An Evolutionary Game Approach to Enhancing Semiconductor Supply Chain Security in China: Collaborative Governance and Policy Optimization

Abstract

In response to the changing international landscape and the risks associated with China’s supply chain security, conducting policy simulations on semiconductor supply chain security helps clarify the industry’s policies and governance strategies for semiconductor supply chain security in China. It also enables a better understanding of the current state and focus areas of China’s semiconductor supply chain security, which is of great significance for improving the security levels of semiconductor supply chains across provinces and cities and for constructing a secure, efficient, and autonomous semiconductor supply chain system. Firstly, this paper reviews the current research on semiconductor supply chains, supply chain security, and industrial policies. Secondly, based on the industrial policies for semiconductor supply chain security, an evolutionary game model is constructed, involving government departments, chain owner enterprises, and upstream and downstream small and medium-sized enterprises (SMEs) within the supply chain. Finally, the MATLAB R2016b system simulation method is employed to conduct a policy simulation analysis of China’s semiconductor supply chain security and further analyze the industrial policies related to semiconductor supply chain security. The results show that: (1) Supply chain security depends on multi-agent collaborative governance, with government leadership, and chain owner enterprises driving innovation in SMEs, improving digitalization levels, and ensuring supply chain autonomy and control. (2) Increasing government management revenue, raising the responsibility costs for chain owner enterprises, and reducing the innovation costs for SMEs can accelerate the achievement of the ideal governance state. Lastly, policy recommendations are proposed to build an autonomous and controllable supply chain system.

1. Introduction

Semiconductor chips are widely used in critical fields such as national defense, high-end manufacturing, and daily life, serving as a core pillar of modern society and economic development. As a strategic, fundamental, and cutting-edge technology, the semiconductor industry not only drives innovation across various sectors but has also become a “choke point technology” in global power competition [1]. The issues of technological competition and supply chain security in this industry are increasingly prominent. Amid the gestation of a new technological revolution, emerging information technologies—such as big data and artificial intelligence—rapidly permeate various fields, reinforcing the role of semiconductor chips as the “brain” of both the information industry and modern manufacturing. Given the industry’s high knowledge, technology, and capital intensity, its long and complex supply chain demands seamless coordination across all stages; a disruption in any single link can jeopardize the entire system [2,3]. From a global perspective, leading semiconductor enterprises are also exposed to supply chain security risks. For instance, Qualcomm occupies a central position in the mobile communication chip sector, but its heavy reliance on foundries such as TSMC and Samsung makes it vulnerable to single-point dependence and potential supply disruptions. Similarly, NVIDIA maintains global leadership in GPU and AI chip design, yet its export business is directly constrained by U.S. government technology controls and policy restrictions. The U.S. CHIPS and Science Act seeks to enhance domestic semiconductor competitiveness through fiscal subsidies, supply chain restructuring, and export restrictions, while simultaneously exerting systemic shocks on the global supply chain landscape, posing direct challenges to China’s access to advanced technologies and overall industrial security [4].

Against this backdrop, semiconductor supply chain security has emerged as a critical issue in global supply chain management. The semiconductor supply chain (SSC) is a critical infrastructure supporting the global technology industry [5], and its stability is paramount for global technological innovation and economic development. However, globalized production models, geopolitical tensions, natural disasters, and public health emergencies expose the vulnerabilities of the semiconductor supply chain. Security concerns within the semiconductor supply chain have become particularly pressing [6]. These concerns include risks related to technology transfer, intellectual property theft, and potential exploitation of supply chain vulnerabilities by foreign governments. In response to these challenges, both governments and enterprises are seeking to reduce reliance on foreign suppliers and protect their intellectual property, leading to a trend of deglobalization and localization within the semiconductor industry [7,8]. In response, governments and enterprises are striving to reduce reliance on foreign suppliers and safeguard intellectual property, thereby enhancing supply chain resilience and security.

Supply chain security underpins high-quality industrial development and national economic security [9]. In the face of trade protectionism and deglobalization, ensuring the stability of industrial and supply chains remains a strategic imperative, particularly as uncertainties intensify due to unpredictable supplier behavior [10,11]. In China, digital technologies not only demonstrate unique value in addressing these global challenges but have also become a key driver of industrial transformation and high-quality economic growth [12]. Particularly in an era of rising global supply chain uncertainties, China’s digital economy leverages advanced technologies to enhance supply chain resilience and security, thereby offering new opportunities and strategic responses to risks such as supply chain disruptions, fragmentation, and regionalization [9].

