Cocreation of social value: A tripartite game analysis with Chinese state-owned enterprises as an example

Abstract

In the context of the digital economy era, it is urgent for Chinese state-owned enterprises (SOEs) to engage in social value cocreation activities. The government and consumers’ roles in SOEs’ social value cocreation system cannot be ignored. Therefore, it is necessary to explore the tripartite social value cocreation model involving the government, SOEs, and consumers. In this respect, this study constructs a tripartite evolutionary game model of the government, SOEs, and consumers, and explores the influencing factors and evolutionary mechanism of the system overall. Matlab software is used to analyze the simulation data. The results reveal that the prerequisite for SOEs’ successful social value cocreation is that consumers receive additional social value benefits greater than the level of improvement in social welfare. The allocation coefficient of consumers’ additional social value benefits, the degree of the government's digital empowerment subsidy, and the level of the punishment for SOEs that violate the government's cocreation requirements will accelerate the achievement of equilibrium in the social value cocreation system, without affecting the final equilibrium result. By analyzing the strategic choices and interactive relationships among the government, SOEs, and consumers in social value cocreation in-depth, this study offers suggestions to promote the government, SOEs, and consumers’ participation in social value cocreation. This research contributes to clarifying SOEs’ social value cocreation model and has significant implications for promoting enterprises’ high-quality development.

Introduction

Value cocreation has become a characteristic of the times in the digital economy era. As Chinese state-owned enterprises (SOEs) are the backbone of national economic development, they need to “keep up with the times” urgently. ¹ As SOEs under public ownership, they have embedded corporate social responsibility (CSR) and the realization of social value into their development DNA since their inception. Particularly in the face of major events or disasters, SOEs’ social function and social value are particularly evident. ² Therefore, SOEs should embrace the characteristics of the times, use digital technology as a vehicle, and be guided by social value cocreation, which will enable them to create more social value for the general public. ³

In the Chinese scenario, when SOEs shoulder the mission of forward-looking investments and government functions, they often form contractual relationships with the government. ⁴ This implies that while the government enjoys the benefits attributable to SOEs’ social value cocreation, it also pays attention to and influences the process of social value cocreation constantly. However, as an important part of SOEs’ social value cocreation, consumers still hold certain stereotypes, such as “SOEs are synonymous with corruption and inefficiency.”^5,6 Influenced further by the digital age, the general public's biases toward SOEs have increased rapidly, damaged SOEs’ reputation and image severely, and made the path of their social value cocreation highly challenging. Therefore, conducting a thorough analysis of the strategic choices and interactive relationships among the government, SOEs, and consumers in social value cocreation will help clarify SOEs’ social value cocreation model, which is of great significance in promoting enterprises’ high-quality development.

Literature review

Value cocreation is derived from value creation^7,8 and refers to enterprises’ establishment of interactive platforms to engage consumers, and promote interaction between enterprises and consumers, and achieve value cocreation with stakeholders ultimately thereby.^9–13 The concept of value cocreation emphasizes that value is not derived solely from producers, but is established on the basis of consumers’ involvement, and originates from the collaborative creation of value between consumers and enterprises or other relevant stakeholders.^10,13,14 Currently, value cocreation is divided into two forms: economic and social.^15,16 Economic value cocreation refers typically to the process in a business environment where enterprises and customers create economic value collaboratively. ⁹ This form of value cocreation emphasizes the importance of customers’ involvement in product or service design, delivery, and enhancement, and increases market exchanges’ efficiency and effectiveness thereby.^17–20

As another extension of value cocreation, corporate social value cocreation refers to the design and implementation of CSR activities that attract and encourage consumers’ participation, as well as interaction, sharing, and cooperation between corporations and consumers. ²¹ To achieve cocreation of corporate social value, it is essential to establish the core element, i.e. the determination of corporate social value. Currently, there is no explicit and widely accepted definition of the connotation of corporate social value. The prevailing concept of social value suggests that corporate social value is the contribution value that businesses generate for society through their value-creating operations, which encompasses the growth in value achieved by fulfilling social responsibilities, the coordination of stakeholder relationships, and the strategic elements of sustainable development. ²² This is manifested principally in a company's production, product sales, provision of products and services to society, addressing employment issues, optimizing social resource allocation, as well as donations to socially disadvantaged groups or organizations in need.^23,24 Thus, as a derivative model of value cocreation, corporate social value cocreation differs significantly from another model in value cocreation—economic value cocreation. ²⁵ The former focuses more on fulfilling social responsibilities, creating social value, and enhancing social development overall, while the latter concentrates on profit-oriented business development and improving competitiveness. ²⁶

In the existing research on corporate social value cocreation, the main subjects are often small and medium-sized enterprises (SMEs), nonprofit organizations, and large private companies. In the case of SMEs, Sigala studied a social restaurant and used case analysis to identify three market capabilities that generate social value and transformation: network structure, market practices, and market scenes. ²⁷ Through simulated experiments on platform enterprises, Jun et al. found significant differences in behavioral rewards and outcome-based rewards’ effect on consumers’ willingness to continue participating in social value cocreation. ²⁸ With respect to nonprofit organizations, Zhu et al. discovered that collaborations between nonprofit organizations and business organizations can establish multiple partnerships with stakeholders effectively, and realize their social value propositions and alleviate economic inequality thereby. With respect to large private companies, Yi et al. proposed the concept of ecosystem social responsibility in their study of digital platforms’ social responsibility, emphasized the cocreation of social value, and classified the main domains of specific social issues for multinational corporations subsequently. ²⁹ Chen suggested that corporate engagement in social issues can bring long-term benefits, strengthen brand image, promote open innovation in e-government, integrate the social environment into service strategies, and create sustainable value with stakeholders jointly. ³⁰

In summary, existing research focuses primarily on social value cocreation in non-SOEs,^29,31,32 and often employs case studies and similar methods. However, there is a lack of relevant research that addresses SOEs’ social value cocreation specifically as the primary research object. Further, while employing traditional case study methods is beneficial for in-depth analysis of the process of social value cocreation in a particular SOE, the findings from such studies may struggle to explain all SOEs’ social value cocreation processes. The use of evolutionary game theory methods helps address these issues from a macroscopic perspective. In addition, the key factors that influence social value cocreation outcomes in SOEs remain unclear. Therefore, establishing an evolutionary game model among the participants of social value cocreation in SOEs—the government, SOEs, and consumers—will help clarify the complex relationship between SOEs and their stakeholders. This will help identify the key factors that influence SOEs’ social value cocreation behavior, explore the evolutionary development patterns of their social value cocreation, and extend the theoretical boundaries of value cocreation to SOEs in China with distinctive characteristics.

Game theory model

Game player

The government acts as the supervisor and guide of SOEs’ social value cocreation, and it acts in its own interest based upon fiscal revenue and economic development.^33,34 In the process of SOEs’ social value cocreation, the government formulates policies to influence both the SOEs’ and the consumers’ strategic choices based on the cocreation stage and its effects. ³⁵ In addition, the government incurs costs for participating in social value cocreation ³⁶ and works to gain a higher reputation while ensuring the smooth progress of the cocreation activities in which it is involved. Therefore, the government engages in a game with the SOEs and the consumers.

SOEs are the proponents and participants in social value cocreation. On the one hand, as the issues related to social value cocreation can affect additional social value, as participants, SOEs attempt to enhance their own additional social value while ensuring the smooth progress of social value cocreation. ³⁷ On the other hand, SOEs adjust their investment in social value cocreation according to their capabilities to avoid investing high costs without clear returns. ³⁸ Based upon this, they engage in a game with the government and the consumers.

Consumers are the creators of SOEs’ social value cocreation and play a crucial role in the social value cocreation system. Whether or not consumers participate determines social value cocreation's success.^39,40 Based on their own needs and the desire to achieve their own value, consumers hope that the benefits that they obtain from participating in social value cocreation are greater than the improvement in the social welfare level overall. ⁴¹ Thus, they engage in a game with the government and the SOEs based on this.

Game relations

From the perspective of the government's constraint on SOEs, SOEs’ behavior is determined by the government's will and interests. Because of SOEs’ special nature, their behavior is related closely to government decisions.^42,43 When the government chooses to participate in cocreation, SOEs, as a crucial part of the cocreation process, need to participate actively and follow the government's lead closely.

From the perspective of the government's constraint on consumers, the government works to obtain higher consumer reputation and reduce fiscal expenditures, ²¹ while consumers hope to achieve personal value and an improvement in social welfare levels through social value cocreation. ⁴⁴

From the perspective of SOEs’ constraint on consumers, social value cocreation cannot be separated from the CSR activities that the enterprises conduct. ²¹ SOEs must still bear the costs of social value cocreation and can not obtain immediate economic returns to compensate for these costs. ⁴⁵ SOEs are also constrained by policies intended to reduce high debt risks, which restricts their ability to invest in social value cocreation without hesitation. ³⁸ However, consumers hope that SOEs can create more social value and gain benefits from it.

