How can we predict the performance of small firms online advertising? An agent-based modelling & simulation approach

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26th Annual SEAANZ Conference 2013

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Small Enterprise Association of Australia and New Zealand

26

th

Annual SEAANZ Conference Proceedings

11-12 Sydney 2013

How can we predict the performance of small

firms’ online advertising? An agent-based

modelling & simulation approach

Jaehu Shimᵃ and Martin Bliemelᵇ

ᵃAustralian Centre for Entrepreneurship Research, Queensland University of Technology, contact: Email: [email protected] ; ᵇSchool of Management, University of New South Wales, contact: Email: [email protected]

Abstract:

Online marketing is becoming essential for a small firm’s survival and growth. Despite the ubiquity of online advertising campaigns, it is hard to predict or estimate the performance of such campaigns. The purpose of this study is to unveil the hidden processes that underlie the performance of online marketing. We do this by using agent-based modelling & simulation (ABMS) built on the Bass model of innovation diffusion. Methodologically, ABMS have a high degree of realism because they can account for heterogeneous activities and attributes of individuals. In our ABMS, we build plausible micro-level processes regarding online marketing at the individual level, which then aggregate to generate macro-level phenomenon of the innovation diffusion. We extend existing ABMS research in this area in two ways. Firstly, our model includes a scale-free network topology, and secondly, we incorporate the possibility of negative word of mouth. Our model can be used to forecast the performance of small firms’ online marketing.

Keywords: online marketing, online advertising, agent-based modelling & simulation, Bass model, innovation diffusion, scale-free network, word-of-mouth

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.

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Introduction

Marketing is important for a firm’s survival and growth. Specifically for small firms, online marketing is an attractive alternative to mass media campaigns, because they can be run more cost-effectively with a relatively small budget, and targeted more specifically based on user profile data. In practice, most small firm owners consider the Internet as an advertising space for their products and services, and make every effort to effectively promote their goods online. Despite the ubiquity of online marketing campaigns, it is hard for practitioners in small firms to predict or even estimate the performance of such campaigns. Meanwhile, the literature includes hundreds of studies about online marketing over the past 20 years (e.g., Corley, Jourdan & Ingram, 2013), and yet our knowledge of the processes and effectiveness of small firm’s online marketing remains limited. The purpose of this study is to unveil the hidden processes that underlie the performance of small firms’ online marketing. We do this by using agent-based modelling & simulation of the diffusion of innovation, which is defined as the spread of a new product, a new process, or a new technology through society (Bass, 1969; Rogers, 2003; Laciana, Revere & Podesta, 2013). Our model is built on the Bass model of innovation diffusion, which is widely used and thoroughly researched (see Keisling, 2012 for a comprehensive review). The elegance of the Bass model is its ability to describe an ‘S-curve’ of cumulative adoption within a population using only two parameters (p and q), where

p is the coefficient of consumers’ adoption due to mass media (innovation parameter), and q is the adoption coefficient due to other adopters’ word-of-mouth (imitation parameter).

Methodologically, ABMS have a high degree of realism when applied to the diffusion of innovation because they can account for heterogeneous activities and attributes of individuals (Dooley, 2002). In our agent-based model, we build plausible micro-level processes regarding online marketing at the level of the individual, which then aggregate to generate macro-level phenomenon of the diffusions of innovations. We extend existing ABMS research in this area, by incorporating two often omitted aspects in ABMS and marketing. Firstly, our model includes a scale-free online network topology like Facebook, and we incorporate the possibility of negative word of mouth based on missed expectations upon adopting a product or service.

Each agent’s behavioural rules are derived from the literature and heuristic knowledge of practitioners. These rules are then programmed into the agent-based simulation program, NetLogo1. We then run 640 separate simulations with this agent-based model. And perform sensitivity analysis on their results to. Our analysis is consistent with the Bass model, in that advertising activities by firms are essential to spread their goods at the introductory stage, but that consumers’ opinions are becoming increasingly important at the maturity stage. Our results reveal situations in which consumers’ negative opinions can prevent widespread diffusion of a firm’s product despite the firm’s continuous advertising efforts.

With this agent-based simulation approach, we can generate and compare multiple plausible future scenarios of small firm’ online marketing. Our agent-based online marketing simulations show that it is hard to persuade every potential customer online, but that it is possible provided that the products generate positive customer reviews and thus also positive word of mouth.