In response to the evolving international landscape and the potential risks facing China’s semiconductor supply chain, policy simulation analysis has become increasingly critical. Such analysis clarifies industrial policies and strategies related to semiconductor supply chain security, identifies vulnerabilities, and provides a scientific basis for enhancing security at both provincial and municipal levels. Previous studies have applied evolutionary game theory to examine strategic interactions and equilibrium conditions in various contexts [13,14,15,16,17,18]. Consequently, constructing an evolutionary game model to simulate stakeholder interactions can elucidate the behavioral evolution of different actors under diverse governance environments.

Building on the above analysis, this study develops a three-party evolutionary game model to investigate several research questions: (a) What are the governance tools, objectives, and actors involved in China’s semiconductor supply chain security policies? (b) What are the industrial policies for ensuring semiconductor supply chain security in China? To address these questions, we construct an evolutionary game model of semiconductor supply chain security to compare and analyze equilibrium outcomes, derive relevant conclusions, and present policy implications.

This study contributes to the literature in two key aspects. First, it integrates MATLAB-based policy simulation analysis into the study of China’s semiconductor supply chain security governance, bridging the gap in the literature regarding the application of policy simulations in supply chain security governance. This approach also enriches the theoretical framework and analytical system of supply chain security research. Second, by constructing an evolutionary game model for semiconductor supply chain security, this study provides an in-depth examination of the industrial policies governing supply chain security. The model clarifies how different governance actors’ strategies influence the level of semiconductor supply chain security, thereby enhancing the theoretical depth and practical relevance of the findings.

The key findings are as follows: (1) Supply chain security relies on multi-actor collaborative governance, with the government taking the lead, chain owner enterprises driving innovation among small and medium-sized enterprises (SMEs), and enhancing digitalization to ensure supply chain autonomy and controllability. (2) Increasing government regulatory benefits, raising the cost of responsibility for chain owner enterprises, and reducing SMEs’ innovation costs can accelerate the attainment of an optimal governance state.

The remainder of this paper is structured as follows. Section 2 provides a brief literature review on semiconductor supply chains, supply chain security, and industrial policies. Section 3 formulates the hypotheses, constructs the evolutionary game model for semiconductor supply chain security, and presents the equilibrium analysis. Section 4 assigns parameter values and conducts a policy simulation analysis of semiconductor supply chain security. Finally, Section 5 presents the conclusions, future research directions, and limitations.

2. Literature Review

In recent years, scholars have paid increasing attention to research on the global semiconductor chip supply chain. This section briefly reviews the research-related literature, focusing on three main areas: semiconductor supply chains, supply chain security, and industrial policy.

2.1. Semiconductor Supply Chain

The semiconductor supply chain forms the core foundation of the modern electronics industry, encompassing multiple stages from design, manufacturing, testing, packaging, to sales, thereby constituting a highly complex global network [19]. With the rapid advancements in artificial intelligence, 5G communications, and the digital era, the strategic importance of the semiconductor industry has become increasingly prominent. As a result, most countries are reassessing their roles and positions within the global semiconductor supply chain, while major economies have elevated the semiconductor industry to a central pillar of their national development strategies [20]. In 2021, European Commission President Ursula Von Der Leyen declared that semiconductors would be at the core of her Commission’s geopolitical vision, emphasizing that the European Union “must master and own key technologies,” including quantum computing, artificial intelligence, blockchain, and critical semiconductor technologies [21]. This underscores the pivotal role of semiconductors in national strategic planning and highlights the significance of technological dominance in ensuring national security and economic competitiveness amid global competition. However, the semiconductor supply chain faces numerous challenges, particularly disruptions in the chip supply process that threaten the stability of the industry [22]. In recent years, frequent semiconductor supply chain disruptions have emerged as a key source of global economic instability. For instance, since late 2020, the COVID-19 pandemic has had a profound impact on global supply chains, with the automotive industry experiencing severe chip shortages, affecting nearly all major automakers and resulting in production halts and capacity backlogs [23,24]. Further exacerbating the crisis, in early 2021, a severe winter storm in Texas, USA, triggered widespread power outages, forcing semiconductor manufacturers such as Samsung Electronics and NXP Semiconductors to shut down local production facilities, thereby intensifying global semiconductor supply chain constraints. Additionally, the outbreak of the Russia-Ukraine conflict in 2022 disrupted access to critical semiconductor raw materials, including neon, krypton, and xenon gases, significantly increasing supply chain risks. The semiconductor supply chain crisis has had a direct impact on 169 industries worldwide [25]. These disruptions not only affected the automotive sector but also triggered ripple effects across consumer electronics, telecommunications, and medical device industries [26]. As Dolgui et al. [27] pointed out, cascading effects within interconnected supply chains can amplify the initial impact of disruptions, leading to systemic failures. To mitigate such risks, national governments must implement macroeconomic regulatory measures to facilitate nationwide resource allocation across all stages of the semiconductor supply chain. Establishing a comprehensive industry-academia-research innovation ecosystem is essential for fostering domestic technological advancements and creating a supportive environment for enterprise development [28]. Liu et al. [29] emphasized that innovation ecosystems and knowledge-intensive enterprises coevolve in shaping industrial upgrading, and their study of China’s IC design industry highlights how ecosystem dynamics influence strategic growth paths. This perspective provides a useful theoretical underpinning for analyzing the collaborative governance of semiconductor supply chains.

