Enterprise sponsored virtual communities (ESVC) are important platforms for user knowledge sharing. User characteristics, as influential factors in these communities, impact the evolution of knowledge sharing processes. In this study, a knowledge sharing evolutionary game model that considers the influence of user characteristics was constructed. A payoff matrix was established, and stable points were identified for further analysis. Simulation analysis was conducted to explore the impact of changes in user characteristics on the knowledge sharing strategies of both parties. This study revealed the following findings: First, the knowledge reservoir of ESVC users affects their willingness to share knowledge, with ordinary users’ willingness initially increasing and then decreasing as their knowledge reservoirs grow. Second, the willingness of leading users to share knowledge initially decreases and then increases as their knowledge reservoirs expand. Third, improvements in the knowledge absorption and transformation capabilities of both leading and ordinary users promote knowledge sharing behaviour, although the extent of this impact differs between the two groups.

1. Introduction

The world is undergoing rapid changes in science and technology, and the ‘zero-sum game’ among major powers has triggered global economic and political interactions. The Chinese Academy of Social Sciences has identified nine major trends in current global development, indicating that modern industries will evolve towards large-scale customisation, dynamic supply chains and intelligent production and services. The ‘China Digital Economy Development Report’ (2023) highlights that China’s digital economy accounts for over 40% of GDP and maintains high growth. Similarly, the development of the world economy and trade is closely intertwined with digital technology. In February 2023, General Angela Ellard, Deputy Director General of the WTO, stated during a speech at the Aspen Institute in Germany that from 2005 to 2019, the annual growth rate of digitally delivered services reached 7.3%, clearly indicating the increasing significance of the digital economy.

Enterprise sponsored virtual communities (ESVC) serve not only as important carriers of the digital economy but also as platforms for enterprises to obtain user feedback and innovative perspectives and to achieve the cocreation of user value and improve organisational performance through open innovation [1, 2]. Enterprises can guide users to express their needs through virtual communities and provide ideas for creativity based on these needs [3]. However, there are numerous practical challenges such as the presence of lurking users [4, 5], value destruction phenomena [6] and information credibility [7], which lead to low efficiency in acquiring innovative ideas [8]. Therefore, several scholars have conducted research on the factors influencing user participation in knowledge sharing [9–11] and knowledge sharing management [12]. Existing research on user knowledge sharing in virtual communities has the following shortcomings: First, there is an overemphasis on the influence of communities on user knowledge sharing. Users, as the primary participants in knowledge sharing, are heavily influenced by their own characteristics during the process, particularly factors such as their knowledge reservoir level and their ability to absorb, transform and utilise knowledge from other users. Second, there is an overemphasis on the behavioural relationships among users, neglecting user characteristics, particularly in evolutionary game analysis.

To address the shortcomings of the existing research, this study primarily focuses on the following two research questions:

RQ1: How do different categories of users differ in their knowledge sharing process?
RQ2: How do variations in user characteristics affect user participation in knowledge sharing in virtual communities?

This study constructed a knowledge-sharing evolutionary game model that considers the influence of user traits and analysed stable points by establishing a payoff matrix. In the numerical analysis stage, the Xiaomi Community was selected as the case community for numerical simulation to explore how changes in user characteristics affect the selection of knowledge-sharing strategies by both parties.

Compared with the previous research, this study makes the following main contributions: First, the study of knowledge reservoir levels explains the reasons for the different knowledge sharing rates among users in the initial state of knowledge sharing and the differences in the evolutionary process of knowledge sharing among different users. Second, studying knowledge absorption, transformation and utilisation abilities enriches our understanding of the characteristics of leading users.

2. Literature Review

2.1. Knowledge Sharing

Numerous scholars have conducted research on knowledge sharing from various theoretical perspectives, including social cognition, social capital, social exchange, social behaviour and motivation theory, achieving significant results. Currently, research in this field encompasses diverse perspectives, such as those focused on innovation processes and the participants in knowledge sharing, as illustrated in Table 1.

Table 1. Theoretical foundations and main research perspectives in knowledge sharing studies.

Theoretical foundations and research perspectives		Literature	Research content or conclusions
Theoretical foundations	Social cognitive theory	Wang et al. [13]	Based on social cognitive theory, the research indicates that opportunity cost negatively impacts knowledge sharing willingness, while trust and reciprocity have a positive impact. The desire to share positively influences sharing behaviour.
	Social exchange theory	Yan et al. [14]	The article proposes a profit and cost knowledge sharing model based on social exchange theory. Individual interests promote knowledge sharing, while costs inhibit knowledge sharing.
	Social capital theory	Chiu et al. [15] Deng and Yuan [16]	Based on social capital theory, the research shows a significant correlation between social capital of online community members and their knowledge sharing. Passive users’ continuance usage intention is very important to the sustainable and healthy development of virtual brand communities.
	Planned/rational behaviour theory	Bock et al. [17]	Based on rational behaviour theory, the research indicates that the expected reciprocal relationship affects individuals’ attitudes towards knowledge sharing, and the expected external rewards negatively impact individuals’ attitudes towards knowledge sharing.
	Motivation theory	Lee and Hyun [18]	Using online travel communities as a research template, the study demonstrates that four factors, namely, altruism, expected reciprocal benefits, reputation and trust, positively impact knowledge sharing motivation.