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Literature Review

Hundreds of studies on online marketing have been conducted. For example, in their review, Corley, Jourdan and Ingram (2013) identified and summarized 433 articles related to online marketing over 18 years (1994 – 2011) published in major journals. They found the most popular research topic within these studies was ‘the business model of online marketing’ (169 articles, 41%), followed by ‘Internet advertising’ (92 articles, 22%).

Despite the impressive number of studies about online advertising, Corely et al. (ibid.) argue these studies’ degree of realism remains lower than the practitioners’ expectation. As a result of this unsatisfactory realism, the practitioners of online advertising maintain little interest in these studies. To provide meaningful implications not only for the scholars but also for the practitioners, future studies would surely benefit from grounding their theoretical models with empirical data, and from applying their methodologies with the complexities of social reality in mind.

The Bass model (Bass, 1969) is a theoretical model of innovation diffusion, which has been widely used, thoroughly researched, and verified in empirical settings. While the model has high descriptive accuracy at the macro-level, further research is required to link it back to micro-level behaviour. For instance, if a small firm’s brand and product is new to a set of consumers, then the adoption of their product (writ large) must be based on each individual’s decision to adopt the innovation. As a research methodology to link the micro- and macro-levels, we utilize ABMS, which has been suggested as a methodology that can raise the degree of realism because ABMS’s can express heterogeneous activities and attributes of individuals (Dooley, 2002), especially when these activities and attributes are based on field data (Corley, Jourdan and Ingram, 2013).

Bass model of diffusion

Diffusion of innovation is defined as “the process by which an innovation, that is new idea, is communicated through certain channels over time among the members of a social system” (Rogers, 2003), or as “the spread of a new product, a new process, or a new technology” (Laciana, Revere & Podesta, 2013). The Bass model builds on Rogers’ 1962 version of this work, and describes the diffusion of innovations as a contagious process in which people’s decision to adopt is a function of how many others have adopted the innovation, and a function of exposure to advertising. The process is triggered by a small proportion of the population, called innovators (Rogers, 2003), who “decide to adopt an innovation independently of the decisions of other individuals in a social system” (Bass, 1969, p. 216). The model dual mechanism of adoption in response to (i) external influences such as advertising, and (ii) in response to inter-personal influences such as word-of-mouth is credited with successfully explaining the macro-level diffusion dynamics of a wide spectrum of products (Bass, 1969; Firth, Lawrence, & Clouse, 2006; Lim, Choi, & Park, 2003; Naseri & Elliott, 2013; Sultan, Farley, & Lehmann, 1990; Wong, Yap, Turner, & Rexha, 2011).

The elegance of the Bass model is that it is based on only two macro-level parameters, p and q. The parameter p reflects people’s intrinsic tendency to adopt an innovation, and the parameter q

reflects imitation or social contagion due to word-of-mouth. These two parameters respectively capture two extreme types of adopters within a wide spectrum of adopters: innovators and imitators. The innovators accept a new product or technology because they perceive it has

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comparative advantages or a positive difference in utility. The innovators’ decision to adopt is a function of influences that are external to the social structure (e.g., advertising). In contrast, the imitators’ decision to adopt is a function of their interactions with others in the social system who have previously adopted the innovation. The Bass model can be represented by the following equation that expresses the rate of adoption at a given point in time as a function of p, q, and the cumulative adopters, n+:

(

)(

)

In the model, each consumer has one of two possible states: + or −. A consumer is in state + if she already has adopted the innovation; −, if not. In the left hand of the equation, the temporal derivative of n+ is the rate of new adopters at the time t. Parameters p and q can be estimated from actual or simulated adoption data. For a wide range of p and q values, the number of cumulative adopters as a function of time results in an S-shaped pattern as shown in Figure 1. Key measures of adoption dates in this model are the time at which the noncumulative new adoption is maximal (t*), and the time at which the rate of adoption is maximal (t**). The latter is also referred to as the ‘take-off time’ at which the product is starting to spread.

Figure 1. Bass (1969) diffusion model for noncumulative adoptions and for cumulative adoptions

Despite the popularity of the Bass model, it has largely remained limited to observations of macro-level patterns of diffusion, from which it is difficult to draw out implications for managers. For the model to work as described above, it needs to start with a small proportion of ‘innovators’ who have already adopted the innovation, and how these innovators first became aware of the innovation is secondary to how they subsequently influence the other adopters. As discussed in the following sections, our use of ABMS unpacks the question of initial adoption by innovators by accounting for their exposure to online advertising. Thus, in order to better understand how to effectively manage

Time Time t* t** Cumulative Adopters, n+ Non-Cumulative Adopters, dn+/dt

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the diffusion process, including marketing campaigns, we need to take a closer look at the micro-level activities which shape the macro-micro-level diffusion patterns.

