2.1. Joint Patent Applications
At first, we should look into diverse contexts of the open innovation of Intellectual Property Rights (IPRs) including patents. Basically, according to industries and firm sizes, the effects of intellectual property rights on innovation and economic performance are different [
9]. A patent among IPRs is the legal right of an inventor to exclude others from making or using a particular invention as an incentive for innovation [
10]. Thus, even though at first glance the two concepts, such as open innovation and IPRs, seem irreconcilable, open innovation and patent have deep relation like a two-edged sword [
11]. Patent can be used to assist in the management of open innovation in a number of ways such as the necessary codification of an invention or technology, patent commons on diffusion of patented technologies, and cross licensing even though it has limits compared to the open science model [
11,
12]. However, making patents accessible royalty-free did not result in any significant increase in diffusion as measured by citing patents in clean and green technology [
13]. In recent years, even though policy discourse has placed much emphasis on the patenting of the outcomes of academic research, it could not confirmed that among several forms of IP (patents, copyright, open source IP, and non-patented innovations) patents are the most effective route for knowledge dissemination of the so-called open innovation channel in the economy [
14].
Patent applications encompass valuable information about the inventive activities of firms such as the degree of open innovation by firms from collaborative assignees as defined by the USPTO [
15]. By analyzing visualizing patent statistics through patent applicant network analysis, network construction among joint patent-applying firms that participated in joint patent applications and the effects of the construction were studied [
16]. In firms who have open search strategies—those who search widely and deeply—the benefits of openness are subject to decreasing returns, which indicate that there is a point at which additional open innovation becomes unproductive [
17,
18,
19,
20,
21]. Companies are increasingly rethinking the fundamental ways in which they generate ideas and bring them to the market [
22]. Therefore, as those who performed funding innovation, generating innovation and commercializing innovation are different in innovation performed by a firm based on its in-house R&D as the applicants or assignees of a patent developed through open innovation in particular are shown to be multiple firms or identities [
22,
23,
24,
25,
26,
27]. Thus, the measurement of levels of open innovation through patents can be divided into the measurement of the breadth of open innovation, which refers to how much is open innovation performed through various channels, and the measurement of the depth of open innovation, which refers to how intensively open innovation is performed. In particular, when open innovation is analyzed through patents, the ratio of the number of joint patent applications of a firm to the total number of patent applications of a firm, that is, the ratio of open innovation patents (ROI) corresponding to the breadth, and the number of applicants per patent of a firm, that is, the intensity of open innovation patents (IOI) corresponding to the depth.
Open innovation is considered to occur mainly when the actor of the patenting of ideas and the actor of external or internal licensing are different from each other; that is, when there are two actors within the entrance of the knowledge funnel [
1,
28]. There are two directions of open innovation, namely, inside-out open innovation, (cases in which patents made within a firm are licensed out to create larger markets and profits) and outside-in open innovation (cases in which a firm license in external patents to create larger markets and profits) [
7,
29]. Open innovation in the stage of joint patent application is distinguished from other existing open innovation channels in that the first part of the knowledge funnel is entered jointly with others. Even among open innovation studies regarding various aspects of open innovation—such as open innovation in value networks, open innovation in Small and Medium Enterprises (SMEs), and open innovation in consumer electronics—joint patent applications are yet to be studied [
30,
31,
32]. All three open innovation process archetypes—outside-in, inside-out, and coupled—focus on firms’ activities performed within company boundaries [
33,
34,
35,
36].
The innovation performance will increase when the level of open innovation goes up in the case of firms with low levels of open innovation but will decrease when the level of open innovation goes up in the case of firms with sufficiently high levels of open innovation [
30,
31,
37,
38,
39,
40].
Open innovation has two aspects such as OI benefits and OI cost. OI benefits include diverse opportunities to meet new markets and technologies, in addition to the benefits of
Table 1. OI costs include uncertainty and complexity, in addition to transaction cost of
Table 1.