2.2. Supply Chain Security

Supply chain security involves managing third-party suppliers and outsourcing the security of various products and information [30]. Traditionally, it has focused on protecting supply chain assets, preventing product losses, and mitigating the risk of hazardous materials entering the system [31,32]. The International Organization for Standardization (ISO) defines supply chain security as the resilience of the supply chain against damage or disruption. In contrast, recent studies redefine the concept as a collaborative effort among supply chain organizations to prevent risks and ensure rapid recovery with minimal time and economic losses [33].

The existing literature on supply chain collaboration mainly addresses three aspects: (1) internal collaboration within organizations, (2) vertical collaboration with upstream or downstream suppliers, and (3) horizontal collaboration with competitors and external entities—such as sharing transportation resources to reduce costs and improve eco-efficiency [34]. The role of each supply chain partner varies with its position, influencing its significance in promoting sustainability [35]. Consequently, close cooperation among partners is essential for maintaining overall supply chain security. Recent research has further broadened the scope of supply chain security by proposing multidimensional classification frameworks. For example, some scholars differentiate between general supply–demand coordination issues and sudden major disruptions based on risk impact [36], while others categorize security management into intra-organizational, inter-organizational, a combination of both, and even cases where security measures are neglected [37].

Ensuring supply chain security and mitigating associated risks are critical across industries. Each industry must develop tailored security policies that balance safety and efficiency. The security of the IoT supply chain, for instance, has become an emerging field, with several studies proposing secure architectures and risk management approaches [38]. Tang and Musa [39] identify two critical dimensions in supply chain risk management: the consequences of risk impact and the anticipated sources of risk. In a similar vein, software supply chain security has emerged as one of the fastest-growing threats—affecting entities from individual users to large enterprises such as Microsoft, Google, and Red Hat [40]. Despite the rising number of security incidents, software supply chains have not received the same attention as physical ones [40]. Given the complexity of cyber supply chains—comprising multiple subsystems with inherent vulnerabilities—identifying and predicting potential threats is crucial for implementing effective security controls [41]. In this context, decision-making frameworks have been developed to mitigate supply chain risks during supplier selection [10].

In maritime supply chains, security challenges have been intensified by geopolitical conflicts, international sanctions, and the COVID-19 pandemic. Researchers have employed the Delphi method to explore risk factors affecting maritime container security during the pandemic [42] and analyzed how effective public–private partnerships can enhance risk and security management [43]. Similarly, in the food supply chain sector, studies have examined the impact of the COVID-19 pandemic on food security, proposing frameworks for more intelligent and resilient global food supply chains in the post-pandemic era [44].

2.3. Industrial Policy

With the advent of the digital age, industrial policy has assumed greater significance, drawing widespread attention from both academia and practice. Scholars have called for a re-examination of traditional governance theories to address the challenges posed by digital transformation. In the context of digital exchange and transactions, these challenges are analyzed through the lens of establishing, maintaining, adjusting, and restoring exchange relationships [45]. As large-scale digital exchanges materialize, digital governance has become increasingly vital. By employing algorithmic protocols, digital governance can automate control, coordination, incentivization, and trust-building mechanisms, thereby facilitating smooth digital transactions and information flow [46,47].