Agent-based modelling & simulation

Agent-based modelling and simulation has been recommended as a third research methodology for the purpose of supplementing quantitative and qualitative methodologies (Axelrod & Tesfatsion, 2006), and as a means to connect heterogeneous micro-level behaviour to the emergence of macro-level patterns and order. It has been suggested as a complementary method to analytical modelling, empirical modelling, consumer behaviour experiments, and system dynamics modelling (Rand & Rust, 2011). Agent-based models are designed to imitate the actual activities of individual humans and their interactions on the basis of their complex and high-level cognitive information-processing capabilities and intrinsic temperament (North & Macal, 2007). This imitation is based on explicitly defining behavioural rules and attributes for each agent in the model, and may include statistical variation of actors’ attributes (i.e., heterogeneous actors) and thus also variation of when any given rule applies.

Simulations are virtual environments in which to model actual systems, processes and events. They are generally performed by computer programs for studying individual-level theories of behaviour (Davis et al., 2007). The benefit of simulations (versus field research) is that provide researchers with the ability to control all the variables of a model and efficiently perform large numbers of repetitive tests (Anderson, 1999; Dooley & Van de Ven, 1999). Through what-if analyses similar to thought experiments, researchers can simulate plausible scenarios by examining how variables change and what effect their change has on conclusions (Harrison et al., 2007).

In addition to this efficiency, a positive by-product of ABMS is better communication, enhanced clarity, and detailed description of relevant actors and concepts in a system. This benefit is attained by the requisite explicitness of the modelling assumptions and behavioural rules, which also allows for comparability of multiple models. Each explicitly defined attribute and rule in the model may be subjected to face validity testing. Therefore, in their aggregated form, the entire simulation may be scrutinized for face validity. In addition to this face validity, external validity may be attained by comparing the input parameters and results of simulation to empirical studies (Crawford, 2009).

Agent-based approaches on diffusion of innovations

Mathematical approaches to the diffusion of innovations have been studied since the 1960s. Recently, the agent-based approach is increasingly applied to this area, because this approach can effectively capture complex phenomena related to the diffusion of innovations. In their comprehensive review of the literature on the ABMS of innovation diffusion, Kiesling et al. (2012), are optimistic that ABMS are increasingly not only useful “to guide intuition and facilitate theory-building, but also as a decision support tool that provides managerial insights and policy recommendations not easily available with more traditional modelling techniques” (p. 222). Interestingly, among the 29 agent-based innovation diffusion models they reviewed, most models assumed lattice or small-world networks as the interaction topology, and thus have lower validity because these network topologies do not reflect the scale-free structure of virtually all social networks (Barabasi, 2002) including facebook (Ugander, 2011). The omission of scale-free network

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topologies persists in more recent ABMS of innovation diffusion (e.g., Laciana, Revere & Podesta, 2013).

Agent-based model of online marketing

Our ABMS of innovation diffusion extends prior research in three important ways: (i) we assume a scale-free network topology, (ii) we link people’s intrinsic tendency to adopt an innovation to their exposure to online advertisements, and (iii) we account for negative reviews post-adoption, which may slow down subsequent diffusion via word-of-mouth, depending on how connected each individual is. In the following subsections, we describe our agent-based model of innovation diffusion complying with the ODD protocol. The ODD protocol was proposed for a rigorous representation of an agent-based model, this protocol consists of three blocks (Overview, Design concepts, and Details) which are subdivided into seven elements (Grimm et al., 2006; Grimm et al., 2010).

Overview: Purpose

The purpose of our agent-based model is twofold. First, we aim to verify whether the micro-level online activities of firms and consumers (e.g., advertising, word-of-mouth) can reproduce macro-level S-curved pattern of innovation diffusion. Second, we identify the degree to which each factor in the model affects consumers’ adoption of a new product.

Overview: Entities, state variables, and scales

In our agent-based model, the only entity is the consumer. Every consumer has four state variables (aka attributes): ‘status’, ‘my-criterion-of-impressions’, ‘current-impressions’, and ‘ my-weight-of-network’. The ‘status’ variable indicates whether a consumer has adopted a new product (an innovation) or not, and also whether the consumer formed a positive or negative opinion about the product upon adoption. Each consumer has a value of ‘my-criterion-of-impressions’ which is a threshold level of how many advertising impressions it will take for them to become more likely to adopt the innovation. This value is normally distributed across the population to reflect Rogers’ (2003) distributions. Each consumer’s cumulative impressions of the advertisements is recorded into each consumer’s ‘current-impressions’ variable. The relative impact of a consumer’s network in the adoption decision is described by the ‘my-weight-of-network’ variable, which is measured by the degree to which the consumer is linked within the network.

