This article investigates the definition and core concepts of Internet brand innovation alongside their influence on performance.
A combined qualitative and quantitative design was used. Interviews of 42 Internet companies were conducted. Over 200 speeches of entrepreneurs were collated and a content analysis and case study of the data were conducted. A total of 309 questionnaires of Honor’s employees were collated. Partial least squares structural equation modelling was employed for data analysis.
Internet brand innovation refers to companies carrying out Internet-based brand innovations, which results in fundamental changes to existing products, marketing or business model practices. This process involves five core concepts with the following influences on performance: Internet information application mediates the relationship between Internet information acquisition and performance. Interaction and cooperation through platform positively influences performance. Internet advanced technology application and Internet strategic capability can strengthen the positive effects of Internet information acquisition on mining potential demands.
Internet companies should explore new avenues, focus on their main channels for conducting continuous brand innovations and build win–win ecosystems to co-create value with stakeholders.
This article proposes an interpretation of a new concept – Internet brand innovation. It reveals ways in which companies can conduct Internet brand innovation to improve performance. Furthermore, for Internet companies, mining potential demands is more important than meeting existing demands and disruptive innovation is more important than incremental innovation.
In recent years, many companies have conducted Internet brand innovation and achieved rapid expansion and high performance. For instance, Xiaomi has encouraged users to fully participate in new product development, sales and brand communication. The company also created a new category of ‘Internet mobile phone’ and reached the top of China’s smartphone market in 2014. DiDi launched an online ride-hailing business model, which covered more than 400 cities in China, has 450 million users, more than 25 million daily orders and market share of over 90%. From its establishment in 2012 to September 2020, DiDi has completed 20 rounds of financing, obtaining over $20 billion and a valuation of more than $60 billion.
Internet brand innovation is becoming increasingly important in practice; however, scholars have not conducted much research on the topic. Amongst the few existing studies, a consensus on the concept of brand innovation has yet to be reached. Therefore, our first research problem is as follows: ‘
We aim to answer these questions through a combined qualitative and quantitative design for the following reasons. Firstly, qualitative researchers claim that the understanding of organisational phenomena must be based on researchers’ subjective interpretation (Lee,
We propose a subjective interpretation of a new concept: Internet brand innovation. We also pay attention to process, models (category) and core concepts (quantity) of Internet brand innovation. Furthermore, we focus on the influencing mechanism of these core concepts on performance (accurate description).
Therefore, we will conduct a combined qualitative and quantitative study using two-stage design method (Creswell,
Some scholars equated brand innovation with product innovation (Beverland, Napoli, & Farrelly,
However, in the Internet era, many companies have achieved success not through marketing innovation or product or technology innovation but through business model innovation (Spiegel et al.,
Another focus of controversial issues on brand innovation is as follows: to what extent does innovation affect existing practices and markets to be counted as brand innovation? Some scholars have held that all innovation activities (from minor innovations, such as product packaging, to major innovations that overturn markets) could be considered brand innovation (Chimhundu, Hamlin, & McNeill,
Thus, our first group of research problems constitutes the following questions:
Some scholars have proposed that brand innovation is a process (Sammour, Chen, Balmer, Botchie, & Faraday,
Absorptive capacity theory examines the process of how companies identify the value of new knowledge, absorb it and apply it to achieve organisational goals (Cohen & Levinthal,
Considering absorptive capacity theory and related studies, we speculate that when companies perform Internet brand innovation, the main influencing path is Internet information acquisition → Internet information application → performance. The Internet information application includes two types of guidance: one is meeting existing demands and the other is mining potential demands (Marvel & Lumpkin,
Based on the preceding discussion, the following hypotheses are proposed:
Internet strategic capability is a company’s ability to integrate information acquired online with internal resources to apply to brand innovations and make innovations that are consistent with the company’s strategic directions (Nguyen et al.,
Based on the preceding discussion, the following hypotheses are proposed:
As social media is only one kind of Internet platform, Internet brand innovation is more meaningful than social media brand innovation. Therefore, in addition to Internet information acquisition, information application and strategic capabilities, Internet brand innovation may include other core concepts that need to be explored.
Therefore, our second group of research problems is as follows: ‘
To answer the aforementioned research problems, a combined qualitative and quantitative investigation is conducted.