Innovation process perspective (roles and stages in innovation)		Cui and Wu [19]	Three innovation roles (CIS, COC and CIN) in knowledge sharing are driven by different factors.
		Liu et al. [20]	Customer-led innovation processes challenge the roles played by senior managers in traditional stage-gate processes.
		Chang and Taylor [21]	User involvement in the ideation stage of new product development can directly or indirectly improve the financial performance of new products, while user involvement in the development stage worsens the financial performance of new products.
		Chang [22]	Customer involvement in the ideation and development stages, as well as the development and launch stages, generates returns through synergistic effects. However, customer involvement in the ideation and launch stages does not create additional benefits.

Knowledge sharing participants	Knowledge sharing subjects	Zhang et al. [23] Zhang et al. [24]	Reputation and reciprocity are among the main factors driving knowledge sharing among knowledge sharing participants. Additionally, some research on Chinese culture has found that ‘face’ also influences knowledge sharing [25, 26].
	Knowledge sharing objects	Kurniawati et al. [27]	Information acquisition motivation, absorption ability and memory capacity of knowledge receivers can enhance willingness for online and offline knowledge sharing, thereby improving individual work performance.
	Knowledge sharing ontology	Polanyi [28] Galunic and Rodan [29]	The former classifies knowledge into tacit and explicit knowledge based on whether it is easily codified, while the latter introduces the concepts of knowledge ambiguity and complexity based on the information content of knowledge.
	Behavioural relationship of knowledge sharing participants	Zhang and Zhu [30]	It is believed that users’ ‘free riding’ behaviour reduces the knowledge sharing willingness of other users.

However, these theories and perspectives are not mutually exclusive. Numerous existing studies are the result of integrating multiple perspectives and theories. For example, Gang and Ravichandran [31] combined social exchange theory and rational action theory and demonstrated that trust between participants positively impact attitudes towards sharing and acquiring knowledge. Chang and Chuang [32] combined user motivation theory with social capital theory and found that altruism, identification, reciprocity and shared language have a significant positive impact on knowledge sharing. Reputation, social interaction and trust positively impact the quality of shared knowledge but not the quantity of shared knowledge. Yang et al. [33] combined LDA model and competency model to construct a comprehensive ability evaluation model for knowledge sharing participants.

2.2. ESVC

The essence of virtual innovation communities is open innovation. This concept was initially proposed by Harvard Professor Chesbrough and scholars have subsequently supplemented it from various perspectives. For example, Di Gangi and Wasko [34] believe that innovation communities are user groups with similar interests or goals, primarily based on communication in the online space. Meelen et al. [35] share a similar view with Di Gangi considering virtual innovation communities as user groups that utilise computer-mediated communication to solve product issues collectively or develop product solutions. Furthermore, Blohm et al. [36] conducted research from a platform perspective and defined virtual innovation communities as collaborative innovation systems formed by individuals within and outside organisations who gather on an online platform with a certain degree of consensus. Additionally, Pirkkalainen et al. [37] indicated that community users join the community by contributing knowledge and innovative viewpoints because of their alignment with the community’s value propositions and the expectation of tangible or intangible rewards.

ESVC are a type of virtual innovation community that is initiated, supported and managed by enterprises or organisations. Unlike other innovation communities, ESVC focus specifically on themes related to the products and services of the sponsoring enterprises. Through enterprise guidance, ESVC promote interaction, collaboration and knowledge sharing among users, thereby contributing to the innovation and improvement of the enterprises’ products.

Current research on knowledge sharing in ESVC is extensive and diverse, encompassing various research angles. For instance, Nambisan and Baron [38] and Renqiang and Wende [39] argue that community trust influences users’ innovation contributions. Kosonen et al. [40] suggested that technological and knowledge support within a community positively impacts user participation in knowledge sharing. Lin and Huang [41], based on rational behaviour theory, concluded that higher levels of user contribution are often driven by virtual community rewards. Hau and Kim [42] and Chen et al. [43] conducted research based on the theory of planned behaviour and motivational theory. Scholars have also investigated the impact of platform environmental factors [39], platform feedback [44], community perception [45] and other influencing factors. Although these studies demonstrate the impact of virtual innovation communities on user knowledge sharing, they do not illustrate a dynamic evolutionary process. Consequently, some scholars have supplemented this perspective with evolutionary game theory. For instance, Ghobadi and Ambra [46] introduced game theory to competitive knowledge sharing, enriching the concept of knowledge sharing strategies. Jiang et al. [47] constructed an evolutionary game model for user knowledge sharing behaviour based on the interaction between community users and revealed that the network structure among users significantly influences the level of knowledge sharing. Samieh and Wahba [48] extend a two-player knowledge sharing game model to a multiplayer game model, and Wang and Li think that the consequences of a comprehensive game of community members are determined by the location of the saddle point, which will evolve to the evolutionary stable strategy [49].