Each model also includes two input parameters reflect the consumer’s susceptibility to be influenced by positive and negative opinions held by their immediate contacts: ‘expected-positive-opinions’ and ‘tolerable-negative-opinions’. The former is a minimum number of adopters with positive opinions to whom a consumer is connected, beyond which they become more likely to adopt the innovation. Likewise, the latter is the maximum tolerable number of adopters with negative opinions to whom a consumer is connected, beyond which they become less likely to adopt the innovation. The counts of positive or negative opinions in a consumer’s immediate network in our model are directly related to the same counts in actual online social networks.

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The time scale in our model does not directly correspond to the calendar time. In order words, with each step in the simulation, an unspecified amount of calendar time passes. In our model the number of advertisement impressions is incremented with each step in the simulation. Therefore, calendar time can be approximated by relating the elapsed calendar time between ad impressions in a real campaign, to each time step.

Overview: Process overview and scheduling

For each simulation, a new scale-free network topology is generated, and every consumer’s ‘status’ is set to ‘potential’, where ‘potential’ means the consumer has not adopted the innovation, and still has the potential to do so. Over each time step, a random subset of consumers is exposed to the advertisement, as set by the input parameter ‘advertisement-rate’ (as a percentage of all consumers). The ‘current-impressions’ count for these consumers then increases by one. Within the same time step, two intermediate subtotals are calculated for each consumer: one counting the number of people to whom they are connected that have formed a negative opinion upon adopting the innovation, and another count for positive opinions.

Analogous to the Bass model, we infer a consumer adopts a new product based on (1) their individual impressions of advertisements and (2) the opinions of others to whom they are linked. More specifically, Bass’ variable p is analogous to our specification that a consumer is more likely to adopt an innovation due to advertising if the concurrent count of advertising impressions (‘ current-impressions’) exceeds their personal threshold level (‘my-criterion-of-impressions’). Likewise, Bass’ variable q is analogous to our specification that a consumer is more likely to adopt an innovation due to word of mouth if the effect of nearby positive opinions (in relation to the ‘ expected-positive-opinions’ threshold) is greater than the effect of nearby negative opinions (in relation to the ‘tolerable-negative-opinions’ threshold).

In our model (and as modelled by Laciana et al., 2013), the process by which consumers adopt innovations is determined by the overall (perceived) utility, U:

( ) (( ) )

Consumer adopt innovations if their U is greater than 0.5. The variable alpha represents the value of each consumer’s ‘my-weight-of-network’, and v is the effect of word-of-mouth on the consumer. We calculate v as: (positive-opinions-nearby / expected-positive-opinions) – (negative-opinions-nearby / (tolerable-negative-opinions +1)). The u value is the effect of advertising, which we calculate as:

(current-impressions / criterion-of-impressions). The whole procedure stops if all the consumers adopt the innovation or if the time step exceeds 200.

Design concepts

The concepts upon which our model is designed include the following:

 Basic principles: Our agent-based model is based on the Bass model of innovation diffusion. Both models include a decision to adopt an innovation contingent on external factors (such

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as advertising) and inter-personal factors (such as word of mouth), and reveals an ‘S-curve’ adoption pattern.

 Adaptation: Each consumer decides to adopt the innovation based on the cumulative impressions of advertising and the net effect of opinions of linked adopters as described in section 3.3.

 Sensing: Every consumer is assumed to see the advertisements they are exposed to.

 Interaction: Every consumer is assumed to be aware of the positive of negative opinions of other adopters to whom they are linked.

 Stochasticity: The network topology for each simulation is generated using a stochastic algorithm resulting in a scale-free structure. Within each simulation, the threshold of advertising impressions it takes for a consumer to consider adopting the innovation (‘ my-criterion-of-impressions’) is random and normally distributed. Also, the size of the subset of consumers who are exposed the advertisement in any given time step is specified as an input parameter, but the membership within this subset is randomly determined.

 Observation: We count the number of adopters at every time step of each simulation run, and test whether these values fit the macro-level pattern of the Bass model.