We were writing an annual report on development of e-commerce with the support of a Chinese chamber of commerce, so we got the opportunity to conduct surveys of its member companies. From May to June 2019, we conducted in-depth interviews with founders, managers and employees of 42 Internet companies in China such as Fabest care, Like and Emao. We designed the interview outline based on the problems identified from the literature review. The questions were as follows: (1) Describe the general condition of your company including history and development status, industry competition, Internet strategy and its implementation. (2) What is brand innovation? (3) What aspects are included in brand innovation? (4) What is Internet brand innovation? (5) What models are included in Internet brand innovation? 6) How does your company conduct Internet brand innovation? (7) What factors affect your company’s performance of Internet brand innovation? We conducted face-to-face semi-structured interviews in which the contents were recorded with the consent of interviewees and then transcribed. The contents of the interviews are restricted by confidentiality agreements.
Becuase of limited resources, our interviews lack first-hand data on the founders and senior executives of the largest Internet companies such as Apple, Huawei and Alibaba. To avoid omitting important viewpoints, we searched for and found over 200 interviews, reports and speeches of famous entrepreneurs such as Steve Jobs, Ren Zheng-Fei and Jack Ma online using keywords such as ‘Internet + brand innovation + performance’.
By combining the first-hand and second-hand data, we built a database of nearly 900 000 Chinese characters.
We used ROST CM 6.0 software for content analysis. Firstly, we performed word segmentation. Secondly, we analysed word frequency.
The word frequency rankings of the top keywords were as follows: Internet (at 4543), innovation (3262), model (1750), marketing (1640), brand (1614) and product (1270). From the perspective of the number of keywords and their correlation, including our subjective interpretation of interview data, we find that Internet brand innovation includes three models: business model innovation, marketing innovation and product innovation.
Meanwhile, when discussing Internet brand innovation, many entrepreneurs emphasised the importance of fundamental changes to existing practices and markets. For example, 360 Company’s founder pointed out that in the Internet era, only disruptive innovation can succeed. Sina’s CEO stressed that in the Internet field, if you do not disrupt yourself, you will be disrupted. Internet brand innovation must have courage to disrupt itself. A medium-sized Internet company’s CEO mentioned that Internet brand innovation is actually a kind of innovation of ‘Internet plus practices’, which combines the existing practice results with Internet thinking to carry out mixed changes and disruptive reforms. Another CEO of a small Internet company observed that the biggest difference between Internet brand innovation and ordinary brand innovation lies in its disruption. Thus, only innovations that result in fundamental changes to existing practices and markets constitute Internet brand innovations.
In summary, we propose the following definition of Internet brand innovation:
Furthermore, we conducted semantic network and social network analysis in five steps: (1) extracting high frequency words; (2) filtering nonsense words; (3) extracting row features; (4) building network; and (5) building matrix. Then, we drew the collinear matrix of keywords, as shown in
Collinear matrix of keywords.
We collected typical cases and summarised representative viewpoints to test the external validity of the five core concepts of Internet brand innovation, as shown in
Core concepts, typical cases and representative viewpoints.
Core concepts | Definitions | Typical cases | Representative viewpoints |
---|---|---|---|
Internet information acquisition | Companies acquire information from users, partners and competitors through various Internet-based platforms. | 360 Total Security Company acquires user information online through 360 Total Security, 360 Security Browser, and other software. Furthermore, 360 Company acquires user information and monitors competitors and user feedback through 360’s bulletin board system, microblog and other Internet platforms, mastering a large volume of valuable information. | ‘360 Company conducts deep analyses on users’ information constantly to form a huge big data system spanning PCs and mobile phones.’ (Zhou Hong-Yi 360 Company’s founder) |
Internet information application: Meeting existing demands | Companies understand and meet existing demands expressed by consumers based on information acquired online. | Huajiao LIVE found three pain points for users to watch live videos on mobile phones. Firstly, users often miss live videos. Secondly, users do not have enough mobile phone flows. Thirdly, users do not have enough mobile phone internal memory. Thus, Huajiao developed three corresponding functions to meet these existing demands. Firstly, playback of live video so that missed live videos can be watched later. Secondly, automatically compressing video sizes to save user flows. Thirdly, cloud storage to free up the internal memory of mobile phones. Having met existing demands, Huajiao has become one of the largest mobile social broadcast platforms in China. | ‘Huajiao has been committed to solving users’ pain points of making friends and improving users’ experience.’ (Huajiao’s chief technical officer) |
Internet information application: Mining potential demands | Companies mine and lead potential demands that consumers are not aware of based on information acquired online. | From iPods to iPhones and iPads, Apple has launched several revolutionary products that have ‘changed the world’, constantly mining and guiding consumers’ demands. Apple leads the trend of global brand innovation, ranking at the top of many brand value lists. | ‘A lot of times, people don’t know what they want until you show it to them.’ (Steve Jobs) |