3. Methodology

3.1. Basic Assumptions and Model Construction

Since users in the ESVC possess varying levels of knowledge reserves and engage in knowledge sharing, categorising them into a single group is unrealistic. This study introduces the concept of lead users, originally proposed by von Hippel [50], with subsequent scholars refining and expanding the definition and characteristics of lead users [51–54]. Based on the research findings of various scholars, this study defines lead users in online communities as individuals or groups with high knowledge reserves in specific fields, strong abilities to absorb, transform and utilise expertise, who hold a leading position in the market, and seek to gain high expected returns through knowledge sharing. Therefore, lead users can be distinguished from ordinary users by their characteristics. Ordinary users, in contrast, have lower knowledge reserves, lower activity levels and weaker abilities to absorb and utilise community knowledge.

Assume there are two user groups, A and B, in the ESVC participating in knowledge sharing, where Group A represents lead users and Group B represents ordinary users. The knowledge reserve of Lead Users A is denoted as M_A, and that of Ordinary Users B is denoted as M_B, satisfying the condition M_A > M_B > 0. The amount of knowledge shared by both user groups can be represented by the sharing rate h, with the knowledge sharing amounts expressed as h_AM_A and h_BM_B, satisfying the condition h_AM_A > h_BM_B.

The subsequent basic assumptions can be divided into two aspects: the user and ESVC aspects.

3.1.1. User Aspect

Leading User A has strategy set S_A {1: participate in knowledge sharing, 0: do not participate in knowledge sharing}. The probability of User A participating in knowledge sharing is x, and the probability of User A not participating is 1 − x. Ordinary User B has strategy set S_B {1: participate in knowledge sharing, 0: do not contribute knowledge}. The probability of B participating in knowledge sharing is y, and the probability of B not participating is 1 − y.

P_A and P_B are the weighted average prices of unit knowledge in the ESVC for all leading and ordinary users, respectively. They are used by users to assess their unrealised benefits and the uncertain benefits obtained from other users and satisfy P_A > P_B.

First, knowledge sharing consumes time and energy when both users share knowledge. The effort invested by users in knowledge sharing is a knowledge sharing cost for users. According to the Joseph function [55], the cost of knowledge sharing is a concave function of the knowledge sharing quantity and can be represented as and , where K_A and K_B are the cost coefficients for Users A and B, respectively.

Second, after both users share knowledge, while one user shares knowledge, the other user absorbs, transforms and utilises the knowledge from the former to enhance their own knowledge benefits based on their knowledge type and reserves. As mentioned earlier, let the absorption and conversion rates for Leading Users A and B be r_A and r_B, respectively. The benefits gained by both users from the knowledge shared with other users can be represented as and P_Br_Bh_AM_A.

Third, one user chooses to share knowledge and the other user chooses not to; if one user chooses to share knowledge and the other user chooses not to, the latter will benefit from the former’s knowledge sharing without contributing any knowledge. The benefits gained from free-riding differ from those obtained by absorbing knowledge shared by others. The former refers to the direct utilisation of other users’ knowledge for sharing and receiving community rewards, whereas the latter refers to absorbing and utilising knowledge shared by others to form new knowledge. In this case, the nonsharing user will ‘capture’ a proportion of the benefits obtained by the sharing user, and the ‘capture’ ratio can be set as ‘γ’. The knowledge redundancy is represented as ‘i’, indicating the similarity between the knowledge of the two user groups. The benefits of free-riding can be represented as γ(1 − i)P_Ah_AM_A and .

Fourth, both users choose not to share knowledge: If both User A and User B choose the strategy of not sharing knowledge, it will bring opportunity costs to the users. This can be understood as follows. If users choose not to share knowledge, they cannot obtain experiences, points and other benefits from the ESVC. The opportunity costs for User A and User B after choosing not to share knowledge can be represented as ‘T’.

3.1.2. ESVC Aspects

The company releases tasks or guides discussions and innovation in ESVC according to its own needs and rewards users who participate. Assuming that after A and B share knowledge, ESVC will reward them based on the effective knowledge sharing quantities, represented as λ_Ah_AM_A and . λ represents the actual rewards obtained by leading users and ordinary users per unit of shared knowledge in ESVC.

When users share knowledge of quantity Q, the benefits of that knowledge are realised by receiving community rewards, thus reducing the users’ total unrealised knowledge benefits. The total unrealised knowledge benefits for Users A and B can be represented as P_A (M_A − h_AM_A) and P_B (M_B − h_BM_B), respectively.

Based on the above information, the payoff matrix can be constructed (see Table 2).

Table 2. Payment matrix for knowledge sharing.

