and as such that the same as in the NetLogo model the hypotheses Ha1, H2a (empirical study), H2b, H2c, H3a and H3b got supported while the hypothesis H1b did not get supported.
4.3 Comparing the platforms The differences might be partially attributed to the smaller sample sizes that we use to average the results, but we think they’re mostly the reason of a different execution ﬂow in the GAMA platform.
It is here that GAMA platform introduces a difference that we ﬁnd important when making social models.
The execution ﬂow of NetLogo for the model of diffusion of innovation is sequential and iterative.
For each of the 25 steps of the simulation the three stages (mass-media, word of mouth, adoption) are executed one after another, where ﬁrst one has to complete for all of the agents before the next stage can commence.
During the simulation of the 25 steps, the only role of the world agent that stands above all other agents (on GAMA platform the world agent acts similar than a main function in many programming languages) is to schedule them, i.e.
During the WoM stage agents will be called upon iteratively and each of them will have larger probability that some of its previously non-aware neighbours have now become aware and can thus share their knowledge about the product.
These agents are called belief, desire and intention (BDI) agents.
The model allows to use more complex and descriptive agent models to represent humans.
It attempts to capture common understanding of how humans reason through: beliefs which represent the individual’s knowledge about the environment and about their own internal state; desires or more speciﬁcally goals (non-conﬂicting desires which the individual has decided they want to achieve); and intentions which are the set of plans or sequence of actions which the individual intends to follow in order to achieve their goals [Adam and Gaudou, 2016].
個人の環境と自己の内的状態に関する知識を表す信念、願望またはより具体的には目標(個人が達成したいと決めた非紛争的願望)、目標を達成するために個人が従おうとする一連の行動のセットである意図(Adam and Gaudou, 2016)。 訳抜け防止モード: 人間の理屈の共通理解を捉えようとする試み : 環境に関する個人の知識を表す信念 そして、彼ら自身の内部状態について;願望またはより具体的には目標(個人が達成したいと決めた非矛盾する欲求) 個人が意図する行動の計画や順序の集合である意図 to follow 目標を達成するために [Adam と Gaudou, 2016 ].
Two other important functionalities a BDI system must have are a rational process by which an agent decides which intentions to follow depending on the current circumstances, and the level of commitment to the set of intentions to achieve a long-term goal.
We will then add different human factors to these agents and observe how they affect the spread of the diffusion of an innovation and it’s speed and whether the results will stay in line with the original model.