Thus, if OI increases in high OI industry such as industry belonging to H03, 04 patents, which are a combination of IT and system technology, a kind of open innovation between IT and other industry. Thus, we build H 1-1 and 1-2. The largest patent holder in the world, IBM, altered their corporate policy on the creation and management of patents substantially in 2006, and released about 100 business method patents to the public. The target patents of this research are business method patents, which IBM released. A skeptic could argue that the IP being given up by large firms, such as IBM, is not very valuable to them, and that pledging allegiance to open innovation is merely a convenient way of saying that they are open to taking others’ ideas without giving up any of their own patents [
11]. The policy of IBM about business model patents exists in same context of H 1-1 and 1-2.
Hypothesis 1-1-1:
The ratio of joint patent applications to the entire patent applications of a firm—that is, the ROI of the firm—will negatively affect the firm’s innovation performance.
Hypothesis 1-1-2:
The number of applicants per patent of a firm—that is, the IOI—will negatively affect the firm’s innovation performance.
2.2. Network of Patents
In various fields, such as the World Wide Web or citation patterns in science, the independence of the system and the identity of its constituents, the probability P(k) that a vertex in the network interacts with k, other vertices decay as a power law, following
, which indicates that large networks self-organize into a scale-free state, which is a feature unexpected by all existing random network models [
53,
54]. The power law is observed in various social phenomena such as the rise in financial data when trading behavior is optimal, distribution of wealth in society, and cognitive lock-in [
55,
56,
57,
58].
Hypothesis 1-2-1:
At least a majority of the joint patent application networks of the 500 largest firms should be located in the largest component of firms’ joint patent application networks.
Hypothesis 1-2-2:
At least a majority of the 500 largest firms should be located in the joint patent application network structures within the 500 largest firms as well as in the entire subject joint patent application network structures.
Hypothesis 1-2-3:
The current global leading smartphone firms, Apple and Samsung, and those firms that were the global leading smartphone firms until recently, Nokia and BlackBerry, should show different characteristics in the joint patent application network structures within the 500 largest firms, as well as in the entire subject joint patent application network structures.
If the power law is effective in joint patent application networks, the 500 largest firms’ networks should belong to the largest component, and at least a majority of the 500 largest firms should naturally belong to the largest network. Therefore, Hypotheses 1-2-1 and 1-2-2 should be valid. Furthermore, two firm groups that create results contrary to each other can be inferred to have joint patent application network structures that are contrary to each other [
59,
60,
61]. Therefore, Hypothesis 1-2-3 should be valid.
The centrality of the dominant is measured by using Freeman’s concept of “betweenness” [
62,
63]. The important idea here is that an actor is central if it lies between other actors on their geodesics, implying that to have a large “betweenness” centrality, the actor must be between many other actors via their geodesics [
64]. In a similar yet different manner, the degree centrality of any group can be defined as the number of nongroup nodes that are connected to group members [
65]. A firm’s network centrality in an alliance network affects the “twin tasks” in exploration—novelty creation on the one hand and its efficient absorption on the other [
66]. Patent or paper citation and patent application networks, betweenness, and degree of centrality have been shown to result in better innovation performance by firms [
62,
67,
68,
69]. Therefore, Hypothesis 1-3-1 is inferred to be valid.
Hypothesis 1-3-1:
Firms with higher centrality should produce better innovation performance.
A structural hole, which means the degree of connectivity or the lack thereof between a firm’s partner, indicates that the people on either side of the hole have access to different flows of information [
67,
70,
71]. Innovative firms that bridge structural holes get a higher performance boost, which suggests that firms need to develop network-enabled capabilities accruing to innovative firms that bridge structural holes [
72]. In fact, from the perspective of the structural hole theory, ego networks—in which a firm’s partners have no links with each other—are prepared to form networks in which the firm’s partners are densely tied with structural holes on the resource-sharing benefits of the network. This reveals a conclusion that is almost diametrically opposite to that reached by knowledge spillover to the same network. There are conflicting positions regarding the effects of structural holes. The hole effect of players rich in structural holes leads to higher rates of return on investment in entrepreneurial motivation research [
70,
73]. At the same time, ego networks with fewer structural holes might promote trust generation and reduce opportunism, leading to more productive collaboration from the perspective of resource sharing [
67,
74,
75]. There is a trade-off between the benefits of connecting non-neighboring nodes and the cost of the effort to maintain links—including settings in which the costs are nonuniform—which reflects the increased difficulty in spanning different parts of a hierarchical organization [
75]. Regarding the firms examined in this study in the area of information communication, including smartphone firms, the scope of connection and modulation that occurs between different firms increases explosively in the process of their cooperation with different technologies and sizes for technology development and collaboration for patent applications [
23,
76,
77,
78,
79]. Therefore, Hypothesis 1-3-2 is inferred to be valid.