Details: Initialization

At the beginning of each simulation, 1,000 consumers are created and connected as members of a scale-free network. We implemented the scale-free network using the codes by Wilensky (2005). Each consumer’s ‘weight-of-network’ is then set between 0.0 and 1.0 according to their percentile position of the number of linked neighbours. Everyone’s initial ‘status’ is set to potential (not adopted), and the ‘my-criterion-of-impressions’ variable is randomly generated for every consumer using a normal distribution (mean=10, standard deviation=2.5). For our model, we set ‘ expected-positive-opinions-nearby’ as 3, and ‘tolerable-negative-opinions-nearby’ as 1.

Details: Input data

This model does not draw on external data as an input.

Details: Submodels

For this study, we performed multiple simulations by varying the values of three input parameters: ‘advertisement-rate’, ‘initial-adopters-rate’, and ‘chance-of-negative-opinion’. Each parameter was specified by four levels of values: the values of ‘advertisement-rate’ were {0.10, 0.20, 0.30, and 0.50}, ‘initial-adopters-rate’ were {0, 0.05, 0.10, and 0.20}, and ‘chance-of-negative-opinion’ were {0, 0.05, 0.10, and 0.30}, for a total of 64 possible combinations of input parameters.

Our simulation model consists of five procedures: ‘setup-colour’, ‘setup-consumers-network’, ‘setup-advertisement’, ‘decide-adoption’, and ‘draw-plots’. Among these procedures the three procedures start with ‘setup-’ perform the initialization process, the ‘decide-adoption’ procedure calculates the overall utility and determines which users adopt and innovation, and the ‘draw-plots’ procedure draws the results at every time step. The Figure 2 shows the interface of our model.

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Page | 9 Figure 2. Interface of agent-based model in NetLogo upon completion of one simulation

Simulation Results

Emergence of macro-level adoption pattern

We conducted 640 simulations (64 combinations of input parameters * 10 runs) by varying the three input parameters as mentioned above. For each of the 64 sets of 10 runs, we then calculated the average p and q values. Table 1 shows eight of the 64 patterns of adoption that represent the most extreme input parameters in our study, along with their p and q values, and nonlinear model fit, R2, calculated using Wolfram Mathematica 9’s NonLinearModelFit function. For all 64 patterns, the range in p values was 0.0025 ~ 0.0083, the range in q values are 0.0445 ~ 0.3335, and their R2 ranged from 0.9993 to 1.0000. These p and q values are within range of the p and q values from actual adoption pattern reported in the literature (Bass, 1969; Bass, Krishnan, & Jain, 1994; Gatignon, Eliashberg, & Robertson, 1989).

These results show that our agent-based model of online marketing reproduces the innovation diffusion pattern according to the Bass model. In other words, the macro-level diffusion processes effectively explained by our agent-based micro model.

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Page | 10 Table 1. Adoption patterns by input parameters

Input Parameters

a-r i-a-r c-n-o a-r i-a-r c-n-o a-r i-a-r c-n-o a-r i-a-r c-n-o

0.1 0.0 0.0 0.1 0.0 0.3 0.1 0.2 0.0 0.1 0.2 0.3 Adoption Patterns Estimations p=0.0025, q=0.0617 (R2=0.9996) p=0.0029, q=0.0480 (R2=0.9994) p=0.0040, q=0.0520 (R2=0.9999) p=0.0039, q=0.0445 (R2=0.9998) Input Parameters

a-r i-a-r c-n-o a-r i-a-r c-n-o a-r i-a-r c-n-o a-r i-a-r c-n-o

0.5 0.0 0.0 0.5 0.0 0.3 0.5 0.2 0.0 0.5 0.2 0.3 Adoption Patterns Estimations p=0. 0034, q=0.3335 (R2=0.9999) p=0.0053, q=0.2503 (R2=0.9999) p=0.0070, q=0.2808 (R2=1.0000) p=0.0081, q=0.2336 (R2=1.0000)

Linking micro-level and macro-level parameters

We investigated the effects of micro-level input parameters in our ABMS on the macro-level parameters in the Bass model. As can be seen at Figure 3, the 'advertisement-rate' parameter affects the p parameter. As expected, people’s intrinsic tendency to adopt an innovation (p) rises with the frequency by which they see ads (‘advertisement-rate’). Interestingly, this effect tapers off and even decrease for higher frequencies. An unexpected finding is that the 'advertisement-rate' parameter also appears to affect the word-of-mouth parameter (q). This is possibly a secondary effect of more advertisements inducing more intrinsic adopters, and the increase in these adopters subsequently affecting adoption by word-of-mouth.