Internet advanced technology application | Companies apply advanced technologies to conduct brand innovations based on the Internet. | Toutiao applies advanced artificial intelligence and machine learning technology to personalise content. Its personalised news recommendation system enables it to understand users well and recommend news with great accuracy, thereby improving users’ experience and extending their usage time. Toutiao has over 600 million users and 140 million active users, with average daily usage time exceeding 76 min. | ‘As a new generation of artificial intelligence technology company, Toutiao is an active practitioner of artificial intelligence technology and its application.’ (Zhang Yi-Ming Toutiao’s founder) |
Internet strategic capability | The capability of companies to integrate information acquired online with internal resources to apply to brand innovations and make brand innovations that are consistent with their strategic directions. | ‘To become a leader, we must strengthen strategic concentration, concentrate our forces on the main channels and battlefields to fight wars of annihilation and occupy high ground.’ (Ren Zheng-Fei Huawei’s founder) |
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‘We ran madly and blindfoldedly, as well as burned our cash in pursuit of scale; our globalisation battle line has stretched too long all at once.’ (Jia Yue-Ting LeEco’s founder) |
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Interaction and cooperation through platform | Companies conduct interactions and deep cooperation with users and partners through online platform in the process of new product development, marketing and product usage. | When Xiaomi is developing new products, thousands of consumers come up with ideas enthusiastically. When Xiaomi is promoting products, millions of consumers create buzz. When Xiaomi’s products have been sold, millions of consumers actively participate in word-of-mouth communication and feedback of products. Xiaomi won No. 1 position in China’s smartphone market in 2014. | ‘Xiaomi model is a “user-engaged Internet development model.” “A sense of engagement” is the biggest secret of Xiaomi’s success.’ (Lei Jun Xiaomi’s founder) |
As shown in
During our interviews, many interviewees emphasised the important impact of Internet advanced technology application during the process of Internet brand innovation. For example:
‘Internet brand innovation is closely related with progress of science and technology, such as biological recognition, neural network and artificial intelligence technology. Using these advanced technologies, companies can apply information acquired from Internet better.’ (Veteran Internet Practitioner)
According to a Xiaomi manager, advanced technology itself may not directly affect the performance of Internet brand innovation. Companies need to use advanced technology to better apply information acquired from Internet. These views suggest that Internet advanced technology application may not directly affect performance, but may enhance the impact of Internet information acquisition on Internet information application.
Based on the preceding discussion, the following hypotheses are proposed:
Many entrepreneurs mentioned the importance of cooperating with business partners through platform to create win–win results when carrying out Internet brand innovation. For example, Haier’s CEO said that in the Internet era, we have changed our suppliers from game relationships to partnerships and it is not fixed, anyone who does well can participate in our platform. Another said that:
‘Huajiao LIVE implements the open platform strategy, launching a variety of forms of cooperation with vertical companies such as Tuniu.com, BitAuto and Baihe.com. From ‘live streaming + e-commerce’ to ‘live streaming + tourism’, from ‘live streaming + agriculture’ to ‘live streaming + public welfare’, these kinds of crossover cooperation have provided rich and diversified contents for Huajiao LIVE and improved its innovation performance.’ (Huajiao LIVE Manager)
Many entrepreneurs also mentioned the important impact of interaction through platform on performance. For example, according to the chairman of Alibaba’s academic committee, only when companies establish a long-term dynamic interactive relationship with users can they get rapid feedbacks and then continuously improve brand performance. Xiaomi’s co-founder noted that the Internet era is not an era of simply selling products but selling a sense of participation. Interacting with users is the real secret behind Xiaomi’s high performance.
Based on the preceding discussion, the following hypothesis is proposed:
In summary, we comprehensively consider the results of literature reviews and qualitative research to construct our research model, as shown in
Research model.
Honor was the fastest-growing smartphone brand in the world in 2018 and has become the leader in the sales volume and revenues of Internet mobile phones in China. Therefore, we select Honor as our research object. Our questionnaires include seven parts: Internet information acquisition (Nguyen et al.,
As questions in the questionnaires are difficult for ordinary consumers to answer our questionnaires were mainly conducted for employees of Honor. A member of our research group was an employee of Honor. We asked her to send the questionnaires to her colleagues. After obtaining the consent of a head of the relevant department and signing a confidentiality agreement, we asked employees of Honor to fill in the questionnaires. The questionnaires were distributed from July to August in 2019, and 309 valid questionnaires were collected.