Further, to obtain a tripartite evolutionary game model of social value cocreation that incorporates the government, SOEs, and consumers into the game system (Figure 1), we examine the factors that influence the social value cocreation system's equilibrium. Starting from ability level, cost and digital cost coefficients, conversion rate, degree of input, level of information improvement, additional social value gains, and distribution coefficients, we conduct a further simulation analysis to verify the model's stability and reliability.

Figure 1.

Tripartite game model.

Hypothesis

To achieve equilibrium among the government, SOEs, and consumers in social value cocreation ultimately, we integrate contributions from the existing literature to propose prerequisite assumptions. This is essential to ensure a smooth evolutionary game analysis. The assumptions for the evolutionary game model are as follows:

Hypothesis 1: There are three participating entities in the process of social value cocreation—the government, SOEs, and consumers—all of which are bounded rational entities. The government's strategy set is S₁= (participate, not participate); the SOEs’ strategy set is S₂= (participate, not participate), and the consumers’ strategy set is S₃= (participate, not participate).

Hypothesis 2: The government's probability of choosing to participate is denoted as x ∈ [0,1], with a probability of 1 − x for choosing not to participate; the SOEs’ probability of choosing to participate is denoted as y ∈ [0,1], with a probability of 1 − y for choosing not to participate, and the consumers’ probability of choosing to participate is denoted as z ∈ [0,1], with a probability of 1 − z for choosing not to participate.

Hypothesis 3: Each participating entity possesses its own level of capability.^46,47 the government has a capability level K₁; SOEs have a capability level K₂, and consumers have a capability level K₃. Participating entities will use a portion of their capabilities based upon their actual situations to engage in cocreation. ⁴⁸ This involves the government's input level α1, the enterprise's input level α₂, and the consumers’ input level α₃, with 0 < α₁, α₂, α₃< 1. In the context of social value cocreation, any participating entity's input transformation ratio refers to the proportion at which that entity converts other participating entities’ input capabilities into its own benefits. ⁴⁹ For example, organizations or individuals that participate or do not participate in the system will all enjoy the improvement in social welfare overall that results from cocreation. Hence, each entity within the system has different perceptions and benefits with respect to this level of improvement. Specifically, the government's input transformation ratio is denoted as β₁, the enterprise's input transformation ratio is denoted as β₂, and the consumers’ input transformation ratio is denoted as β₃, with 0 < β₁, β₂, β₃< 1.

Hypothesis 4: When multiple parties participate in cocreating together, value cocreation will generate additional output beyond each party's individual value creation within the cocreation system. ⁵⁰ For instance, there is reciprocity when enterprises engage in cocreating social value with consumers, indicating that the government and enterprises gain higher consumer loyalty and reputation by satisfying consumers’ needs, while consumers obtain spiritual and material satisfaction from cocreation. ³⁷ Therefore, the additional benefits derived from social value cocreation are defined as R. When participating entities choose to engage in cocreation, the additional benefits that result from social value cocreation are distributed according to a certain proportion. This implies that the government's distribution coefficient for additional benefits is γ₁, the enterprise's distribution coefficient is γ₂, and the consumers’ distribution coefficient is γ₃, with γ₁+ γ₂+ γ₃= 1, and 0 ≤ γ₁, γ₂, γ₃< 1.

Hypothesis 5: When the government and SOEs participate in cocreation, they need to incur fixed costs associated with participation. ⁵¹ The government's participation cost coefficient is denoted as C₁, the enterprise's participation cost coefficient is denoted as C₂, and both the government and SOEs will pay costs commensurate with their capability levels. Consumers provide information, such as new product demands and expectations to SOEs, which enable them to participate in cocreation directly or indirectly thereby. ⁵² In this process, consumers do not incur any actual costs for participating in social value cocreation. Thus, this article assumes that consumers do not need to pay any costs to participate in social value cocreation.

Hypothesis 6: When the government and SOEs are empowered by digital technology, information transparency improves because of enhanced information exchange capabilities. However, they also need to bear the development and maintenance costs associated with digital technology. The government's fixed cost for digital technology is denoted as DC₁ and the enterprise's fixed cost for digital technology is denoted as DC₂. The government's degree of improvement in digital technology is denoted as δ₁, the enterprise's degree of improvement is denoted as δ₂, and the consumers’ degree of improvement is denoted as δ₃, with 0 < δ₁, δ₂, δ₃< 1. It is assumed that there is no information asymmetry between the government and SOEs, and after they are empowered by digital technology, SOEs will report all technological improvements to the government. ⁵³ Therefore, there is no difference in the degree of technological improvement between them, i.e. δ₁= δ₂.

Hypothesis 7: Because of the SOEs’ special guidance in fulfilling national missions and responding to national calls, if the government chooses to participate, but SOEs choose not to participate, they will be subject to punishment and incur additional cost C₄.

Function

The trilateral game above is a process of strategy combination and selection, and there are differences in each party's benefits under different strategy combinations. The payoff matrix for the trilateral evolutionary game between the government, SOEs, and consumers is shown in Table 1.

Table 1.

Tripartite evolutionary game payment matrix between government, SOEs, and consumers.

		Consumer	SOE
			Participate	Not participate
Government	Participate	Participate	γ1R + (1 + δ1)β1(α2K2 + α3K3) − (1 − δ1) (C1 + DC1)K1	γ1R + (1 + δ1)β1α3K3 − (1 − δ1) (C1 + DC1)K1
			γ2R + (1 + δ2)β2(α1K1 + α3K3) − (1−δ2) (C2 + DC2)K2	β2((1 + δ1)α1K1 + (1 + δ3)α3K3) − C4K1
			γ3R + (1 + δ3)β3(α1K1 + α2K2)	γ3R + (1 + δ3)β3α1K1
		Not participate	γ1R + (1 + δ1) β1α2K2 − (1 − δ1) (C1 + DC1) K1	−(1 − δ1) (C1 + DC1) K1
			γ2R + (1 + δ2) β2α1K1 − (1 − δ2) (C2 + DC2) K2	(1 + δ1) β2α1K1
			β3((1 + δ1) α1K1 + (1 + δ2) α2K2)	(1 + δ1) β3α1K1
	Not participate	Participate	β1((1 + δ2) α2K2 + (1 + δ3) α3K3)	(1 + δ3) β1α3K3
			γ2R + (1 + δ2) β2α3K3 − (1 − δ2) (C2 + DC2) K2	(1 + δ3) β2α3K3
			γ3R + (1+δ3) β3α2K2	0
		Not Participate	(1 + δ2) β1α2K2	0
			−(1 − δ2) (C2 + DC2) K2	0
			(1 + δ2) β3α2K2	0

Analysis

Evolutionary games attempt to capture the dynamic adjustment process of strategy choices over time, assuming that the players in the game are bounded rationally and seek a balance of average expected payoffs. The average expected payoffs of the three parties involved in the game of SOEs’ social value cocreation behavior are derived from the probabilities of strategy choices and their corresponding expected payoffs.

From the analysis of the payoff matrix, it can be seen that the government's participation in social value cocreation yields a payoff function given by:

$$\begin{array}{c}{\mathrm{U}}_{\mathrm{x}}=yz({\gamma }_1\mathrm{R}+(1+{\delta }_1){\beta }_1({\alpha }_2{\mathrm{K}}_2+{\alpha }_3{\mathrm{K}}_3)-(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1)\end{array}$$

$$\begin{array}{c}+y(1-\mathrm{z})({\gamma }_1\mathrm{R}+(1+{\delta }_1){\beta }_1{\alpha }_2{\mathrm{K}}_2-(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1)\end{array}$$

$$\begin{array}{c}+(1-\mathrm{y})z({\gamma }_1\mathrm{R}+(1+{\delta }_1){\beta }_1{\alpha }_3{\mathrm{K}}_3-(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1)\end{array}$$

$$\begin{array}{c}-(1-\mathrm{y})(1-\mathrm{z})(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1\end{array}$$

(1)

Government's payoff function for the choice of not participating in cocreation is:

$$\begin{array}{c}{\mathrm{U}}_{(1-\mathrm{x})}=yz({\beta }_1((1+{\delta }_2){\alpha }_2{\mathrm{K}}_2+(1+{\delta }_3){\alpha }_3{\mathrm{K}}_3))\end{array}$$

$$\begin{array}{c}+y(1-\mathrm{z})((1+{\delta }_2){\beta }_1{\alpha }_2{\mathrm{K}}_2)\end{array}$$

$$\begin{array}{c}+(1-\mathrm{y})z((1+{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3)\end{array}$$

(2)

The government's average expected payoff is:

$$\begin{array}{c}\overline{{\mathrm{U}}_{\mathrm{x}}}={\mathrm{xU}}_{\mathrm{x}}+(1-\mathrm{x}){\mathrm{U}}_{(1-\mathrm{x})}\end{array}$$

(3)