Leading User A	Ordinary User B
Leading User A	Participate in knowledge sharing	Do not participate in knowledge sharing
Participate in knowledge sharing
Do not participate in knowledge sharing		P_AM_A − T P_BM_B − T

3.2. Stable Strategy Analysis

The benefits Leading User A obtain when choosing a knowledge sharing strategy are as follows:

()

The benefits Leading User A obtain when choosing a knowledge nonsharing strategy are as follows:

()

The average benefits of the mixed strategy of the Leading User A are as follows:

()

The benefits Ordinary User B obtains when choosing a knowledge sharing strategy:

()

The benefits Ordinary User B obtains when choosing a knowledge nonsharing strategy are as follows:

()

The average benefits of the mixed strategy of the Ordinary User B are as follows:

()

Based on the formula above, we establish the replicator dynamics for Users A and B as follows:

()

Setting the above replicator dynamics equation to zero, we obtain five local equilibrium points: (0, 0), (0, 1), (1, 0), (1, 1), and (x^∗, y^∗), where and .

Using Jacobian stability analysis to analyse the stability of the local equilibrium points, we obtain the Jacobian matrix by taking the partial derivatives of F(x) and F(x): J =

()

The resulting Jacobian matrix is a 2 × 2 square matrix. If the determinant of the Jacobian matrix det(J) = dF(x)/dx∗dF(y)/dy dF(x)/dy∗dF(y)/dx > 0 and the trace of the Jacobian matrix tr is (J) = dF (x)/dx + dF (y)/dy < 0 for the local equilibrium point, then the local equilibrium point is in a locally asymptotically stable state.

To analyse the stability of the equilibrium points, we need to first analyse PhM + 1/2K(hM)² − λhM − T, PrhM − γ(1 − i)PhM, and which one is greater or smaller.

Scenario 1: and P_Ar_Ah_BM_B − γ(1 − i)P_Ah_AM_A < 0, P_Br_Bh_AM_A − γ(1 − i)P_Bh_BM_B < 0.

By substituting the local equilibrium point, we can calculate that only point (0, 0) is stable. Users in ESVC choose not to share their knowledge. This is because users believe that the potential benefits of not sharing that knowledge, even after subtracting the opportunity cost, are greater than the net benefits obtained from sharing knowledge, including the rewards from the company and costs incurred in sharing that knowledge. In other words, users perceive that the net unit benefits obtained from knowledge sharing do not reach the average level in the community. Therefore, they choose not to share knowledge, and there is no active participation in knowledge sharing in ESVC. The phase diagram at this point is shown in Figure 1, Scenario 1.

Scenario 2: and P_Ar_Ah_BM_B − γ(1 − i)P_Ah_AM_A > 0, P_Br_Bh_AM_A − γ(1 − i)P_Bh_BM_B > 0.

Details are in the caption following the image — **Figure 1**
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Evolutionary phase diagram of knowledge sharing in enterprise-led virtual communities.

By calculation, the equilibrium point (1, 1) is the only stable equilibrium point at which users in ESVC actively engage in knowledge sharing. The benefits obtained from knowledge sharing are greater than the average level of the community. Therefore, as long as users participate, satisfactory returns can be obtained. Hence, all community users chose knowledge sharing strategies. The phase diagrams at this point are shown in Figure 1, Scenario 2.

Scenario 3: and P_Ar_Ah_BM_B − γ(1 − i)P_Ah_AM_A < 0, P_Br_Bh_AM_A − γ(1 − i)P_Bh_BM_B < 0. According to the symbols, it can be obtained that x^∗ > 0 and y^∗ > 0.

In this case, when x^∗ and y^∗ are greater than zero, there exists a stable point (1, 1) only when PhM + 1/2K(hM)² − λhM − T < PrhM − γ(1 − i)PhM. At this point, the benefits obtained from sharing knowledge are greater than the community price for that knowledge, and the difference between them is greater than the difference between the benefits obtained from absorbing and utilising knowledge and those obtained from free-riding. If users choose a knowledge sharing strategy, they gain returns that are higher than the average price of knowledge in the community. Therefore, users will choose the knowledge sharing strategy, the phase diagram of which is shown in Figure 1, Scenario 3.

Scenario 4: and P_Ar_Ah_BM_B − γ(1 − i)P_Ah_AM_A > 0, P_Br_Bh_AM_A − γ(1 − i)P_Bh_BM_B > 0 and .

Substituting the local equilibrium point, (0, 0) becomes a stable point. At this point, the net benefits obtained from knowledge sharing are smaller than the potential net benefits of not sharing knowledge. Although users can absorb and utilise others’ knowledge during the knowledge sharing process, the value of these benefits is smaller than the sum of the costs incurred in this process and the losses incurred from free-riding. Therefore, users perceive that choosing a knowledge sharing strategy will bring negative returns. Consequently, users in ESVC will choose not to share their knowledge. The phase diagrams at this point are shown in Figure 1, Scenario 4.

Scenario 5: and P_Ar_Ah_BM_B − γ(1 − i)P_Ah_AM_A > 0, P_Br_Bh_AM_A − γ(1 − i)P_Bh_BM_B > 0, and . The following results were obtained by substituting the above five local equilibrium points (see Table 3).