Respondent’s profile (
Demographic information | Frequency | % |
---|---|---|
Male | 173 | 55.99 |
Female | 136 | 44.01 |
Under 30 | 110 | 35.60 |
30–50 | 169 | 54.69 |
Over 50 | 30 | 9.71 |
High school | 27 | 8.74 |
Bachelor’s degree | 190 | 61.49 |
Master’s degree and above | 92 | 29.77 |
Research and development | 142 | 45.95 |
Sales | 15 | 4.85 |
Delivery and service | 69 | 22.33 |
Strategy and marketing | 19 | 6.15 |
Manufacturing and supply chain | 25 | 8.03 |
Others | 39 | 12.69 |
Partial least squares structural equation modeling (PLS–SEM) was used to analyse the data. According to our research model (
Factor loading of each indicator is higher than the restricted level of 0.7. Cronbach’s alpha and Composite Reliability (CR) of each construct are higher than the restricted level of 0.7, thereby indicating that our scales have good reliability (Hair et al.,
Reliability and convergent validity test.
Latent variable | Indicators | Loadings | Cronbach’s α | CR | AVE |
---|---|---|---|---|---|
Internet Information acquisition | - | - | 0.848 | 0.898 | 0.688 |
IIA1 | 0.806 | - | - | - | |
IIA2 | 0.860 | - | - | - | |
IIA3 | 0.840 | - | - | - | |
IIA4 | 0.809 | - | - | - | |
Internet advanced technology application | - | - | 0.804 | 0.911 | 0.836 |
IATA1 | 0.916 | - | - | - | |
IATA2 | 0.912 | - | - | - | |
Internet strategic capability | - | - | 0.867 | 0.910 | 0.715 |
ISC1 | 0.839 | - | - | - | |
ISC2 | 0.853 | - | - | - | |
ISC3 | 0.852 | - | - | - | |
ISC4 | 0.838 | - | - | - | |
Meeting existing demands | - | - | 0.812 | 0.889 | 0.727 |
MED1 | 0.837 | - | - | - | |
MED2 | 0.912 | - | - | - | |
MED3 | 0.807 | - | - | - | |
Mining potential demands | - | - | 0.869 | 0.911 | 0.719 |
MPD1 | 0.801 | - | - | - | |
MPD2 | 0.857 | - | - | - | |
MPD3 | 0.863 | - | - | - | |
MPD4 | 0.869 | - | - | - | |
Interaction and cooperation through platform | - | - | 0.900 | 0.921 | 0.624 |
ICP1 | 0.777 | - | - | - | |
ICP2 | 0.791 | - | - | - | |
ICP3 | 0.797 | - | - | - | |
ICP4 | 0.822 | - | - | - | |
ICP5 | 0.812 | - | - | - | |
ICP6 | 0.780 | - | - | - | |
ICP7 | 0.750 | - | - | - | |
Performance of internet brand innovation | - | - | 0.886 | 0.914 | 0.639 |
PIBI1 | 0.763 | - | - | - | |
PIBI2 | 0.835 | - | - | - | |
PIBI3 | 0.812 | - | - | - | |
PIBI4 | 0.835 | - | - | - | |
PIBI5 | 0.790 | - | - | - | |
PIBI6 | 0.755 | - | - | - |
Discriminant validity test.
Variable | ICP | IIA | ISC | IATA | PIBI | MPD | MED |
---|---|---|---|---|---|---|---|
ICP | 0.790 |
- | - | - | - | - | - |
IIA | 0.583 | 0.829 |
- | - | - | - | - |
ISC | 0.779 | 0.596 | 0.846 |
- | - | - | - |
IATA | 0.696 | 0.487 | 0.576 | 0.914 |
- | - | - |
PIBI | 0.760 | 0.528 | 0.700 | 0.730 | 0.799 |
- | - |
MPD | 0.755 | 0.584 | 0.794 | 0.605 | 0.711 | 0.848 |
- |
MED | 0.664 | 0.695 | 0.704 | 0.551 | 0.628 | 0.673 | 0.853 |
Note: Non-square root values are the correlation values between constructs.
ICP, Interaction and Cooperation through Platform; IIA, Internet Information Acquisition; ISC, Internet Strategic Capability; IATA, Internet Advanced Technology Application; PIBI, Performance of Internet Brand Innovation; MPD, Mining Potential Demands; MED, Meeting Existing Demands.