The payoff function for SOEs that participate in social value cocreation is:

$$\begin{array}{c}{\mathrm{U}}_{\mathrm{y}}=xz({\gamma }_2\mathrm{R}+(1+{\delta }_2){\beta }_2({\alpha }_1{\mathrm{K}}_1+{\alpha }_3{\mathrm{K}}_3)-(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2)\end{array}$$

$$\begin{array}{c}+x(1-\mathrm{z})({\gamma }_2\mathrm{R}+(1+{\delta }_2){\beta }_2{\alpha }_1{\mathrm{K}}_1-(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2)\end{array}$$

$$\begin{array}{c}+(1-\mathrm{x})z({\gamma }_2\mathrm{R}+(1+{\delta }_2){\beta }_2{\alpha }_3{\mathrm{K}}_3-(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2)\end{array}$$

$$\begin{array}{c}-(1-\mathrm{x})(1-\mathrm{z})(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2\end{array}$$

(4)

The payoff function for SOEs that choose not to participate in cocreation is:

$$\begin{array}{c}{\mathrm{U}}_{(1-\mathrm{y})}=xz({\beta }_2((1+{\delta }_1){\alpha }_1{\mathrm{K}}_1+(1+{\delta }_3){\alpha }_3{\mathrm{K}}_3)-{\mathrm{C}}_4{\mathrm{K}}_2)\end{array}$$

$$\begin{array}{c}+x(1-\mathrm{z})(1+{\delta }_1){\beta }_2{\alpha }_1{\mathrm{K}}_1\end{array}$$

$$\begin{array}{c}+(1-\mathrm{x})z(1+{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3\end{array}$$

(5)

The SOEs’ average expected payoff is:

$$\begin{array}{c}\overline{{\mathrm{U}}_{\mathrm{y}}}={\mathrm{yU}}_{\mathrm{y}}+(1-\mathrm{y}){\mathrm{U}}_{(1-\mathrm{y})}\end{array}$$

(6)

The payoff function for consumers who participate in social value cocreation is:

$$\begin{array}{c}{\mathrm{U}}_{\mathrm{z}}=xy({\gamma }_3\mathrm{R}+(1+{\delta }_3){\beta }_3({\alpha }_1{\mathrm{K}}_1+{\alpha }_2{\mathrm{K}}_2))\end{array}$$

$$\begin{array}{c}+x(1-\mathrm{y})({\gamma }_3\mathrm{R}+(1+{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1)\end{array}$$

$$\begin{array}{c}+(1-\mathrm{x})y({\gamma }_3\mathrm{R}+(1+{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2)\end{array}$$

(7)

The payoff function for consumers who choose not to participate in cocreation is:

$$\begin{array}{c}{\mathrm{U}}_{(1-\mathrm{z})}=xy({\beta }_3((1+{\delta }_1){\alpha }_1{\mathrm{K}}_1+(1+{\delta }_2){\alpha }_2{\mathrm{K}}_2))\end{array}$$

$$\begin{array}{c}+x(1-\mathrm{y})((1+{\delta }_1){\beta }_3{\alpha }_1{\mathrm{K}}_1)\end{array}$$

$$\begin{array}{c}+(1-\mathrm{x})y((1+{\delta }_2){\beta }_3{\alpha }_2{\mathrm{K}}_2)\end{array}$$

(8)

The consumers’ average expected payoff is:

$$\begin{array}{c}\overline{{\mathrm{U}}_{\mathrm{z}}}={\mathrm{zU}}_{\mathrm{z}}+(1-\mathrm{z}){\mathrm{U}}_{1-\mathrm{z}}\end{array}$$

(9)

Government stabilization strategy

The replicator dynamics equation in evolutionary game theory delineates the process of proliferation and dissemination of different strategies within a population. ⁵⁴ Presented typically as a mathematical model, the replicator dynamics equation encompasses variables that represent diverse strategies, fitness functions, and differential equations that describe evolutionary rules. Within these equations, different strategies’ success or failure depends upon their relative fitness. This concept has also been introduced into the social sciences, such as in economics and sociology, to study the evolutionary dynamics of human behavior and cultural phenomena. The objective of the replicator dynamics equation is to characterize individual behaviors’ dynamic evolution and to explore different strategies’ dissemination and effect within a population. ⁵⁵

According to the rules of replicator dynamic equations, let F(x) be the probability that the government chooses to participate in the cocreation of social value. Then,

$$\mathrm{F}(\mathrm{x})=\mathrm{x}({\mathrm{U}}_{\mathrm{x}}-\overline{{\mathrm{U}}_{\mathrm{x}}})$$

$$\begin{array}{c}=x(1-\mathrm{x})({\mathrm{U}}_{\mathrm{x}}-{\mathrm{U}}_{(1-\mathrm{x})})\end{array}$$

(10)

By substituting equations (1), (2), and (3) into equation (10), we obtain the replicator dynamic equation for government strategy selection:

$$\begin{array}{c}F(\mathrm{x})=x(1-\mathrm{x})\left(\begin{array}{c}y{\gamma }_{1}R+z{\gamma }_{1}R-yz{\gamma }_{1}R\\ +z({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3\\ -(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1\end{array}\right)\end{array}$$

(11)

Analyzing the replicator dynamic equation and its properties using differential equations’ stability principle, we can determine the stable strategy for the government. Theorem 1 characterizes this stability.

Conclusion 1:

When $\mathrm{z}={\mathrm{z}}_0=\frac{(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1-\mathrm{y}{\gamma }_1\mathrm{R}}{{\gamma }_1\mathrm{R}(1-\mathrm{y})+({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3}$ , the government's behavior remains constant as an equilibrium strategy and does not change over time.

When $\mathrm{z}<\frac{(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1-\mathrm{y}{\gamma }_1\mathrm{R}}{{\gamma }_1\mathrm{R}(1-\mathrm{y})+({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3}$ , there is a stable point at x = 0, indicating that the government chooses not to participate in value cocreation activities.

When $\mathrm{z}<\frac{(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1-\mathrm{y}{\gamma }_1\mathrm{R}}{{\gamma }_1\mathrm{R}(1-\mathrm{y})+({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3}$ , there is an evolutionary equilibrium point at x = 1, indicating that the government chooses to participate in value cocreation activities.

Proof:

The first derivative of the replicator dynamic equation (11) for the government strategy is:

$${\mathrm{F}}^{\mathrm{\prime }}(\mathrm{x})=(1-2\mathrm{x})(\mathrm{y}{\gamma }_1\mathrm{R}+\mathrm{z}{\gamma }_1\mathrm{R}-\mathrm{yz}{\gamma }_1\mathrm{R}+\mathrm{y}({\delta }_1-{\delta }_2){\beta }_1{\alpha }_2{\mathrm{K}}_2-({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1)$$

We have $\mathrm{z}=\frac{(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1-\mathrm{y}{\gamma }_1\mathrm{R}}{{\gamma }_1\mathrm{R}(1-\mathrm{y})+({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3}$ . When $(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1-\mathrm{y}{\gamma }_1\mathrm{R}=0$ , ${\mathrm{F}}^{\mathrm{\prime }}(\mathrm{x})=0$ holds constant. In this case, the government's strategy selection is not affected by any value of x. When $\mathrm{z}<\frac{(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1-\mathrm{y}{\gamma }_1\mathrm{R}}{{\gamma }_1\mathrm{R}(1-\mathrm{y})+({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3}$ , $F^{\mathrm{\prime }}(0)⟨0,F^{\mathrm{\prime }}(1)⟩0$ , indicating that x = 0 is an evolutionary equilibrium point. When $z>\frac{(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1-\mathrm{y}{\gamma }_1\mathrm{R}}{{\gamma }_1\mathrm{R}(1-\mathrm{y})+({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3}$ , $F^{\mathrm{\prime }}(0)>0,F^{\mathrm{\prime }}(1)<0$ , indicating that x = 1 is an evolutionary equilibrium point.

Proof completed

According to Conclusion 1, when SOEs’ and consumers’ strategy choices satisfy certain conditions, the government will not change its current strategy. When SOEs’ and consumers’ strategy choices result in $\mathrm{z}<\frac{(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1-\mathrm{y}{\gamma }_1\mathrm{R}}{{\gamma }_1\mathrm{R}(1-\mathrm{y})+({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3}$ , the government tends to choose not to participate in value cocreation. Conversely, when SOEs’ and consumers’ strategy choices result in $\mathrm{z}>\frac{(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1-\mathrm{y}{\gamma }_1\mathrm{R}}{{\gamma }_1\mathrm{R}(1-\mathrm{y})+({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3}$ , the government tends to choose to participate in value cocreation.