Figure 3. Relationship between 'advertisement-rate' and p, q in Bass model

As can be seen at Figure 4, the 'initial-adopters-rate' affects only on the p parameter, does not substantially affect the q parameter. This is also an unexpected result, since one would expect marketing campaigns to generate more initial adopters who then increase word-of-mouth effects.

0.000 0.002 0.004 0.006 0.008 0.010 0.00 0.10 0.20 0.30 0.40 0.50 p (ma x) p (a vg) p (min) 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.00 0.10 0.20 0.30 0.40 0.50 q (ma x) q (a vg) q (min)

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Instead, we see the opposite, that more initial adopters somehow induces more intrinsic adoption, and has a nearly negligible effect on word-of-mouth.

Figure 4. Relationship between 'initial-adopters-rate' and p, q in Bass model

Figure 5 shows how the 'chance-of-negative-opinion' affects the p and q parameters. While the apparent lack of an effect may appear as a surprise, this is partly due to an assumption that adoption followed by formation of a negative opinion still counts as adoption.

Figure 5. Relationship between 'chance-of-negative-opinion' and p, q in Bass model

Sensitivity analysis

While the above comparisons reveal the relative balance of intrinsic adoption and adoption by word-of-mouth for each parameter, they do not provide a full picture of the temporal effects. Here, we investigate the effects of the ABMS parameters on the take-off time, the step reaching the maximum adopters, and the number of final adopters by changing the input parameters. Table 2 shows the effects of changing the values of input parameters.

0.000 0.002 0.004 0.006 0.008 0.010 0.00 0.05 0.10 0.15 0.20 p (ma x) p (a vg) p (min) 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.00 0.05 0.10 0.15 0.20 q (ma x) q (a vg) q (min) 0.000 0.002 0.004 0.006 0.008 0.010 0.00 0.10 0.20 0.30 p (ma x) p (a vg) p (min) 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.00 0.10 0.20 0.30 q (ma x) q (a vg) q (min)

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Page | 12 Table 2. Effects of changing the values of input parameters

Parameters advertisement-rate initial-adopters-rate chance-of-negative-opinion

Values 0.1 0.2 0.3 0.5 0 0.05 0.1 0.2 0 0.05 0.1 0.3 T max-rate (t**) 26.7 15.6 12.0 9.1 17.4 16.5 15.5 14.0 15.8 15.9 15.9 15.8 T max-new (t*) 50.4 27.4 19.8 13.7 28.9 28.3 27.7 26.6 26.7 27.4 27.9 29.3 T max-total 198.3 119.9 83.3 55.9 116.2 112.3 116.5 112.3 106.5 114.2 116.9 119.7 N final-adopters 988.7 989.4 988.2 988.8 985.0 987.8 989.6 992.6 999.9 998.6 995.3 961.3

Tmax-rate : the time at which the increase in the rate of adoption across time periods is maximal (t**,

aka take-off time)

Tmax-new : the time at which the new adoption per time period is maximal (t*)

Tmax-total : the time at which the cumulative total adoption is maximal

Nfinal-adopters : the number of final adopters

As can be seen at the Figure 6, the ‘advertisement-rate’ does not seems to affects the total number of adopters, but it does accelerate the take-off time (t**) and time until the maximal new adoptions per period (t*). These results demonstrate that online advertising is still an effective way to quickly promote a small firm’s products and services. However, the desired rate of adoption may not be possible due to advertising budget limitations, so it is important to balance the effectiveness and the cost of an online marketing campaign.

Figure 6. Effects of 'advertisement-rate'

As shown in Figure 7, the ‘initial-adopters-rate’ does not appear to affect the temporal dynamics of the innovation diffusion. These results are a little surprising when considering how larger populations of initial adopters might be expected to generate more word-of-mouth adoption. Further research may be required to resolve this curiosity. What is apparent though is that larger ‘initial-adopters-rate’ values lead to a greater total number of adopters, as reflected in the right half of Figure 7. 930 940 950 960 970 980 990 1,000 0.00 0.10 0.20 0.30 0.40 0.50 tota l (ma x) tota l (a vg) tota l (min) 0 10 20 30 40 50 60 0.00 0.10 0.20 0.30 0.40 0.50 t* (ma x) t* (a vg) t* (min) t** (ma x) t* (a vg) t** (min)

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Page | 13 Figure 7. Effects of 'initial-adopters-rate'

Lastly, Figure 8 shows the impact of ‘chance-of-negative-opinion’ on the temporal dynamics (or lack thereof). While the overall rate of adoption appears to be consistent across a range of values of this parameter, its effect shows up when considering the maximum level of adoption. There appears to be a relatively pronounced effect of the ‘chance-of-negative-opinion’ on the number of final adopters (right half of Figure 8), especially beyond 10%.