, square root values of the AVE of each construct.
We attempted to reduce the potential effects of response pattern biases by incorporating reverse-coded items on our questionnaires (Hinkin,
We used two steps to test multicollinearity (Hair et al.,
We run the bootstrapping procedure with 5000 bootstrap samples. The results are presented in
Significance testing results of structural model path coefficients.
Paths | Path coefficients | Significance levels | ||
---|---|---|---|---|
Internet information acquisition → Meet existing demands | 0.696 | 17.077 | 0.000 | |
Internet information acquisition → Mining potential demands | 0.587 | 11.763 | 0.000 | |
Meet existing demands → Performance of internet brand innovation | 0.140 | 2.382 | 0.017 | |
Mining potential demands → Performance of internet brand innovation | 0.259 | 3.268 | 0.001 | |
Interaction and cooperation through platform → Performance of internet brand innovation | 0.474 | 5.760 | 0.000 |
Note: Bootstrap confidence intervals for 5% probability of error (
As shown in
We conducted Sobel, Aroian and Goodman tests to conduct mediator analysis. The results are shown in
Mediator analysis.
Mediating effects | Paths | ||||
---|---|---|---|---|---|
Sobel test | Aroian test | Goodman test | |||
IIA→MED→PIBI | IIA→MED | 17.077 | 2.359 |
2.355 |
2.363 |
MED→PIBI | 2.382 | - | - | - | |
IIA→MPD→PIBI | IIA→MPD | 11.763 | 3.149 |
3.138 |
3.159 |
MPD→PIBI | 3.268 | - | - | - |
IIA, Internet Information Acquisition; MED, Meeting Existing Demands; MPD, Mining Potential Demands; PIBI, Performance of Internet Brand Innovation.
As shown in
SmartPLS v3.2.7 software was used to create moderating effects 1 and 2 (Hair et al.,
Moderator analysis.
Paths | Path coefficients | Significance levels | ||
---|---|---|---|---|
Moderating effect 1→ Meeting existing demands | 0.022 | 0.432 | 0.666 | NS |
Moderating effect 2→ Mining potential demands | 0.068 | 1.830 | 0.067 | |
Moderating effect 3→ Meeting existing demands | 0.050 | 1.088 | 0.277 | NS |
Moderating effect 4→ Mining potential demands | 0.081 | 2.330 | 0.020 |
Note: Bootstrap confidence intervals for 10% probability of error (α = 0.1).
NS, not significant.
As shown in
Hypothesis 2a is not supported for the following reason: Internet strategic capability can help companies identify potential market opportunities and risks from massive information quickly and accurately and focus deeply on mining potential demands rather than blind expansion. This capability is more relevant to future and unknown fields than existing and known fields. Hypothesis 3a is not supported for the following reasons: the main purpose of applying Internet advanced technology to conduct brand innovation is to constantly create new blue oceans, mine potential demands that even consumers are unaware of themselves and overturn existing products, markets or business models, whereas companies have few motivations to apply Internet advanced technology to meet existing demands.
When focusing on marketing issues, an
Firstly, Internet brand innovation is defined as follows: ‘Companies carry out brand innovations based on the Internet, which result in fundamental changes to existing products, marketing or business model practices’. Based on the two driving factors of innovation, the existing research has proposed that brand innovation included two models: marketing innovation and product or technology innovation. We supplement a new model for Internet brand innovation: business model innovation. In addition, existing literature has not reached a consensus on the extent to which brand innovation affects existing practices and markets. We find that only innovations that result in fundamental changes to existing practices and markets can be counted as Internet brand innovations. Thus, this article defines the concept of Internet brand innovation more comprehensively and accurately, which lays the foundation for future research.
Secondly, Internet brand innovation is a process that involves five core concepts: Internet information acquisition, Internet information application (meeting existing demands and mining potential demands), Internet advanced technology application, Internet strategic capability and interaction and cooperation through platform. The influencing mechanism of these core concepts on performance is as follows: Internet information acquisition → Internet information application (meeting existing demands and mining potential demands) → performance (main influencing path). Internet advanced technology application and Internet strategic capability can enhance the positive impact of Internet information acquisition on mining potential demands (moderating effects). Interaction and cooperation through platform positively affect performance. Research has proposed that social media brand innovation involved three core concepts: knowledge acquisition, knowledge application and strategic capability. We supplement two new core concepts for Internet brand innovation: advanced technology application and interaction and cooperation through platform. The existing literature had not examined the main effect of ‘knowledge acquisition from social media → social media knowledge application → performance’, nor had it examined the impact of social media brand innovation on performance. Based on absorptive capacity theory, we find a main influencing path of ‘Internet information acquisition → Internet information application → performance’; we also confirm the moderating effects of Internet strategic capability and advanced technology application, as well as the important influence of interaction and cooperation through platform on performance. Thus, this article initially opens the black box of ‘how companies can conduct Internet brand innovation better to improve performance’.