Figure 1 illustrates that among the five local equilibrium points, only points (0, 0) and (1, 1) are stable, representing evolutionarily stable strategies. Points (0, 0) correspond to both leading and ordinary users adopting the strategy of not sharing knowledge, whereas points (1, 1) correspond to adopting the strategy of sharing knowledge. Additionally, the ESVC also has two unstable points and one saddle point.

Table 3. Evolutionary game analysis of knowledge sharing in enterprise-led virtual innovation communities considering user characteristics.

Equilibrium point.	The symbol of the determinant of J	The symbol of the trace of J	Result
(0, 0)	Symbol: +	Symbol: −	ESS
(0, 1)	Symbol: +	Symbol: +	Unstable
(1, 0)	Symbol: +	Symbol: +	Unstable
(1, 1)	Symbol: +	Symbol: −	Unstable
(x^∗, y^∗)	Symbol: −	0	Saddle point

The phase diagram shown in Figure 1 illustrates the situation described in Scenario (5). The five local equilibrium points divide the region into ABCE and ADCE. The points in region ABCE converge towards (0, 0), indicating the direction of evolution towards the strategy of not sharing knowledge. However, the points in region ADCE converge towards (1, 1), indicating the direction of evolution towards adopting the knowledge sharing strategy. The initial position of a point within these regions determines its evolutionary outcome. For the main enterprises, reaching a stable point (1, 1) within the ESVC allows them to receive knowledge feedback from users, which facilitates product and service improvements. As for the target users, being in a stable state at point (1, 1) enables them to share their views and opinions on products/services and obtain satisfactory benefits. Therefore, although both (0, 0) and (1, 1) are stable states, (1, 1) represents an optimal strategy. The initial position of a point determines its evolutionary direction, and the areas of the two regions are crucial factors influencing the initial position. Enterprises should adopt measures, such as reducing user-sharing costs and mitigating the difficulty of knowledge absorption and utilisation by users, to encourage the saddle point to move towards the lower-left direction, thereby expanding the area of ADCE. This increases the probability that the initial point falls within the ADCE region, thereby increasing the probability of achieving equilibrium using the optimal strategy.

4. Evolutionary Analysis

To better analyse the impact of user characteristics (knowledge reserves and the ability to absorb and transform others’ knowledge) on knowledge sharing strategies within ESVC, we conducted numerical simulations using MATLAB. The Xiaomi Community was selected as a numerical analysis case due to its representative characteristics as a mature ESVC. Xiaomi Community was founded in 2010 and is one of the earliest ESVCs established in China. The Xiaomi Community plays a role in various stages of Xiaomi’s product development, testing and promotion. One-third of the creative ideas for Xiaomi’s MIUI system come from community users, and 80% of the modification suggestions come from the Xiaomi Community. Xiaomi Community is an open innovation platform that facilitates user communication, consultation, assistance, complaints and proposals. It is an important bridge connecting enterprises, products and users and is currently one of the mature and highly active enterprise led user virtual innovation communities in China.

The authors have engaged in research related to the Xiaomi Community for an extended period and are well versed in its rules and mechanisms, which facilitated the setting of numerical values. We invited five experts to use the Delphi method to set parameters for numerical simulations. The criteria for selecting experts were as follows: researchers in the fields of knowledge management or virtual communities (with at least three published academic papers in these fields) and users familiar with the operational rules of the Xiaomi Community (having registered for at least 3 years and holding a community level of Lv4 or above). The final expert panel consisted of three university professors and two users in Xiaomi Community. Detailed information about the experts is provided in Table 4.

Table 4. Expert information.

	Category	Gender	Age	Education level	Occupation
1	Research expert	Male	40	PhD	Professor
2	Research expert	Female	38	PhD	Associate professor
3	Research expert	Male	41	PhD	Associate professor
4	Xiaomi Community user	Male	29	Bachelor’s	Student
5	Xiaomi Community user	Male	38	Master’s	Auditor

The implementation of the Delphi method is as follows: First, the research background and objectives were thoroughly explained to the experts. Then, each expert independently set the parameters. After each round of scoring, the research team calculated Kendall’s W coefficient and the mean and median values of the parameters, and these statistical results were anonymously fed back to the expert panel. Based on this feedback, the experts adjusted their scores. After three rounds of iteration, the W values for the first to third rounds were 0.45, 0.68 and 0.79, respectively. By the third round, the W value exceeded 0.7, and the expert panel expressed no objections to the results, leading to the termination of the scoring process. The final parameter values for the simulation were determined based on the mean scores from the third round of expert ratings (see Table 5). In addition, the probability of ordinary users and leading users initially participating in knowledge sharing is set to 0.5. The numerical assumptions must satisfy the inequality conditions mentioned in Figure 1, Scenario 5.

Table 5. Parameter assignment.