Hypothesis 1-3-2:
Firms with larger structural holes will achieve lower innovation performance.
Figure 1b shows a structure with closure represented by A, B, and C. In such a structure with closure, B and C can combine to provide a collective sanction or reward the other for sanctioning A [
80] (Coleman 1988). However, B and C in
Figure 1a have no relations with one another, but have relations with the others instead (D and E). Because of this, they cannot combine forces to sanction A in order to constrain actions.
Closure has two effects. The first is that information quality deteriorates as it moves from one person to the next in a chain of intermediaries. The second effect is the benefit more emphasized by Coleman—network closure facilitates sanctioning, which makes it less risky for people in the network to trust one another [
81]. However, forward citation can be negatively predicted by the closure position in the early and mature stages [
82]. According to another study, the effect of closure on a firm’s innovation performance has a U shape, which means that, at a low level, closure has negative effects of constrained creativity and innovation [
83]. According to Coleman, closure generates positive effects in learning, while closure in a parental network has negative effects [
84]. This study infers that the direct effects of closure will be more positive, as indicated by Hypothesis 1-3-3, when more firms implement joint patent applications in the form of closure because it can logically be inferred that collaboration between any two firms that collaborate with a given firm may directly lead to joint patent applications with the given firms.
Hypothesis 1-3-3:
Firms with larger closure will achieve better innovation performance.
In Korean SMEs, networking has been an effective way to facilitate open innovation among SMEs [
40]. Well-orchestrated companies’ networks allow them to sufficiently commercialize their innovations [
32]. Strong dyadic interfirm ties can be the basis of a distinctive lead firm’s relational capability when it is integrated with a core of strong ties [
85]. Thus, even cyber community networks can have positive effects on individual or team performance [
86]. The innovation itself, the innovator, and the environment (particularly, the characteristics of networks of innovators), have modulating effects on innovation diffusion; that is, innovation performance [
87]. The results of previous studies suggest that the characteristics of firms’ joint patent application network structures, that is, centrality, structural holes, and closure, have direct and indirect effects on firms’ open innovation. Firms’ joint patent application network structures should have modulating effects on the quantitative performance of firms’ joint patent applications, that is, the relationship between ROI/IOI and innovation performance [
88,
89,
90,
91,
92].
Hypothesis 2-1-1:
The relationship between ROI and a company’s innovation performance is moderated by (degree and betweenness) centrality. Firms that have high centrality in the network of joint patent applications will have lower innovation performance.
Hypothesis 2-1-2:
The relationship between IOI and a company’s innovation performance is moderated by (degree and betweenness) centrality. Firms that have high centrality in the network of joint patent applications will have lower innovation performance.
Hypothesis 2-2-1:
The relationship between ROI and a company’s innovation performance is moderated by structural holes. Firms that have many structural holes in the network of joint patent applications will have higher innovation performance.
Hypothesis 2-2-2:
The relationship between IOI and a company’s innovation performance is moderated by structural holes. Firms that have many structural holes in the network of joint patent applications will have higher innovation performance.
Hypothesis 2-3-1:
The relationship between ROI and a company’s innovation performance is moderated by closure. Firms that have closure in the network of joint patent applications will have lower innovation performance.
Hypothesis 2-3-2:
The relationship between IOI and a company’s innovation performance is moderated by closure. Firms that have closure in the network of joint patent applications will have lower innovation performance.
With regard to the direction of the modulating effects in Hypothesis 2, centrality and closure are inferred to have positive effects and structural holes are inferred to have negative effects for the same reason as that for Hypothesis 1-3.