This transition from traditional analog governance—where decisions are reached through negotiations and consensus among exchange participants—to digital governance signifies a fundamental shift. In the digital realm, decision-making authority increasingly rests with technologists and system designers who develop the governance tools, thereby decoupling governance decisions from direct transaction execution [48,49]. The digital transformation of manufacturing enterprises has been widely recognized as a crucial pathway to enhancing supply chain resilience [50]. It not only improves the flexibility of firms in responding to internal and external environmental changes but also supports stability and growth in high-uncertainty contexts by strengthening the connections with upstream and downstream partners, thereby amplifying the positive effects of digital transformation [51,52]. In particular, digitalization is reshaping logistics, where the integration of manufacturing and logistics enables rapid supply responses, a process often referred to as the digitalization of logistics [53]. Given the increasingly complex and volatile risk environment as well as the acceleration of technological innovation, enhancing supply chain resilience has become a strategic necessity for modern manufacturing enterprises to sustain competitiveness and achieve long-term development [54]. Moreover, digital technologies can drive enterprises to optimize processes, improve efficiency, reduce costs, foster innovation, and ensure product quality, thus offering both technological support for industrial transformation and a key impetus for sustainable and high-quality development of industries and the economy as a whole [55,56]. This shift redefines industrial policy. In academia, research on industrial policy often simulates industry governance via evolutionary game models. For instance, studies have constructed three-party models involving government, platform enterprises, and users to explore strategic choices in addressing issues such as data abuse by platforms and corporate speculative behavior [57,58]. These models, which construct a tripartite evolutionary game model using binary strategies, not only clarify the interactive relationships among governance subjects but also provide practical solutions for addressing industrial governance challenges. Feng et al. [59] applied a three-party evolutionary game model to reveal that semiconductor supply chains (SSC) face obstacles in data sharing and collaboration. Their findings suggest that SSC requires more effective and efficient mechanisms to foster cooperation and synergy, thereby improving the potential for successful transition.

Regarding supervision and management, existing literature distinguishes between two types of industrial policies. Official or government-based mechanisms rely on market contracts, intellectual property protection, and legally binding agreements to ensure compliance and transparency among platform members [60]. In contrast, unofficial or platform-based mechanisms emphasize mutual trust, negotiated codes of conduct, and shared cultural values, promoting voluntary cooperation without mandatory legal clauses [61]. In the platform ecosystem, organizations must balance these formal and informal policies to incentivize fair competition, foster innovation, and achieve win–win outcomes.

Current research predominantly examines the intrinsic characteristics and development trends of the semiconductor industry, with limited focus on semiconductor supply chain security. On the one hand, international studies have primarily focused on single-firm cases or macro-level industrial policies, while relatively few have examined the multi-agent interactions among governments, chain owner enterprises, and SMEs from the perspective of evolutionary game theory. On the other hand, research remains insufficient regarding how to enhance the security of China’s semiconductor supply chain through digital transformation and collaborative governance in the face of international policy shocks such as the CHIPS and Science Act. Digitalization is crucial for enhancing supply chain resilience and security; thus, investigating semiconductor supply chain security clarifies industrial policies related to China’s semiconductor sector and improves its digitalization, safety, stability, and autonomy. While academic work on supply chain security has largely focused on risk sources and response strategies, analyses of industrial policies in this domain remain insufficient. A deeper exploration of industrial policies can elucidate the current governance landscape and the influence of various governance actors and strategies on supply chain security. Although some studies have examined the impact of supply chain security policies on overall security, further exploration is needed—especially by integrating supply chain security policies into the broader discussion of industrial policies. This paper addresses these gaps by analyzing China’s semiconductor supply chain security policies and exploring strategies to enhance security governance.

3. Model Assumptions and Construction

3.1. Model Assumption

This paper builds a three-party evolutionary game model of the semiconductor supply chain security governance process of government departments, chain owners and upstream and downstream small and medium-sized micro-enterprises in the supply chain, which puts forward the following assumptions:

Assumption 1. 

Semiconductor supply chain security governance involves the government, chain owner enterprises and supply chain upstream and downstream small and medium-sized micro-enterprises, the three governance subjects are limited rationality.

Assumption 2. 