Symbol	Numerical values
M_A	100
h_A	0.4
λ_A	6
P_A	8
K_A	0.004
r_A	0.5
γ	0.1
T	40
M_B	50
h_B	0.4
λ_B	3
P_B	5
K_B	0.002
r_B	0.3
i	0.4

4.1. Impact of Knowledge Reserve on Evolutionary Results

4.1.1. The Impact of Changes in Knowledge Reserves for Regular Users on Evolutionary Results

The knowledge reserve of the regular user MB gradually increased from 50 to 70, 90, 100 and 110 (all satisfying the inequality assumptions in Scenario 5). A system evolution graph (Figure 2) was obtained. Due to the difference in knowledge reserves between regular and leading users, the initial speeds at which both parties reach knowledge sharing stability are different. Initially, regular users achieved knowledge sharing stability at a slightly higher speed than the leading users. The graph shows that when the knowledge reserve of Leading User A remains constant at 100, the threshold for Regular User B’s knowledge reserve is between 100 and 110. When the knowledge reserve MB of regular users is below the threshold, as MB increases, the system converges to the equilibrium state (knowledge sharing, knowledge sharing) at gradually faster and then slower speeds. The fastest evolution speed of the system is achieved when the knowledge reserve is approximately 70. The closer the knowledge reserve of regular users is to the threshold, the longer it takes the system to reach the equilibrium state. When the knowledge reserve MB of regular users exceeds the threshold, the evolutionary result moves towards an equilibrium state (no knowledge sharing, no knowledge sharing) and knowledge sharing behaviour does not occur.

This phenomenon occurs because, when the knowledge reserve of regular users falls below a certain threshold, the rewards they receive for sharing knowledge approximate those received by leading users within the community. Consequently, regular users are incentivised to share knowledge as the benefits align with community reward standards. Furthermore, the active participation of regular users in knowledge sharing motivates leading users to adopt knowledge sharing strategies to achieve higher rewards. As the knowledge reserve of regular users approaches or surpasses that of leading users, while remaining below the threshold, the rewards provided by the ESVC remain relatively low. Regular users, perceiving a misalignment between their knowledge reserve and the benefits received, opt not to share their knowledge. Based on the stability analysis table previously mentioned, it is evident that the system becomes unstable when regular users unilaterally decide not to share knowledge, leading to the ‘free-riding’ of leading users’ knowledge, a loss that cannot be recuperated. Consequently, leading users will also choose not to share knowledge, resulting in the system evolving towards a state of (0, 0).

4.1.2. Impact of Changes in Knowledge Reserves for Leading Users on Evolutionary Results

The knowledge reserve of the leading user, MA, increases from 100 to 107, 115 (all satisfying the conditions mentioned earlier in Scenario 5), and a system evolution graph is obtained (Figure 3). From the graph, it can be observed that as the knowledge reserve of the leading users increases, the time required for the system to reach the equilibrium state gradually increases. When the threshold is exceeded, the willingness of leading users to share knowledge declines significantly, followed by a rebound.

Leading users begin with a high level of knowledge reserves, and increasing their knowledge reserves requires greater effort. They then face three situations: a fixed community reward, the risk of free-riding and the possibility that the knowledge shared by regular users is too small or too simple to allow users to absorb and utilise. These three situations decrease leading users’ willingness to share their knowledge. In this situation, leading users’ loyalty to the community and their proprietary knowledge within the community limit their withdrawal from the community to some extent. After a game, leading users continue to choose knowledge sharing under a tolerable level of unchanging rewards. The willingness of both parties to share will again reach a state of (1, 1), but the time required will increase significantly.

4.2. The Impact of Changes in User Absorption and Transformation Ability on Evolution Results

Users’ abilities to absorb and utilise others’ knowledge are based on their individual capabilities. Under certain absorption and transformation costs, the stronger the ability to absorb and transform others’ knowledge, the greater the benefits they can gain in the knowledge sharing game.

4.2.1. Impact of Changes in the Absorption and Transformation Abilities of Regular Users on the Evolutionary Results

The absorption and transformation ability of regular users increases from 0.3 to 0.4 and 0.5, and the system evolution results (Figure 4) are as follows. The improvement in the absorption and transformation ability of regular users significantly enhances the benefits they gain from absorbing and transforming the knowledge of leading users. This increase in benefits encourages regular users to participate actively in knowledge sharing processes. The increase in absorption and transformation ability accelerates the speed at which the evolutionary game system reaches the stable strategy of (1, 1), and both leading and regular users ultimately adopt the knowledge sharing strategy.

4.2.2. Impact of Changes in the Absorption and Transformation Abilities of Leading Users on Evolutionary Results

The absorption and transformation ability of leading users increases from 0.5 to 0.6, 0.7, and the evolutionary system graph (Figure 5) is as follows: Under the same conditions, as leading users share knowledge in the ESVC, the stronger their absorption and transformation ability in relation to regular users, the higher the benefits they obtain. The more willing the leading users are to participate in the knowledge sharing process. Regular users’ knowledge reserves are already relatively low during the knowledge sharing process. By absorbing and utilising the knowledge of leading users to gain greater benefits, they are more willing to engage in knowledge sharing, and regular users can gain more benefits from participating in knowledge sharing. Shorter time is required for both parties to reach the state of (1, 1) in terms of willingness to share knowledge.