Thirdly, for Internet companies, mining potential demands is more important than meeting existing demands and disruptive innovation is more important than incremental innovation. Disruptive innovation or incremental innovation – which kind of innovation model can usher in higher returns? The answer to this controversial question may vary according to industry, enterprise type, and the nature of the enterprise (Chang, Franke, Butler, Musgrove, & Ellinger,
Firstly, for Internet companies, mining potential demands and disruptive innovation is more important. In our investigation process, we found that many industries closely related to the Internet (such as online ride-hailing, live streaming and short video creation) are rapidly changing, and few successful business models are fully universal and consistently feasible. Many Internet companies are ‘crossing the river by feeling the stones’ because they face new situations. Their current strategies and businesses differ from their original ideas. ‘There is no future in imitating business models of giants when they have already established their ecosystems’, according to the founder of 360 Company. Only by constantly mining potential demands, discovering new blue oceans, and solving the pain points of industry better and faster than competitors can companies establish their own ecosystems and ultimately improve performance. In summary, Internet companies should explore new avenues.
Secondly, continuous innovation is important; however, blind innovation is dangerous. Internet companies should conduct brand innovation activities according to their strategic direction and choice. Internet companies should adhere to Huawei’s ‘principle of pressure’, allocating resources to the main channel in a way that exceeds that of their major competitors. Furthermore, Internet companies should concentrate their resources to achieve breakthroughs in key fields. However, ‘Internet companies should oppose blind innovations’, as Huawei’s founder said. Jack Welch, former CEO of GE, emphasised that the company has to be either No. 1 or No. 2 in every industry it enters or walk away from it. Therefore, we advise Internet companies to avoid blind innovations, diversification and expansion. In summary, Internet companies should focus on their main channels for conducting continuous brand innovations.
Thirdly, in the process of Internet brand innovation, we suggest that companies encourage users to participate in the entire process and conduct open cooperation with partners to build win–win ecosystems. Encouraging users to participate in the process of product development, communication, sales and after sales. ‘Xiaomi is selling a sense of participation, this is the real secret behind Xiaomi’s success’, as mentioned by the Xiaomi’s founder. Another example is building up a boundaryless company as Jack Welch did with GE. Furthermore, in the mobile Internet era, the ‘boundaryless management’ can be extended outside of the company, that is, by carrying out open cooperation with partners through Internet platform. Thus, Internet companies should build win–win ecosystems and co-create value with stakeholders (Gamble, Clinton, & Diaz-Moriana, in press).
Firstly, owing to limited resources, our interviewees were mainly Internet start-ups that lack first-hand information on the founders and senior executives of the largest Internet companies such as Alibaba, Tencent and Baidu. These business elites may provide important insights into our research topics from their unique perspectives. However, without face-to-face communication with these business elites, we cannot co-construct knowledge with them (Marshall & Rossman,
We would like to thank Professor Zhang Xin-Rui for inspiring our thoughts, thank the anonymous reviewers for their insightful comments and suggestions, and thank editors for their kindly help and support.
The authors declare that they have no financial or personal relationships that may have inappropriately influenced them in writing this article.
Y.Y-W. and T.X-B. conceived of the presented idea. Y.Y-W. developed the theory and performed the computations. T.J-B. and L.P. verified the analytical methods. L.J-P. encouraged Y.Y-W. to investigate typical cases and supervised the findings of this work. All authors discussed the results and contributed to the final manuscript.
This article followed all ethical standards for carrying out research.
This work was supported by the National Natural Science Foundation of China (grant number 71802005), the National Natural Science Foundation of China (grant number 71832015), the Beijing Social Science Foundation (grant number 17GLC068), the National Natural Science Foundation of China (grant number 71702002), the Beijing Natural Science Foundation (grant number 9182003), and General Program of Social Science Plan of Beijing Municipal Education Commission (grant number SM201910009007).
The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available owing to restrictions set out in a confidentiality agreement with Huawei Technologies Company.
The views and opinions expressed in this article are those of the authors and do not necessarily reflect the official policy or position of any affiliated agency of the authors.