The governance strategy of the government department is to choose between “establishing a security risk management system” and “not establishing a security risk management system”, and the set of strategies is {establishing a security risk management system, not establishing a security risk management system}. As for chain owners, in order to guide upstream and downstream SMEs to strengthen digital technology innovation and improve digitalization level, two governance strategies can be adopted: “positive-led” and “negative-led”, with the strategy set as “positive-led and negative-led”. For example, TSMC, in its 2024 Supply Chain Security Workshop, collaborated with over 480 key suppliers to improve cybersecurity practices and share risk management mechanisms, demonstrating a positive orientation where the lead firm proactively supports and elevates its upstream and downstream partners. However, Apple has extensively applied big data analytics and artificial intelligence in its supply chain management, significantly enhancing transparency and efficiency in its internal production and logistics processes. However, Apple typically exercises strict control over access to core data and digital platforms, which limits the ability of its suppliers—particularly small and medium-sized enterprises (SMEs)—to benefit equally from digitalization. While this strategy strengthens Apple’s own competitive advantage, it simultaneously widens the digital divide across the supply chain and constrains the digital upgrading of upstream and downstream partners. From the perspective of supply chain security governance, such an approach illustrates a negative orientation, whereby the lead firm prioritizes consolidating its dominant position through digital transformation rather than actively promoting collaborative innovation and risk-sharing across the entire supply chain. For upstream and downstream SMEs, in the process of pursuing their own interests and realizing digital transformation, the governance of supply chain security can adopt two governance strategies: “strengthen digital technology innovation” and “do not strengthen digital technology innovation”. The set of strategies is “Strengthen digital technological innovation, don’t strengthen digital technological innovation”, which regards the behavior of the chain owner enterprise negatively leading and the upstream and downstream SMEs not strengthening digital technological innovation as insecure behavior, and the government doesn’t set up a security risk management system and the negative leading of the chain owner enterprise is defined as the failure to provide rewards and punishments for the behaviors of the chain owner enterprise and the upstream and downstream SMEs in the supply chain.

Assumption 3. 

The probability that the government chooses the governance strategy of “establishing a security risk management system” is x (0 ≤ x ≤ 1), and the probability that it chooses “not to establish a security risk management system” is 1 − x; the probability that the chain-owning enterprise adopts the governance strategy of “positive dominance” is x (0 ≤ x ≤ 1). The probability of the chain owner enterprise adopting the “positive dominance” governance strategy is y (0 ≤ y ≤ 1), and the probability of “negative dominance” is 1 − y; the probability of the upstream and downstream SMEs in the supply chain adopting the governance strategy of “strengthening digital technological innovation” is z (0 ≤ z (0 ≤ z ≤ 1), and the probability of “not strengthening digital technology innovation” is 1 − z.

Assumption 4. 

As long as the government establishes a security risk management system, the insecure behaviors of the chain owner and the upstream and downstream SMEs in the supply chain can be detected.

Based on the above assumptions, the logical relationship between the governance bodies is determined as shown in Figure 1.

3.2. Parameterization and Model Construction

(1)

Parameterization

When the government adopts the governance strategy of “not establishing a security risk management system”, the management cost is ${\mathrm{C}}_{\mathrm{a}}$, including management personnel, management equipment and so on. When the government adopts the governance strategy of “establishing a security risk management system”, the government needs to establish a supply chain security risk management system for risk prevention and control, monitoring and early warning, risk assessment, risk response, etc., and the cost of security management is related to the soundness of the security risk management system α (α > 1), which is denoted as $\mathsf{\alpha }{\mathrm{C}}_{\mathrm{a}}$. At this time, the trust of the chain owner and the SMEs upstream and downstream of the supply chain in the government department increases, and the government department obtains the security cost ${\mathrm{C}}_{\mathrm{a}}$. When upstream and downstream SMEs’ trust in the government department increases, the government department obtains the security management benefit R. When the chain owner enterprise actively leads and the upstream and downstream SMEs’ digital technology innovation is strengthened to improve the security level of the semiconductor supply chain, the government’s security management benefit improves ${\mathrm{R}}^{\prime }$. In order to guide the chain owner enterprises and supply chain upstream and downstream SMEs to actively lead and strengthen digital technology innovation to the ideal state of evolution, the government departments will take incentives and penalties to guide the chain owner enterprises to actively lead to ensure the semiconductor supply chain security, stability and autonomy of the governance behavior to give incentives ${\mathrm{R}}_{\mathrm{a}}$ (tax incentives, financial support, etc.). The chain owner enterprises negatively lead to the governance behavior of the penalties ${\mathrm{K}}_{\mathrm{a}}$ (Warning, fine, etc.); government departments to supply chain upstream and downstream SMEs to strengthen digital technology innovation to enhance the level of enterprise digitization and supply chain security level of behavior to give incentives ${\mathrm{R}}_{\mathrm{a}\mathrm{a}}$ (tax incentives, talent support, etc.). Supply chain upstream and downstream SMEs do not strengthen the digital technology innovation behavior to be punished ${\mathrm{K}}_{\mathrm{a}\mathrm{a}}$ (warning, fines, suspension of business, etc.). In addition, when the chain owner enterprise is negatively leading or the upstream and downstream MSMEs do not strengthen digital technology innovation, the loss of the semiconductor supply chain’s security level is reduced to K.