5. Conclusions

This study focused on user perspectives within enterprise-led virtual innovation communities with an emphasis on two indicators: knowledge reserves and the ability to absorb and utilise knowledge. Through system modelling and simulation, this study investigated the impact of various factors on the knowledge sharing strategies of both parties and drew the following conclusions:

First, when the knowledge reserve of ordinary users increases, the speed at which the evolutionary system converges to an equilibrium state (knowledge sharing, knowledge sharing) initially increases and then slows down until it converges to a new equilibrium state (knowledge not shared, knowledge not shared). The threshold of the knowledge reserves of ordinary users divides them into two groups based on the equilibrium state reached by the evolutionary system. When the knowledge reserve of ordinary users increases but has not reached the threshold, there is a critical point at which the evolutionary system reaches equilibrium the fastest. When the knowledge reserve of ordinary users is below this critical point, the rate of knowledge sharing by ordinary users does not change significantly as their knowledge reserve increases; however, the rate of knowledge sharing by leading users gradually increases, leading to a faster convergence of the entire evolutionary system to an equilibrium state. When the knowledge reserve of ordinary users is above this critical point, the convergence speed of both ordinary and leading users towards knowledge sharing stability slows. Compared with ordinary users, the slowdown in the speed at which leading users reach knowledge sharing stability is more pronounced, and at this point, the speed at which the entire evolutionary system reaches the equilibrium state (knowledge sharing, knowledge sharing) also starts to slow down. When the knowledge reserves of ordinary users continue to increase and surpass a threshold, a fixed level of community rewards limits ordinary users’ willingness to share knowledge, resulting in an evolutionary system transitioning to an unstable state (knowledge sharing, knowledge not shared). According to the stability of evolution and the presence of ‘free-riding’ in the community, leading users will make the same transition due to the change in the sharing strategy of ordinary users, and the evolutionary system will eventually reach a new equilibrium state (knowledge not shared, knowledge not shared).

Second, leading users operate with a higher level of knowledge reserves. When they choose a knowledge sharing strategy, their benefits are greater than those of regular users, but they also bear a higher risk of being ‘free riders’ and suffer greater losses. Therefore, leading users must be more cautious in choosing a knowledge sharing strategy, resulting in a slower speed for leading users to reach a stable state of knowledge sharing compared to regular users at the initial stage. A slight increase in the knowledge reserves of the leading users can significantly affect the evolutionary system. There is a special threshold for the knowledge reserves of leading users, which differs significantly from the threshold for regular users. When the knowledge reserves of regular users exceed the threshold, both parties’ willingness to share decreases to zero. However, when the knowledge reserves of leading users exceed this threshold, their willingness to share decreases significantly. In contrast, regular users have a lower risk of being ‘free riders’ due to the lower interest of leading users in absorbing and exploiting their knowledge. This results in a lower risk of loss for regular users; therefore, their willingness to share is not significantly affected. Although the knowledge reserves of leading users are higher, their specialised and focused knowledge allows them to tolerate the psychological imbalance caused by an increase in knowledge reserves when community rewards remain unchanged. Therefore, after a certain period, the willingness of leading users to share knowledge increases significantly, and the system again reaches a state of evolutionary equilibrium (knowledge sharing, knowledge sharing).

Third, the improvement in the regular users’ ability to absorb and utilise knowledge promotes their active participation in the knowledge sharing process. The absorption and transformation of knowledge stimulate the generation of new knowledge, which is distinctly different from ‘free-riding’. Therefore, to some extent, regular users’ active participation also influences their willingness of leading users to participate in the knowledge sharing process. Although the knowledge of leading users is higher than that of regular users, the improvement in their absorption and transformation abilities allows them to better utilise the knowledge of regular users, leading to higher benefits. Therefore, leading users are more willing to participate in the knowledge sharing processes. The improvement in the absorption and transformation abilities of both regular and leading users accelerates the rate of system evolution, leading both parties to share knowledge more quickly. However, the impact of improvement in the absorption and transformation abilities of regular users on the system is more pronounced than that of leading users.

6. Implications

6.1. Theoretical Implications

This study classified users into two categories based on their traits, treated the factors between the community and users and between users as control variables and considered user traits as the dependent variable. It aimed to mitigate the impact of the community on users and users on knowledge sharing, while emphasising the influence of user traits on knowledge sharing. Thereby, this study enriches the current understanding of knowledge sharing in the following ways. First, the study suggests that a high level of knowledge reserve brings greater caution to leading users, providing an explanation from the perspective of knowledge reserves for the initially lower knowledge sharing rates among leading users. Second, by controlling for the increase in knowledge reserves, significant differences in the evolutionary processes of different users were identified, which significantly clarified the complex mechanism of knowledge sharing. Third, by examining the ability to absorb, transform and utilise knowledge, it was found that enhanced ability has a more pronounced promoting effect on the knowledge sharing rate of leading users, thereby enriching the characteristics of leading users.