Further, by integrating $\mathrm{z}=\frac{(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1-\mathrm{y}{\gamma }_1\mathrm{R}}{{\gamma }_1\mathrm{R}(1-\mathrm{y})+({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3}$ , we obtain the distribution function of the probability that the government will choose to participate in social value cocreation:

$${\mathrm{V}}_{\mathrm{x}}=\underset{0}{\overset{1}{\int }}\underset{0}{\overset{1}{\int }}{\displaystyle \frac{(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1-\mathrm{y}{\gamma }_1\mathrm{R}}{{\gamma }_1\mathrm{R}(1-\mathrm{y})+({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3}dxdy}$$

$$=1-{\displaystyle \frac{\left(\begin{array}{c}{\gamma }_{1}R+({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1(-1+{\delta }_1)\\ +{\mathrm{K}}_3{\alpha }_3{\beta }_1({\delta }_1-{\delta }_3)\end{array}\right)\mathrm{Log}[{\gamma }_{1}R+{\mathrm{K}}_3{\alpha }_3{\beta }_1({\delta }_1-{\delta }_3)]}{{\gamma }_{1}R}}$$

$$\begin{array}{c}+{\displaystyle \frac{\left(\begin{array}{c}{\gamma }_{1}R+({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1(-1+{\delta }_1)\\ +{\mathrm{K}}_3{\alpha }_3{\beta }_1({\delta }_1-{\delta }_3)\end{array}\right)\mathrm{Log}[{\mathrm{K}}_3{\alpha }_3{\beta }_1({\delta }_1-{\delta }_3)]}{{\gamma }_{1}R}}\end{array}$$

(12)

Thus, the probability distribution of the government's inclination to participate in social value cocreation is:

$$\begin{array}{c}{\mathrm{V}}_{(1-\mathrm{x})}=1-{\mathrm{V}}_{\mathrm{x}}\end{array}$$

$$\begin{array}{c}={\displaystyle \frac{\left(\begin{array}{c}{\gamma }_{1}R+({\mathrm{C}}_1+{\mathrm{DC}}_1)K1(-1+{\delta }_1)\\ +{\mathrm{K}}_3{\alpha }_3{\beta }_1({\delta }_1-{\delta }_3)\end{array}\right)\left(\mathrm{Log}\left[{\displaystyle \frac{{\gamma }_1\mathrm{R}+{\mathrm{K}}_3{\alpha }_3{\beta }_1({\delta }_1-{\delta }_3)}{{\mathrm{K}}_3{\alpha }_3{\beta }_1({\delta }_1-{\delta }_3)}}\right]\right)}{{\gamma }_1\mathrm{R}}}\end{array}$$

Taking partial derivatives of equation 13 with respect to C₁ and DC₁, we find $\frac{\mathrm{\partial }{V}_{(1-x)}}{\mathrm{\partial }{C}_1}$ , $\frac{\mathrm{\partial }{V}_{(1-x)}}{\mathrm{\partial }D{C}_1}<0$ . This result explains that as fixed costs and digital empowerment costs increase, the government tends to choose not to participate in cocreation. Let the additional social value that the government gains in cocreation be denoted as A₁ = γ₁R, then $\frac{\mathrm{\partial }{V}_{(1-x)}}{\mathrm{\partial }{A}_1}>0$ . This indicates that as the government's additional social value benefits increase, the probability that the government will choose to participate in cocreation also increases.

SOEs’ stabilization strategy

According to the rules of replicator dynamics equations, let F(y) be the probability that SOEs will choose to participate in social value cocreation. Then,

$$\mathrm{F}(\mathrm{y})=\mathrm{y}({\mathrm{U}}_{\mathrm{y}}-\overline{{\mathrm{U}}_y})$$

$$\begin{array}{c}=y(1-\mathrm{y})({\mathrm{U}}_y-{\mathrm{U}}_{(1-\mathrm{y})})\end{array}$$

(14)

Substituting equations (4), (5), and (6) into equation (14), we obtain the replicator dynamic equation for government strategy selection as:

$$\begin{array}{c}F(\mathrm{y})=y(1-\mathrm{y})\left(\begin{array}{c}x{\gamma }_{2}R+z{\gamma }_{2}R-xz{\gamma }_{2}R\\ +z({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3\\ -(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2+{\mathrm{xzC}}_4{\mathrm{K}}_2\end{array}\right)\end{array}$$

(15)

Analyzing the replicator dynamic equation and its properties for SOE strategies based upon the stability principle of differential equations reveals the stable strategies for SOEs. Theorem 2 characterizes this.

Conclusion 2:

When $\mathrm{x}={\mathrm{x}}_0=\frac{(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2-\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3}{(1-\mathrm{z}){\gamma }_2\mathrm{R}+{\mathrm{zC}}_4{\mathrm{K}}_2}$ , at this point, any behavior of SOEs is always an equilibrium strategy and will not change over time.

When $\mathrm{x}<\frac{(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2-\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3}{(1-\mathrm{z}){\gamma }_2\mathrm{R}+{\mathrm{zC}}_4{\mathrm{K}}_2}$ , there is a stable point at y = 0, indicating that SOEs choose not to participate in value cocreation activities.

When $\mathrm{x}>\frac{(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2-\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3}{(1-\mathrm{z}){\gamma }_2\mathrm{R}+{\mathrm{zC}}_4{\mathrm{K}}_2}$ , there is an evolutionary equilibrium point at y  =  1, indicating that SOEs choose to participate in value cocreation activities.

Proof:

The first derivative of the replicator dynamic equation (15) for SOE strategies is:

$${\mathrm{F}}^{\mathrm{\prime }}(\mathrm{y})=(1-2\mathrm{y})(\mathrm{x}{\gamma }_2\mathrm{R}+\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{xz}{\gamma }_2\mathrm{R}+\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3$$

$$-(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2+{\mathrm{xzC}}_4{\mathrm{K}}_2)$$

Then, we have $\mathrm{x}=\frac{(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2-\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3}{(1-\mathrm{z}){\gamma }_2\mathrm{R}+{\mathrm{zC}}_4{\mathrm{K}}_2}$ . When $(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2)$ ${\mathrm{K}}_2-\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3=0$ , ${\mathrm{F}}^{\mathrm{\prime }}(\mathrm{y})=0$ holds constant. In this case, no value affects the selection of SOE strategies. When $\mathrm{x}<\frac{(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2-\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3}{(1-\mathrm{z}){\gamma }_2\mathrm{R}+{\mathrm{zC}}_4{\mathrm{K}}_2}$ , $F^{\mathrm{\prime }}(0)⟨0,F^{\mathrm{\prime }}(1)⟩0$ ; therefore, y = 0 is an evolutionary equilibrium point. When $\mathrm{x}>\frac{(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2-\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3}{(1-\mathrm{z}){\gamma }_2\mathrm{R}+{\mathrm{zC}}_4{\mathrm{K}}_2}$ , $F^{\mathrm{\prime }}(0)>0,F^{\mathrm{\prime }}(1)<0$ ; therefore, y = 1 is an evolutionary equilibrium point.

Proof completed.

According to Conclusion 2, when the government and consumers’ strategy selection satisfies a certain condition, SOEs will not change their current strategy. When the government and consumers’ strategy selection leads to $\mathrm{x}<\frac{(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2-\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3}{(1-\mathrm{z}){\gamma }_2\mathrm{R}+{\mathrm{zC}}_4{\mathrm{K}}_2}$ , SOEs are more inclined to choose not to participate in value cocreation. Conversely, when the government and consumers’ strategy selection results in $\mathrm{x}>\frac{(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2-\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3}{(1-\mathrm{z}){\gamma }_2\mathrm{R}+{\mathrm{zC}}_4{\mathrm{K}}_2}$ , SOEs are more inclined to choose to participate in value cocreation.

Further, integrating with respect to $\mathrm{x}=\frac{(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2-\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3}{(1-\mathrm{z}){\gamma }_2\mathrm{R}+{\mathrm{zC}}_4{\mathrm{K}}_2}$ , we can obtain the distribution function for the probability that SOEs choose to participate in social value cocreation as:

$${\mathrm{V}}_{\mathrm{y}}=\underset{0}{\overset{1}{\int }}\underset{0}{\overset{1}{\int }}{\displaystyle \frac{(1-{\delta }_2)({\mathrm{C}}_2+{\mathrm{DC}}_2){\mathrm{K}}_2-\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3}{(1-\mathrm{z}){\gamma }_2\mathrm{R}+{\mathrm{zC}}_4{\mathrm{K}}_2}\mathrm{dzdy}}$$

$$\begin{array}{c}=-{\displaystyle \frac{\begin{array}{c}({\mathrm{C}}_4{\mathrm{K}}_2-\mathrm{R}{\gamma }_2)(\mathrm{R}{\gamma }_2+{\mathrm{K}}_3{\alpha }_3{\beta }_2({\delta }_2-{\delta }_3))\\ +({\mathrm{C}}_4{\mathrm{DC}}_2{\mathrm{K}}_2^2(-1+{\delta }_2)+{\mathrm{C}}_2{\mathrm{K}}_2({\mathrm{C}}_4{\mathrm{K}}_2-R{\gamma }_2)(-1+{\delta }_2)\\ -R{\gamma }_2(\mathrm{R}{\gamma }_2+{\mathrm{DC}}_2{\mathrm{K}}_2(-1+{\delta }_2)+{\mathrm{K}}_3{\alpha }_3{\beta }_2({\delta }_2-{\delta }_3)))\left(Log\left[{\displaystyle \frac{{\mathrm{C}}_4{\mathrm{K}}_2}{\mathrm{R}{\gamma }_2}}\right]\right)\end{array}}{{({\mathrm{C}}_4{\mathrm{K}}_2-\mathrm{R}{\gamma }_2)}^2}}\end{array}$$