Figure 8. Effects of ‘chance-of-negative-opinion’

Conclusion and Implications

We conducted this research to clarify the hidden processes and the unclear performance of small firms’ online marketing by applying ABMSs of innovation diffusion. The results of the simulations indicate that our agent-based online marketing model reproduces the macro-level phenomenon of Bass innovation diffusion, and with this micro-level model, we can explain some of the mechanisms of the online diffusion and marketing processes.

Limitations

One of the largest limitations of our model is the assumption that positive or negative opinions about a product or a service are made only after adoption. In reality, non-adopters can form positive or negative opinions, too. Moreover, consumers who form negative opinions may not adopt any

0 10 20 30 40 50 60 0.00 0.05 0.10 0.15 0.20 t* (ma x) t* (a vg) t* (min) t** (ma x) t* (a vg) t** (min) 930 940 950 960 970 980 990 1,000 0.00 0.05 0.10 0.15 0.20 tota l (ma x) tota l (a vg) tota l (min) 0 10 20 30 40 50 60 0.00 0.10 0.20 0.30 t* (ma x) t* (a vg) t* (min) t** (ma x) t* (a vg) t** (min) 930 940 950 960 970 980 990 1,000 0.00 0.10 0.20 0.30 tota l (ma x) tota l (a vg) tota l (min)

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subsequent products made by the same company. So it is not appropriate to underestimate the impact of consumers’ negative opinions based solely on this study.

Theoretical implications

We constructed a plausible agent-based model of innovation diffusion to explain the process of online marketing. For this, we implemented scale-free network, and considered the effects of advertising and negative (post-adoption) opinions. We expect the findings from our agent-based micro model contribute to the theoretical sophistication of the innovation diffusion model. Our model shows how innovation diffusion can occur despite there not being a set of innovators to seed the process (cf. Bass’s model). It also reflects the general shape of the Bass model, despite our model being able to account for incomplete market adoption (e.g., market size reduction due to the effects of negative opinions discouraging others from adopting). Because of the rapidity by which positive and negative word-of-mouth travels within online social networks, this variable market size phenomenon should be considered as a characteristic of the online diffusion process and remains a fruitful area for future research.

Practical implications

The effects of ‘the advertisement-rate’ on the temporal aspects are remarkable. A doubling of the advertising rate, virtually halves the take-off time and time to maximal adoption rate. This almost 1:1 ratio suggests that the word-of-mouth aspect of many campaigns may be overestimated. These results show us that firms’ online advertising is still the most effective way to promote their products and services, and that some negative word-of-mouth can be overcome by more aggressive marketing. Obviously, such aggressive marketing may come at a substantial cost if the negative word-of-mouth tips beyond 10% and a large marketing budget is simply not available. In such a case, available budgets might be better spent on improving the product or service.

If practitioners find the design of our model realistic enough, they may specify different values for the parameters or initial conditions in order to attempt to forecast the performance of their next online advertising campaign. This may be done by:

1. Estimating the total potential adopters for a focal product (service). This estimation can be done through considering the number of consumers who have already adopted similar products of the firm or by measuring the number of queries for specific keywords representing the firm’s goods in search engines.

2. Estimating the threshold causing a consumer to adopt a product and the chances of the adopters forming a negative opinion. With advanced advertising targeting possibilities due to the availability of user profile data, adoption may occur with minimal frequencies of advertising impressions. It may also be critical to estimate or measure the willingness of consumers to share positive or negative opinions, and the degree to which they listen for such opinions prior to adoption. These criteria may be estimated through customer surveys from following rebroadcasts of social media mentions (e.g., Facebook comments or Twitter re-tweets about products), and simple low dollar value split-tests of campaigns (Ries, 2011).

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3. Planning the rate of advertising in consideration of the online advertising media and available budget for the campaign. The specific unit of period can be day, week, or month. In combination with point 1 above, if advertising effectiveness decreased beyond targeting 25% of the market on a regular basis, then it may be more prudent to spend less on a more targeted sub-segment of the market. Provided the product does not receive negative reviews, then the sub-segment would ideally be people with many connections in their network.

References

Anderson, P. (1999). Complexity theory and organization science. Organization Science, 10(3), 216-232.