6.2. Practical Implications

First, the knowledge reserves of regular users affect the direction of the community knowledge sharing evolution. Communities should promptly assess users’ knowledge reserves and make appropriate adjustments. Emerging virtual innovation communities can use the posting frequency and activities of leading users in the ESVC as benchmarks. They can enhance knowledge sharing among regular users by adjusting community rewards and organising special events. This includes launching exclusive product activities alongside new product releases and implementing corresponding reward mechanisms. Additionally, they can establish a ranking system that evaluates users based on their engagement and the practicality of their feedback, with regular rewards for top-ranked participants. Furthermore, collecting user feedback on an ongoing basis and providing rewards based on its actual value can encourage active participation and meaningful contributions. Community rewards and actions against ‘free-riding’ behaviours can further encourage regular users to engage in knowledge sharing, thus achieving a new optimal state. When the knowledge reserves of regular users exceed a certain threshold, the community can adjust community rewards to address the psychological imbalance among regular users and stimulate continued participation in knowledge sharing.

Second, leading users begin with a high level of initial knowledge reserves, and a slight increase can cause a transition in the community’s knowledge sharing state. Therefore, virtual innovation communities should pay more attention to changes in knowledge sharing volumes and methods of leading users. The community can organise exclusive events or offer special rewards for leading users. For example, user rating cards and activity coefficients can serve as ‘tickets’ for participation in these exclusive activities. By taking part, users can not only earn rewards such as points and prizes but also gain early access to the latest products or even participate in the actual product development process, receiving tangible rewards. These initiatives help retain leading users and encourage their continued engagement. This ensures continuous and stable knowledge sharing in the community.

Third, improving users’ abilities to absorb, transform and utilise knowledge contributes to the rapid attainment of a stable state of knowledge sharing in the community. Communities can facilitate this process by simplifying complex or highly technical knowledge, modularising different types of knowledge sharing and encouraging broader user engagement in knowledge absorption and utilisation. To further promote knowledge sharing, communities should establish an effective and efficient platform that streamlines user participation, diversifies engagement channels, lowers entry barriers and reduces participation thresholds. Additionally, integrating AI-driven content recommendation systems and knowledge graph functions can help users easily locate and comprehend relevant information. Organising targeted community activities can also foster interactions between key users and regular users, encouraging knowledge exchange and strengthening the overall knowledge-sharing ecosystem.

7. Limitations and Future Research

This study primarily focused on two indicators—user knowledge reserves and the ability to absorb and transform knowledge—and thoroughly analysed their impact on community knowledge sharing. However, this study has certain limitations. First, while we classified users into ‘leading users’ and ‘ordinary users’ based on lead user theory, we acknowledge that user knowledge reserves exist on a continuous scale rather than as a strict binary classification. The binary distinction was adopted to simplify the model and highlight key behavioural differences, but future research could develop models incorporating a continuous distribution of user knowledge reserves to more accurately reflect real-world user diversity. Empirical studies could also be conducted to validate the robustness of this approach. Second, our model assumes that the benefits of knowledge sharing are linearly additive, meaning that an increase in the proportion of users sharing knowledge leads to a proportional increase in benefits. While this assumption is common in evolutionary game theory, we recognise that knowledge sharing may exhibit nonlinear characteristics, particularly in cases where knowledge redundancy or diminishing marginal returns occur. Future research could explore models that incorporate nonlinear benefit functions to capture more complex knowledge-sharing dynamics, such as threshold effects or knowledge saturation. Third, we introduced a single reward variable to capture the overall impact of incentives on user behaviour, without distinguishing between different types of rewards such as material incentives and psychological incentives. Future research can continue to discuss by distinguishing reward types or incorporating reward preferences into user heterogeneity. Additionally, this study did not comprehensively explore the effects of continued increases in knowledge reserves among leading users after reaching a certain threshold. Since knowledge reserves evolve over time, future research can integrate this dynamic aspect into the replication equation to provide a more rigorous analysis of how user knowledge accumulation influences knowledge-sharing strategies.

By addressing these limitations, future studies can develop a more refined understanding of knowledge-sharing behaviour in virtual communities, ultimately improving theoretical models and practical applications.

Conflicts of Interest

The authors declare no conflicts of interest.

Funding

This research was supported by the National Social Science Post-Funded Project (Grant numbers: 22FGLB065), the Shandong Natural Science Foundation Project (Grant No. ZR2022MG021) and the Qingdao Social Science Planning Project (Grant No. QDSKL2201190).

Acknowledgements

This research was supported by the National Social Science Postfunded Project (Grant No. 22FGLB065), the Shandong Natural Science Foundation project (Grant No. ZR2022MG021) and the Qingdao Social Science Planning Project (Grant No. QDSKL2201190).

Open Research

Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon request.

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All articles

Evolutionary Game Analysis of Knowledge Sharing in Enterprise Sponsored Virtual Communities Considering User Characteristics

Abstract

1. Introduction