(16)

Therefore, the probability that SOEs tend to choose to participate in social value cocreation is:

$${\mathrm{V}}_{(1-\mathrm{y})}=1-{\mathrm{V}}_{\mathrm{y}}$$

$$\begin{array}{c}=1+{\displaystyle \frac{\begin{array}{c}({\mathrm{C}}_4{\mathrm{K}}_2-\mathrm{R}{\gamma }_2)(\mathrm{R}{\gamma }_2+{\mathrm{K}}_3{\alpha }_3{\beta }_2({\delta }_2-{\delta }_3))\\ +({\mathrm{C}}_4{\mathrm{DC}}_2{\mathrm{K}}_2^2(-1+{\delta }_2)+{\mathrm{C}}_2{\mathrm{K}}_2({\mathrm{C}}_4{\mathrm{K}}_2-R{\gamma }_2)(-1+{\delta }_2)\\ -R{\gamma }_2(\mathrm{R}{\gamma }_2+{\mathrm{DC}}_2{\mathrm{K}}_2(-1+{\delta }_2)+{\mathrm{K}}_3{\alpha }_3{\beta }_2({\delta }_2-{\delta }_3)))\left(Log\left[{\displaystyle \frac{{\mathrm{C}}_4{\mathrm{K}}_2}{\mathrm{R}{\gamma }_2}}\right]\right)\end{array}}{{({\mathrm{C}}_4{\mathrm{K}}_2-\mathrm{R}{\gamma }_2)}^2}}\end{array}$$

(17)

Taking partial derivatives of Equation (17) with respect to its constituents, we have $\frac{\mathrm{\partial }{V}_{(1-y)}}{\mathrm{\partial }{C}_2}<0$ , indicating that as the cost of SOEs’ participation in cocreation increases, their probability of choosing to participate decreases. $\frac{\mathrm{\partial }{V}_{(1-y)}}{\mathrm{\partial }{\mathrm{C}}_4}>0$ , showing that the probability that SOEs will participate in cocreation is influenced positively by the setting of penalty fines.

Consumers’ stabilization strategy

According to the rule of replicator dynamics, let us define F(z) as the change probability for consumers to choose to participate in social value cocreation:

$$\mathrm{F}(\mathrm{z})=\mathrm{z}({\mathrm{U}}_z-\overline{{\mathrm{U}}_z})$$

$$\begin{array}{c}=z(1-\mathrm{z})({\mathrm{U}}_z-{\mathrm{U}}_{(1-\mathrm{z})})\end{array}$$

(18)

Substituting equations (7), (8), and (9) into equation (18), we obtain the replicator dynamic equation for the government's strategy selection as:

$$\begin{array}{c}F(\mathrm{z})=z(1-\mathrm{z})\left(\begin{array}{c}x{\gamma }_{3}R+y{\gamma }_{3}R-xy{\gamma }_{3}R\\ -x({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1\\ -y({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2\end{array}\right)\end{array}$$

(19)

By analyzing the replicator dynamic equation and its properties of consumers’ strategy using the principle of stability of differential equations, we can determine consumers’ stable strategies. Theorem 3 characterizes this situation.

Conclusion 3:

When $\mathrm{y}={\mathrm{y}}_0=\frac{-\mathrm{x}{\gamma }_3\mathrm{R}+\mathrm{x}({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1}{(1-\mathrm{x}){\gamma }_3\mathrm{R}-({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2}$ , any action by the consumers is an equilibrium strategy that remains unchanged over time.

When $\mathrm{y}<\frac{-\mathrm{x}{\gamma }_3\mathrm{R}+\mathrm{x}({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1}{(1-\mathrm{x}){\gamma }_3\mathrm{R}-({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2}$ , there is a stable point at z = 0, indicating that consumers choose not to participate in value cocreation activities.

When $\mathrm{y}>\frac{-\mathrm{x}{\gamma }_3\mathrm{R}+\mathrm{x}({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1}{(1-\mathrm{x}){\gamma }_3\mathrm{R}-({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2}$ , there is a stable point at z = 1, indicating that consumers choose to participate in value cocreation activities.

Proof:

The first derivative of the replicator dynamic equation given by equation (19) is:

$${\mathrm{F}}^{\mathrm{\prime }}(\mathrm{z})=(1-2\mathrm{z})\left(\begin{array}{c}x{\gamma }_{3}R+y{\gamma }_{3}R-xy{\gamma }_{3}R\\ -x({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1\\ -y({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2\end{array}\right)$$

When $\mathrm{y}=\frac{-\mathrm{x}{\gamma }_3\mathrm{R}+\mathrm{x}({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1}{(1-\mathrm{x}){\gamma }_3\mathrm{R}-({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2}$ , if $-\mathrm{x}{\gamma }_3\mathrm{R}+\mathrm{x}({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1=0$ , then $F^{\mathrm{\prime }}(\mathrm{z})=0$ always holds. In this case, any value of y will not affect the consumers’ strategy selection. When $\mathrm{y}<\frac{-\mathrm{x}{\gamma }_3\mathrm{R}+\mathrm{x}({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1}{(1-\mathrm{x}){\gamma }_3\mathrm{R}-({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2}$ , we have $F^{\mathrm{\prime }}(0)⟨0,F^{\mathrm{\prime }}(1)⟩0$ , indicating that z = 0 is an evolutionary equilibrium point. When $F^{\mathrm{\prime }}(0)⟨0,F^{\mathrm{\prime }}(1)⟩0$ , we have $F^{\mathrm{\prime }}(0)>0,F^{\mathrm{\prime }}(1)<0$ , indicating that z = 1 is an evolutionary equilibrium point.

Proof completed

According to Conclusion 3, when the government and SOEs’ strategy choices satisfy a specific condition, consumers will not change their current strategies. When the government and SOEs’ strategy choices result in $\mathrm{y}<\frac{-\mathrm{x}{\gamma }_3\mathrm{R}+\mathrm{x}({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1}{(1-\mathrm{x}){\gamma }_3\mathrm{R}-({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2}$ , consumers are more likely to choose not to participate in value cocreation. Conversely, when the government and SOEs’ strategy choices lead to $\mathrm{y}>\frac{-\mathrm{x}{\gamma }_3\mathrm{R}+\mathrm{x}({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1}{(1-\mathrm{x}){\gamma }_3\mathrm{R}-({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2}$ , consumers are more likely to choose to participate in value cocreation.

Further, by integrating $\mathrm{y}=\frac{-\mathrm{x}{\gamma }_3\mathrm{R}+\mathrm{x}({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1}{(1-\mathrm{x}){\gamma }_3\mathrm{R}-({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2}$ , we obtain the distribution function for the probability that consumers participate in social value cocreation:

$$\begin{array}{c}{\mathrm{V}}_{\mathrm{z}}=\underset{0}{\overset{1}{\int }}\underset{0}{\overset{1}{\int }}{\displaystyle \frac{-\mathrm{x}{\gamma }_3\mathrm{R}+\mathrm{x}({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1}{(1-\mathrm{x}){\gamma }_3\mathrm{R}-({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2}dxdy}\end{array}$$

$$\begin{array}{c}={\displaystyle \frac{\begin{array}{c}({\gamma }_3\mathrm{R}-{\beta }_3{\alpha }_1{\mathrm{K}}_1({\delta }_1-{\delta }_3))\\ \left({\gamma }_3\mathrm{R}+({\gamma }_3\mathrm{R}-{\beta }_3{\alpha }_2{\mathrm{K}}_2({\delta }_2-{\delta }_3))\left(\mathrm{Log}\left[{\displaystyle \frac{{\beta }_3{\alpha }_2{\mathrm{K}}_2({\delta }_2-{\delta }_3)}{-{\gamma }_3\mathrm{R}+{\beta }_3{\alpha }_2{\mathrm{K}}_2({\delta }_2-{\delta }_3)}}\right]\right)\right)\end{array}}{{\gamma }_3{\mathrm{R}}^2}}\end{array}$$

(20)

Thus, the probability of consumers’ inclination to participate in social value cocreation is:

$$\begin{array}{c}{\mathrm{V}}_{(1-\mathrm{z})}=1-{\mathrm{V}}_{\mathrm{z}}\end{array}$$

$$\begin{array}{c}=1-{\displaystyle \frac{\begin{array}{c}({\gamma }_3\mathrm{R}-{\beta }_3{\alpha }_1{\mathrm{K}}_1({\delta }_1-{\delta }_3))\\ \left({\gamma }_3\mathrm{R}+({\gamma }_3\mathrm{R}-{\beta }_3{\alpha }_2{\mathrm{K}}_2({\delta }_2-{\delta }_3))\left(\mathrm{Log}\left[{\displaystyle \frac{{\beta }_3{\alpha }_2{\mathrm{K}}_2({\delta }_2-{\delta }_3)}{-{\gamma }_3\mathrm{R}+{\beta }_3{\alpha }_2{\mathrm{K}}_2({\delta }_2-{\delta }_3)}}\right]\right)\right)\end{array}}{{\gamma }_3{\mathrm{R}}^2}}\end{array}$$

The partial derivative of Equation 21 with respect to each element indicates that $\frac{\mathrm{\partial }{V}_{(1-z)}}{\mathrm{\partial }{A}_2}>0$ , which suggests that when consumers can allocate more additional social value benefits, the probability of their participation in cocreation increases.