Axelrod, R., & Tesfatsion, L. (2006). Appendix A A guide for newcomers to agent-based modelling in the social sciences. Handbook of Computational Economics, 2, 1647-1659.

Barabasi, A.-L. (2002). Linked - The new science of networks. Cambridge, MA: Perseus.

Bass, F. (1969). A new product growth model for product diffusion. Management Science, 15(5), 215-227.

Bass, F. M., Krishnan, T. V., & Jain, D. C. (1994). Why the Bass model fits without decision variables.

Marketing Science, 13(3), 203-223.

Corley II, J. K., Jourdan, Z., & Ingram, W. R. (2013). Internet marketing: a content analysis of the research. Electronic Markets, 1-28.

Crawford, G. C. (2009). A review and recommendation of simulation methodologies for entrepreneurship research. Retrieved from http://ssrn.com/abstract=1472113

Davis, J. P., Eisenhardt, K. M., & Bingham, C. B. (2007). Developing theory through simulation methods. Academy of Management Review, 32(2), 480-499.

Dooley, K. J. (2002). Simulation research methods. In J. A. Baum (Ed.), The blackwell companion to organizations (pp. 829-848). Oxford: Blackwell Publishers.

Dooley, K. J. & Van de Ven, A. H. (1999). Explaining complex organizational dynamics. Organization Science, 10(3), 358-372.

Firth, D. R., Lawrence, C., & Clouse, S. F. (2006). Predicting Internet-based online community size and time to peak membership using the bass model of new product growth. Interdisciplinary Journal of Information, Knowledge, and Management, 1(1), 1-12.

Gatignon, H., Eliashberg, J., & Robertson, T. S. (1989). Modeling multinational diffusion patterns: An efficient methodology. Marketing Science, 8(3), 231-247.

Grimm, V., Berger, U., Bastiansen, F., Eliassen, S., Ginot, V., Giske, J. & DeAngelis, D. L. (2006). A standard protocol for describing individual-based and agent-based models. Ecological Modelling, 198(1), 115-126.

Grimm, V., Berger, U., DeAngelis, D. L., Polhill, J. G., Giske, J., & Railsback, S. F. (2010). The ODD protocol: A review and first update. Ecological Modelling, 221(23), 2760-2768.

Harrison, J. R., Lin, Z., Carroll, G. R., & Carley, K. M. (2007). Simulation modeling in organizational and management research. Academy of Management Review, 32(4), 1229-1245.

(16)

Page | 16

Kiesling, E., Günther, M., Stummer, C., & Wakolbinger, L. M. (2012). Agent-based simulation of innovation diffusion: a review. Central European Journal of Operations Research, 20(2), 183-230.

Laciana, C. E., Rovere, S. L., & Podestá, G. P. (2013). Exploring associations between micro-level models of innovation diffusion and emerging macro-level adoption patterns. Physica A: Statistical Mechanics and its Applications, 392(8), 1873-1884.

Lim, B-L., Choi, M., & Park, M-C. (2003). The late take-off phenomenon in the diffusion of

telecommunication services: network effect and the critical mass. Information Economics and Policy, 15(4), 537-557.

Naseri, M. B., & Elliott, G. (2013). The diffusion of online shopping in Australia: Comparing the Bass, Logistic and Gompertz growth models. Journal of Marketing Analytics, 1(1), 49-60.

North, M. J. & Macal, C. M. (2007). Managing business complexity. New York: Oxford. Rand, W., & Rust, R. T. (2011). Agent-based modeling in marketing: Guidelines for rigor.

International Journal of Research in Marketing, 28(3), 181-193.

Ries, E. (2011). The Lean Startup: How today's entrepreneurs use continuous innovation to create radically successful businesses. New York: Crown Business.

Rogers, E. M. (2003). Diffusion of innovations (5th ed.), Free Press, New York, NY.

Sultan, F., Farley, J. U., & Lehmann, D. R. (1990). A meta-analysis of applications of diffusion models.

Journal of Marketing Research, 70-77.

Ugander J., Karrer B., Backstrom L., Marlow C. (2011). The anatomy of the Facebook social graph.

Retrieved from http://arxiv.org/abs/1111.4503

Wilensky, U. (2005). NetLogo Preferential Attachment model.

http://ccl.northwestern.edu/netlogo/models/PreferentialAttachment. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.

Wong, D. H., Yap, K. B., Turner, B., & Rexha, N. (2011). Predicting the diffusion pattern of Internet-based communication applications using bass model parameter estimates for Email. Journal of Internet Business, 9, 26-50.