The modeling and analysis of the word-of-mouth marketing
Introduction
Promotion is a common form of product sales. The third-party advertising on mass media such as TV and newspaper has long been taken as the major means of promotion. However, this promotion strategy suffers from expensive cost [[1], [2]]. Furthermore, it has been found that, beyond the early stage of product promotion, the efficacy of advertising diminishes [3]. Word-of-mouth (WOM) communications are a pervasive and intriguing phenomenon. It has been found that satisfied and dissatisfied consumers tend to spread positive and negative comments, respectively, regarding the items they have purchased and used [[4], [5]]. As compared to positive comments, negative comments are more emotional and, hence, are more likely to influence the receiver’s opinion. By contrast, positive comments are more cognitive and more considered [[6], [7], [8], [9]]. The significant role of WOM in product sales is supported by broad agreement among practitioners and academics. Indeed, both positive and negative WOM will affect the purchase decision of potential consumers. Due to striking advantages such as significantly lower cost and much faster propagation, the WOM marketing outperforms the traditional advertising marketing [[10], [11]]. With the increasing popularity of online social networks such as Facebook, Myspace, and Twitter, the WOM marketing has come to be one of the main forms of product marketing [12].
Currently, the major concern on WOM marketing focuses on finding a set of seeds such that the expected number of individuals activated from this seed set is maximized [13]. Toward this direction, large number of seeding algorithms have been reported [[14], [15], [16], [17], [18], [19], [20], [21], [22], [23]]. Additionally, a number of dynamic models capturing the WOM spreading processes have been suggested [[24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34]]. However, all the previous work builds on the premise that a single product or a few competing products are on sale. Typically, customers involved in a marketing campaign may purchase multiple products. The ultimate goal of such marketing campaigns is to maximize the overall profit. To achieve the goal, it is crucial to determine those factors that have significant influence on the overall profit. To our knowledge, so far there is no literature in this aspect.
This paper addresses the modeling and analysis of the WOM marketing for a consistent set of items. First, a dynamic model, which is known as the SIPNS model, that characterizes the WOM marketing processes with both positive and negative comments is established. Second, a measure of the overall profit of a WOM marketing campaign is introduced. Third, the SIPNS model is shown to admit a unique equilibrium, and the equilibrium is figured out. Next, the impact of different factors on the equilibrium of the SIPNS model is expounded through theoretical analysis, and extensive experiments show that the equilibrium is much likely to be globally attracting. Finally, the impact of different factors on the expected overall profit of a WOM marketing campaign is ascertained through both theoretical analysis and simulation experiment. On this basis, some promotion strategies are recommended. To our knowledge, this is the first time the WOM marketing is modeled and analyzed in this way.
The subsequent materials are organized as follows. Section 2 describes the SIPNS model, and presents a measure of the overall profit. Section 3 studies the SIPNS model. Section 4 reveals the influence of different factors on the expected overall profit. Finally, Section 5 closes this work.
Section snippets
The modeling of the WOM marketing
Suppose a marketer is asked to plan a WOM marketing campaign for promoting a batch of items, with the goal of achieving the maximum possible overall profit. To achieve the goal, the marketer needs to establish a mathematical model for the WOM marketing campaign and, thereby, to make a comparison among different marketing strategies in terms of the overall profit. This section is devoted to the modeling of the WOM marketing.
The dynamics of the SIPNS model
The key to the enhancement of the expected overall profit of a WOM marketing campaign is to gain insight into the dynamics of the SIPNS model. This section is dedicated to the study of the dynamics of the SIPNS model.
The expected overall profit of a WOM marketing campaign
This section is dedicated to the study of the impact of different factors on the expected overall profit of a WOM marketing campaign. First, it should be noted that, when is large enough, the expected overall profit can be approximated by the following quantity.
Conclusions and remarks
WOM marketing processes with both positive and negative comments have been modeled as the SIPNS model, and a measure of the overall profit of WOM marketing campaigns has been proposed. The SIPNS model has been shown to admit a unique equilibrium, and the impact of different factors on the equilibrium has been determined. Furthermore, extensive experiments have shown that the equilibrium is much likely to be globally attracting. Finally, the influence of different factors on the expected overall
Acknowledgments
The authors are grateful to the anonymous reviewers and the editor for their valuable comments and suggestions. This work is supported by Natural Science Foundation of China (Grant No. 61572006), National Sci-Tech Support Program of China (Grant No. 2015BAF05B03), and Fundamental Research Funds for the Central Universities (Grant No. 106112014CDJZR008823).
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