Evolutionary game path analysis

According to the replicator dynamic equations of the government, SOEs, and consumers, the Jacobian matrix of the system can be obtained as follows:

$$J=\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]$$

$${\mathrm{a}}_{11}=(1-2\mathrm{x})(\mathrm{y}{\gamma }_1\mathrm{R}+\mathrm{z}{\gamma }_1\mathrm{R}-\mathrm{yz}{\gamma }_1\mathrm{R}$$

$$+\mathrm{z}({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3-(1-{\delta }_1)({\mathrm{C}}_1+{\mathrm{DC}}_1){\mathrm{K}}_1)$$

$${\mathrm{a}}_{12}=\mathrm{x}(1-\mathrm{x})({\gamma }_1\mathrm{R}-\mathrm{z}{\gamma }_1\mathrm{R})$$

$${\mathrm{a}}_{13}=\mathrm{x}(1-\mathrm{x})({\gamma }_1\mathrm{R}-\mathrm{y}{\gamma }_1\mathrm{R}+({\delta }_1-{\delta }_3){\beta }_1{\alpha }_3{\mathrm{K}}_3$$

$${\mathrm{a}}_{21}=\mathrm{y}(1-\mathrm{y})({\gamma }_2\mathrm{R}-\mathrm{z}{\gamma }_2\mathrm{R}+{\mathrm{zC}}_4{\mathrm{K}}_2)$$

$${\mathrm{a}}_{22}=(1-2\mathrm{y})(\mathrm{x}{\gamma }_2\mathrm{R}+\mathrm{z}{\gamma }_2\mathrm{R}-\mathrm{xz}{\gamma }_2\mathrm{R}+\mathrm{z}({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3-(1-{\delta }_2)$$

$${\mathrm{a}}_{23}=\mathrm{y}(1-\mathrm{y})({\gamma }_2\mathrm{R}-\mathrm{x}{\gamma }_2\mathrm{R}+({\delta }_2-{\delta }_3){\beta }_2{\alpha }_3{\mathrm{K}}_3+{\mathrm{xC}}_4{\mathrm{K}}_2)$$

$${\mathrm{a}}_{31}=\mathrm{z}(1-\mathrm{z})({\gamma }_3\mathrm{R}-\mathrm{y}{\gamma }_3\mathrm{R}-({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1)$$

$${\mathrm{a}}_{32}=\mathrm{z}(1-\mathrm{z})({\gamma }_3\mathrm{R}-\mathrm{x}{\gamma }_3\mathrm{R}-({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2)$$

$${\mathrm{a}}_{33}=(1-2\mathrm{z})(\mathrm{x}{\gamma }_3\mathrm{R}+\mathrm{y}{\gamma }_3\mathrm{R}-\mathrm{xy}{\gamma }_3\mathrm{R}$$

$$-\mathrm{x}({\delta }_1-{\delta }_3){\beta }_3{\alpha }_1{\mathrm{K}}_1-\mathrm{y}({\delta }_2-{\delta }_3){\beta }_3{\alpha }_2{\mathrm{K}}_2)$$

By setting the aforementioned parties’ replicator dynamic equations to zero and solving them simultaneously, we can determine the equilibrium points that need to be discussed in the system. These equilibrium points are P₁ (00,0), P₂ (10,0), P₃ (01,0) P₄ (00,1), P₅ (11,0), P₆ (10,1), P₇ (01,1), P₈ (11,1).

In the evolutionary game theory, the Jacobian matrix's eigenvalues provide crucial insights into the system's stability and equilibria. ⁵⁶ The Jacobian matrix describes the local dynamics near equilibrium points in evolutionary game models, and its eigenvalues serve to elucidate these equilibria's stability or instability. Eigenvalues indicate how changes in strategy combinations near equilibrium points will influence the system's dynamic evolution. If all eigenvalues are negative, the equilibrium point is stable, signifying that the system will tend to return to this point when perturbed. Conversely, the presence of positive eigenvalues suggests that the equilibrium point may be unstable, and deviations from the equilibrium lead the system away from it. Complex eigenvalues imply potential oscillatory or periodic behavior in the system. Hence, the Jacobian matrix's eigenvalues offer critical insights into the evolutionary game models’ stability. Analysis of these eigenvalues allows for a better understanding of the influence of different strategy combinations on system stability and the dynamic behavior around equilibrium points. By substituting the eight equilibrium points above into the Jacobian matrix, the eigenvalues of the system's Jacobian matrix can be obtained as shown in Table 2.

Table 2.

Eigenvalues of Jacobian matrix at equilibrium points and stability analysis.

Equilibriumpoint	Jacobian matrix eigenvalue		Conclusion	Condition
	λ1, λ2, λ3	Sign
(00,0)	(0, −(1 − δ1) (C1 + DC1) K1, −(1 − δ2) (C2 + DC2) K2)	(0, −, −)	Uncertainty
(10,0)	(Rγ3 − K1α1β3 (δ1 − δ3), (1 − δ1) (C1 + DC1) K1, Rγ2 − (1 − δ2) (C2 + DC2) K2)	(+, +, +)/ (×, +, +)	Saddle point
(01,0)	(Rγ3 − K2α2β3 (δ2−δ3), (1−δ2) (C2 + DC2) K2, Rγ1 − (1 − δ1) (C1 + DC1) K1)	(+, +, +)/ (×, +, +)	Saddle point
(00,1)	(0, Rγ1 + K3α3β1 (δ1 − δ3) − (1 − δ1) (C1 + DC1) K1, Rγ2 + K3α3β2 (δ2 − δ3) − (1 − δ2) (C2 + DC2) K2)	(0, +, +)	Uncertainty
(11,0)	(Rγ3 − K1α1β3 (δ1 − δ3) − K2α2β3 (δ2 − δ3), (1 − δ1) (C1 + DC1) K1 − Rγ1, (1 − δ2) (C2 + DC2) K2 − Rγ2	(+, −, −)/(−, −, −)	Saddle point/ESS	(1)/(3)
(10,1)	(K1α1β3 (δ1 − δ3) − Rγ3, (1-δ1)(C1 + DC1)K1-Rγ1-K3α3β1(δ1-δ3), Rγ2 − (1 − δ2) (C2 + DC2) K2 + C4K2 + K3α3β2 (δ2 − δ3)	(−, −, +)/(×, −, +)	Saddle point
(01,1)	(K2α2β3(δ2-δ3)-Rγ3, Rγ1 + K3α3β1(δ1 − δ3) − (1 − δ1) (C1 + DC1) K1, (1−δ2) (C2 + DC2) K2 − Rγ2 − K3α3β2 (δ2 − δ3))	(−, +, −)/(×, +, −)	Saddle point
(11,1)	(K1α1β3 (δ1 − δ3) + K2α2β3 (δ2 − δ3) − Rγ3, (1 − δ1) (C1 + DC1) K1 − Rγ1 − K3α3β1 (δ1 − δ3), (1 − δ2) (C2 + DC2) K2 − Rγ2 − K3α3β2 (δ2 − δ3)) − C4K2	(−,−,−)/(+, −, −)	ESS/saddle point	(1)(2)/(3)

Note: (1) As consumers do not need to pay for the cost of participating in cocreation, they are willing to participate in cocreation only if the additional social value that they obtain from cocreation is greater than their benefits from SOEs and government, i.e. K₁α₁β₃ (δ₁ – δ₃) + K₂α₂β₃ (δ₂ − δ₃) < Rγ₃. (2) The cost of each party's cocreation is always less than the total benefits that they receive from participating in cocreation. (3) When K₁α₁β₃ (δ₁− δ₃) + K₂α₂β₃ (δ₂ − δ₃)>Rγ₃, i.e. when the additional social value consumers gain is less than their conversion benefits, consumers are more inclined not to engage in cocreation.

SOE: state-owned enterprise.

Based on Table 2, it is evident that in the context of a three-player game, equilibrium (ESS) is achieved and stabilized only if all eigenvalues λ_i associated with the tripartite interaction are negative. Specifically, the presence of any eigenvalue λ_i> 0 or λ_i= 0 for any individual player would denote the existence of a saddle point or an indeterminate point.

Because of the consumers’ autonomy, the government or SOEs cannot force consumers to participate in cocreation or impose punishment mechanisms. Therefore, this article discusses and considers only two situations: successful cocreation and consumers’ unilateral nonparticipation, i.e. Situation 1 P8 (11,1) and Situation 2 P5 (11,0). The equilibrium phase diagram for these two situations overall is shown in Figure 2.

Figure 2.

Overall phase diagram under different situations.

Situation 1: When both conditions (1) and (2) are present, P8 (11,1) is the system's unique evolutionary equilibrium strategy. This means that when the government or SOEs propose value cocreation issues as the proponents of social value cocreation, and the system satisfies both conditions (1) and (2), the system will reach an equilibrium point eventually where all parties choose to participate in cocreation. To achieve a final equilibrium strategy that satisfies the government or SOEs, conditions (1) and (2) are the basic requirements for successful value cocreation.

Situation 2: When condition (3) occurs, P8 (11,1) is no longer the unique evolutionary equilibrium strategy, but becomes an unstable point. On the other hand, P5 (11,0) transitions from an unstable point to a stable equilibrium point. This means that although the consumers do not need to pay any co-creation costs and the other two parties are involved in cocreation highly, if the additional social value that the consumers gain is less than their conversion benefits from the other two parties, the consumers are still more inclined not to participate in cocreation. Because of the consumers’ unilateral passivity, the co-creation activity fails to reach a successful equilibrium point.

Simulation analysis

To analyze various factors’ effect on the evolution trend of the social value cocreation system in SOEs further, this study uses MATLAB2019a to simulate the evolutionary states of the three parties in the game within the system. This is performed to provide a more intuitive analysis of different factors’ influence on the participating entities’ behavioral choices.

Evolutionary analysis process under different situations

In order to more intuitively reflect the evolutionary path of the system, this study will use numerical simulation, combined with simulated data provided by an SOE in China, to set the initial parameter values as shown in Table 3.

Table 3.

The initial value settings of the parameters for each situation.

Parameter	Situation 1	Situation 2	Parameter	Situation 1	Situation 2
C1	0.05	0.05	γ3	0.33	0.33
C2	0.05	0.05	α1	0.5	0.5
K1	20	20	α2	0.5	0.5
K2	20	20	α3	0.5	0.5
K3	10	10	β1	0.01	0.01
R	9	0.1	β2	0.01	0.01
DC1	0.02	0.02	β3	0.01	0.01
DC2	0.02	0.02	δ1	0.5	1
C4	0.05	0.05	δ2	0.5	1
γ1	0.33	0.33	δ3	0.5	0
γ2	0.33	0.33

The evolution results of the various game players in the social value cocreation system under different situations are shown in Figure 3. In the figure, it can be observed that in Situation 1, the convergence points of all game players within the system are “participate in cocreation” and reach equilibrium quickly. In Situation 2, the convergence points of the government and SOEs are “participate in cocreation,” but the convergence speed is slower compared to Situation 1. The convergence point of consumers is “not participate in cocreation,” and the convergence speed is also slow.

Figure 3.

The evolution results of game players in the system under different situations.

When the system's parameter settings satisfy the equilibrium condition P8 aforementioned, the consumer's additional social value gain exceeds its transformation gain. Therefore, the consumer is more inclined to participate in cocreation and accelerates the convergence of the government and SOE players. Conversely, when the parameter settings satisfy the equilibrium condition P5 aforementioned, the consumer's additional social value gain is less than its transformation gain. As a result, the consumer is unwilling to participate in cocreation, which affects the government and SOE players’ convergence speed negatively. However, because of the government and SOE players’ mission or call, both still converge toward the “participate in cocreation” side.

The evolution results of the system under different situations overall are shown in Figure 4. The figure shows that in Situation 1, the strategy choices of all game players within the system converge to “participate, participate, participate,” while in Situation 2, the system's strategy choices converge to “participate, participate, not participate.” As consumers are the only game players in the system who are difficult to incentivize through rewards and punishments for cocreation, their strategy choices determine the success or failure of cocreation in the system overall. Therefore, to achieve success, where the strategy choices converge to “participate, participate, participate,” regardless of the adjustable coefficients set within the system, the primary condition is that the proponents of value propositions must predict cocreation outcomes and ensure the satisfaction of the conditions aforementioned ((1) and (2)).

Figure 4.

The evolution results of the system in different situations.

Effect of additional social value allocation coefficients on participants’ strategy choices

To explore parameter variations’ effects on the success of social value cocreation behaviors, this subsection sets the initial evolution parameters according to Situation 1 in Table 3.

There are three types of allocation coefficients in the system, i.e. equal distribution, “to each according to their ability and contribution,” and “favoring the people” policy. In equal distribution, the additional social value created through cocreation is distributed evenly among the three parties. In the “to each according to their ability and contribution” scenario, the party with greater abilities and contributions receives a larger allocation coefficient. Conversely, in the “favoring the people” policy, the party with greater abilities relinquishes a portion of their allocation to the other parties willingly. For ease of calculation, the allocation coefficient formula for the “to each according to their ability and contribution” scenario is defined as:

$$\begin{array}{c}{\gamma }_i={\displaystyle \frac{{\alpha }_i{K}_i}{{\sum }_{j=1}^3{a}_j{K}_j}}\end{array}$$

(22)

Keeping other parameters constant, the three scenarios’ allocation coefficient values are as follows: γ1 = γ2 = γ3 = 0.33； γ1 = γ2 = 0.4, γ3 = 0.2； γ1 = γ2 = 0.1, γ3 = 0.8.

The four subgraphs in Figure 5 correspond to the additional social value allocation coefficients’ effect on the convergence process and outcomes for the government, SOEs, consumers, and the cocreation among the three parties overall. In Figure 5, it can be observed that the convergence results for the government and SOEs that choose to participate in cocreation are not affected by their allocation coefficients and converge eventually toward participation. However, their convergence speed slows to some extent as the allocation coefficients decrease. Under the background of Situation 1, the convergence results for consumers are also unaffected by their allocation coefficients and converge ultimately toward participation in cocreation. However, their convergence speed increases to some extent as their allocation coefficients increase.

Figure 5.

The evolutionary simulation diagram of each game player with different distribution coefficients.

The simulation results of the system overall are shown in Figure 6. The figure shows that when the allocation coefficients are at different levels, the strategy set of the game system overall converges to “participate, participate, participate.” However, the convergence trends vary to some extent:

When the allocation coefficients are in the equal distribution scenario, the convergence trend of the system overall is stable and increasing.

In the “to each according to their ability and contribution” scenario, because of the fewer additional social value gains for consumers, they exhibit a slower convergence speed. This affects SOEs’ initial enthusiasm to participate in social value cocreation slightly.

In the “favoring the people” policy scenario, with higher allocation coefficients for consumers, their convergence speed in participating in cocreation increases significantly. This encourages the government and SOEs further to invest actively in the social value cocreation system. In this state, the system's convergence speed overall is the highest.

Figure 6.

The evolutionary simulation diagram of the distribution coefficient to the overall system.

From the above, it can be concluded that although the asymmetry in allocation coefficients does not affect social value cocreation's final evolutionary outcome, it does have an effect on the evolutionary process. Social value cocreation is a continuous process in which all game players join continuously and create social value together. To ensure system stability and achieve the fastest equilibrium speed, adopting the “favoring the people” policy with higher allocation coefficients for consumers can be a good choice.

Influence of the digital empowerment cost coefficient

In general, enterprises are responsible for covering the costs of digital empowerment embedded within a cocreation system of social value. However, when SOEs incur such costs, the government may provide varying degrees of subsidies that lead to continuous fluctuations in the cost coefficient of digital empowerment for both the government and SOEs. When SOEs pay for digital costs, the government may provide them with subsidies that result in continuous changes in the digital empowerment cost coefficient for both the government and SOEs. To facilitate simulation analysis, this study examines three representative subsidy scenarios: full government subsidy; half government subsidy, and no government subsidy. While other parameters are held constant, the parameter settings for these three subsidy scenarios are as follows: DC₁= 0.04, DC₂= 0; DC₁= DC₂= 0.02; DC₁= 0, DC₂= 0.04.

Figure 7 consists of four subfigures that represent the convergence process and the digital empowerment cost coefficient's effect on the government, SOEs, consumers, and the triple graph. The figure shows that the convergence results of the government's strategy choice are unaffected by the level of its subsidies for SOEs. However, the convergence speed will decrease slightly as the subsidy increases. The convergence results of SOEs are also unaffected by the government's subsidy level, but their convergence speed will accelerate as the subsidy level increases. The convergence results and speed of consumer strategy choices are not influenced by the subsidy level.

Figure 7.

Evolutionary simulation graphs of the digital empowerment cost for various game entities.

The simulation results of the system overall are given in Figure 8. As the figure shows, when the digital cost coefficient keeps changing, all game entities’ strategy sets converge to (participate, participate, participate), but the convergence speed and trend vary to a certain extent. When the government provides full subsidies, the system converges fastest, and all game entities respond actively. When the government provides half subsidies, the SOEs’ proactiveness in social value cocreation is weakened to some extent, but the consumers’ proactiveness is also weakened slightly within a small range. When the government does not provide subsidies, SOEs’ proactiveness in social value cocreation is weakened significantly, but it does not affect the final evolutionary results. From the results, it can be concluded that as the level of government subsidies increases, the system's convergence speed and all parties’ proactiveness in choosing to participate in social value cocreation will increase continuously. Although short-term cocreation outcomes may vary slightly, they do not affect the final results.

Figure 8.

Evolutionary simulation graph of the digital empowerment on the system overall.

Influence of the penalty coefficient

The government has a responsibility for SOEs, and SOEs also have an obligation to respond to the government. When SOEs choose not to respond to the government, and therefore do not participate in social value cocreation for reasons such as reducing debt risk, the government may require them to pay penalties. If the penalty's size is set uniformly, it may be inconsequential for large enterprises, but detrimental to small enterprises. Therefore, this article adopts a coefficient model for penalties that vary with the size of the enterprise's capability. It explores three meaningful settings for the penalty coefficient: the penalty coefficient equals the total cost coefficient of the enterprise's participation in cocreation (C_T); no penalty coefficient is imposed, and the penalty coefficient is smaller than the total cost coefficient of the enterprise's participation in social value cocreation. While keeping other coefficients constant, the parameter settings for these three penalty coefficient scenarios are as follows: C₄> C_T; C₄= 0; C₄< C_T.

Figure 9 consists of four subfigures that represent the convergence process and the penalty coefficient's effect on the government, SOEs, consumers, and the triple graph. The figure shows that the convergence results of the government's strategy choice are unaffected by the penalty, and the influence on the convergence speed is minimal. The convergence outcome of SOEs’ strategic choices is not influenced by the penalty coefficient, but as the penalty coefficient increases, the convergence speed of SOEs’ strategic choices accelerates significantly. The convergence outcome of consumers’ strategic choices also is not affected by the penalty coefficient; however, as the penalty coefficient increases, their convergence speed accelerates slightly.

Figure 9.

Evolutionary simulation graphs of the penalty coefficient on various game entities.

The simulation results of the system overall are shown in Figure 10. From the figure, it can be seen that the change in the penalty coefficient does not affect the convergence speed of the game between the government and consumers. However, as the penalty coefficient increases, SOEs’ willingness to participate in cocreation increases, albeit only slightly. This phenomenon suggests that because of reasons such as the national mission that SOEs carry out, it is difficult for them not to respond to the government's call. Therefore, although setting penalties accelerates the speed of SOEs’ participation in social value co-creation slightly, its influence is small and does not affect the final equilibrium point. During the convergence process, the system's convergence speed overall experiences a certain degree of acceleration as the penalty coefficient increases.

Figure 10.

Evolutionary simulation graph of the penalty coefficient on the overall system.

Discussion

Based on the evolutionary game model, this study investigates the social value cocreation on the part of the government, SOEs, and consumers, and draws the following conclusions: (1) By studying different scenarios of the social value cocreation system, it is found that social value cocreation's success depends upon the balance between the additional social value benefits that consumers obtained and their conversion gains. Because of government policies and appeals, as well as SOEs’ mission and nature, both parties tend to participate in social value cocreation under any circumstances. Therefore, consumers become the decisive factor in social value cocreation. When the additional social value benefits that consumers obtain are less than their conversion gains, the three parties cannot achieve social value cocreation. Conversely, all parties are willing to participate and achieve social value cocreation. (2) By adjusting the coefficient of additional social value allocation, it is found that this coefficient affects the process of social value cocreation for individual game entities and the system overall. Compared to “equal distribution” and “according to labor contribution” policies, the “pro-people policy” accelerates all parties’ cooperative behavior in the social value cocreation system. (3) By observing the changes in the cost of digital empowerment, it is found that the cost of digital empowerment and the implementation of subsidy policies have a certain effect on the government and SOEs’ participation in social value cocreation, and thus affect the speed at which both parties achieve social value cocreation. Specifically, compared to when the government does not implement subsidy policies or implements them only partially, providing full subsidies accelerates SOEs’ participation in cocreation, but slows the government's own participation. However, the cost of digital empowerment for SOEs and the government's subsidy policies do not affect the consumers, who have sufficient autonomy and flexibility. (4) By varying the penalty coefficient, it is found that setting the penalty coefficient has a relatively small effect on the government and consumers’ participation and the probability of cocreation, but it does have some influence on SOEs with a national mission. Different levels of penalty mechanisms will cause fluctuations in SOEs’ participation process. Specifically, increasing the penalty amount will increase SOEs’ willingness to participate in cocreation within a unit time. Moreover, the penalty's size does not affect SOEs’ ultimate willingness to participate in social value cocreation, which is consistent with SOEs’ special nature, as they respond actively to the national call and shoulder national missions.

Theoretical implications

This article makes three theoretical contributions. (1) It reveals the effect of SOEs’ cocreation of social value and its influencing factors on the cocreation process and outcomes. Unlike non-SOEs, the role that SOEs play requires them to undertake heavier social responsibilities and create more social value. SOEs’ cocreation of social value is also subject to a certain degree of government control. Therefore, the paper attempts to understand how government intervention in cocreation will change the willingness to cocreate social value on the part of the government, SOEs, and consumers, as well as the cocreation process and results overall. Addressing this issue holds profound significance for the government, SOEs, consumers, and related research in managing the relationship of cocreating social value. (2) The paper focuses on the popular topic of digital empowerment, using SOEs as the research subject. By integrating digital empowerment with SOEs and value cocreation, it not only embodies SOEs’ cocreation of social value in the new era, but also broadens the theory and application scope of value cocreation. (3) The paper models SOEs’ cocreation of social value using evolutionary game theory and conducts a subsequent simulation analysis to validate the model's effectiveness and its results’ reliability. This provides a new methodological and practical foundation for future research in the field of SOEs’ value cocreation.

Practical implications

Based on the analysis of the government, SOEs, and consumers’ participation strategies in social value cocreation through the establishment of an evolutionary game model, it can be concluded that there are two possible states for SOEs in social value cocreation: ideal state in which all parties participate in cocreation, and nonideal state in which the government and SOEs are willing to participate, but consumers choose not to participate. In light of this, three implications are proposed to promote social value cocreation on the part of SOEs: (1) The government should set phased goals and adjust distribution policies, digital empowerment subsidy policies, and penalty mechanisms flexibly. In response to the situation, the government should set phased cocreation goals. When the government needs to achieve certain social value cocreation behaviors rapidly, compared to the ideal state's equal distribution of benefits, the government should adopt subsidies actively for the cost of introducing digital technologies and impose higher penalties on SOEs. This helps achieve social value cocreation in a short period. When the government prioritizes stability in the cocreation process and the pressure for all parties to participate is relatively low, the government should adjust the distribution of benefits, subsidies for cost, and penalty amounts accordingly. This ensures the system's stability, reduces the burden on all parties, and achieves goals for each stage. In addition, the government should implement relevant policies to enhance consumers’ sense of identification, satisfaction, and both spiritual and material benefits from participating in cocreation, ensuring that SOEs do not hesitate to engage in social cocreation because of costs. (2) SOEs should prioritize consumers’ needs and propose strong social value propositions to encourage social value cocreation among all parties effectively. In the context of the “new era,” as proponents of value propositions in cocreation, SOEs should prioritize consumers’ needs and consider their satisfaction, recognition, and experiential aspects over the improvement in their social welfare levels obtained from the system. It is necessary that the total benefits that each participant in the system received exceed their individual costs, which is a necessary condition for achieving social value cocreation. Moreover, SOEs should engage actively in research on, and development of, digital technologies, select suitable digital technologies that reduce the cost of digital empowerment, and alleviate the pressure on themselves to engage in social value cocreation activities and keep up with the demands of the “new era.” (3) Consumers should communicate their own needs and participate actively in social value cocreation that is consistent with their interests and realize personal value thereby. As parties with autonomy and flexibility in the SOE social value cocreation system, consumers should communicate their social value needs to SOEs or the government actively as well. They should engage in cocreation activities that are suitable for their own needs, which can reduce the unpredictability associated with their participation and allow them to immerse themselves quickly in cocreation activities that serve their interests. By doing so, consumers can experience the satisfaction, sense of achievement, and engagement gained from participating in cocreation, while enjoying the increased social welfare that resulted from their involvement.

Limitations and future research

There are limitations to this article. The article considers the internal influencing factors of the social value cocreation system in SOEs alone, and adjusts them to identify the key factors that affect the cocreation process and results, without considering external factors such as the environment or influences from non-SOEs. Therefore, future research could examine primarily external factors’ effects on SOEs’ social value cocreation. In addition, this article is a study based upon the Chinese context of SOEs. Hence, future research can be oriented toward other countries and regions.

Conclusion

This article is based on an evolutionary game model and uses MATLAB to model the social value cocreation among the government, SOEs, and consumers. The findings are as follows: (1) When the additional social value gain for consumers is less than their conversion gain, the three parties cannot achieve social value cocreation; (2) Providing consumers with additional social value allocation will accelerate cooperative behavior within the social value cocreation system; (3) Full subsidies from the government will accelerate SOEs’ participation in cocreation, but will slow the government's own involvement, and (4) Increasing government penalties will increase SOEs’ willingness to participate in co-creation per unit time, but will not affect the final outcome. These conclusions will be beneficial in encouraging SOEs to achieve social value cocreation and integrate value cocreation theory with distinctive SOEs in China to expand the boundaries of the theory.