The chain owner enterprise in the supply chain mainly provides technical support and services to small and medium-sized enterprises (SMEs) upstream and downstream of the supply chain by integrating digital industry resources and innovative elements. This improves the digital technological innovation awareness and capabilities of SMEs in the supply chain and strengthens the semiconductor industry cluster effect. The chain owner enterprise can obtain a benefit, denoted as ${\mathrm{R}}_{\mathrm{b}}$. When the chain owner enterprise adopts a “passive leadership” strategy, it only provides technical services to SMEs in the supply chain without fulfilling its guiding responsibility toward these SMEs. In this case, the operating cost of the chain owner enterprise is ${\mathrm{C}}_{\mathrm{b}}$ (technical service cost, operational cost). Since the chain owner enterprise is passively leading and does not perform its guiding role, the trust of the upstream and downstream SMEs in the chain owner enterprise decreases, leading to a loss in revenue, denoted as $\Delta {\mathrm{R}}_{\mathrm{b}}$. If the government adopts the governance strategy of “not establishing a safety risk management system,” the chain owner enterprise will not be penalized, and the total revenue will be ${\mathrm{R}}_{\mathrm{b}}-{\mathrm{C}}_{\mathrm{b}}-\Delta {\mathrm{R}}_{\mathrm{b}}$. If the government adopts the strategy of “establishing a safety risk management system,” the chain owner enterprise will be penalized with ${\mathrm{K}}_{\mathrm{a}}$, and the total revenue will be ${\mathrm{R}}_{\mathrm{b}}-{\mathrm{C}}_{\mathrm{b}}-\Delta {\mathrm{R}}_{\mathrm{b}}-{\mathrm{K}}_{\mathrm{a}}$. When the chain owner enterprise adopts an “active leadership” strategy, it integrates digital industry resources and innovation elements to provide technical services to SMEs in the supply chain while also guiding these SMEs to strengthen digital technological innovation, improve their digitalization levels, and enhance the supply chain’s security level. In this case, the enterprise needs to bear the basic operating cost of the industry, denoted as ${\mathrm{C}}_{\mathrm{b}}$, and also incur additional operational costs, such as resource integration costs and guiding costs. The operating cost of the chain owner enterprise is influenced by the degree of passive leadership, denoted as μ (μ > 1), and the operating cost is represented as $\mathsf{\mu }{\mathrm{C}}_{\mathrm{b}}$. If the government adopts the governance strategy of “not establishing a safety risk management system,” the chain owner enterprise will not receive any reward from the government, and the total revenue will be ${\mathrm{R}}_{\mathrm{b}}-\mathsf{\mu }{\mathrm{C}}_{\mathrm{b}}$. If the government adopts the strategy of “establishing a safety risk management system,” the chain owner enterprise will receive a reward from the government, and the total revenue will be ${\mathrm{R}}_{\mathrm{b}}-\mathsf{\mu }{\mathrm{C}}_{\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}}$. To guide the upstream and downstream SMEs in the supply chain to jointly maintain supply chain security, the chain owner enterprise will also implement relevant reward and punishment measures. It will reward actions that strengthen digital technological innovation and improve supply chain security, with a reward denoted as ${\mathrm{R}}_{\mathrm{b}\mathrm{b}}$ (e.g., technical support, strengthening cooperation), and it will punish actions that fail to strengthen digital technological innovation and harm the supply chain security, with a penalty denoted as ${\mathrm{K}}_{\mathrm{b}\mathrm{b}}$ (e.g., terminating cooperation, technology blockade).

The SMEs upstream and downstream of the supply chain obtain a benefit, denoted as ${\mathrm{R}}_{\mathrm{c}}$, through industrial development. When these SMEs adopt the governance strategy of “not strengthening digital technological innovation,” they need to bear the industry operating cost, denoted as ${\mathrm{C}}_{\mathrm{c}}$. When the government adopts the governance strategy of “not establishing a safety risk management system” and the chain owner enterprise adopts a “passive leadership” governance strategy, the SMEs will not be penalized by either the government or the chain owner enterprise, and the total revenue will be ${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}$. When the government adopts the governance strategy of “establishing a safety risk management system” and the chain owner enterprise adopts a “passive leadership” governance strategy, the SMEs will face a penalty from the government, and the total revenue will be ${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}-{\mathrm{K}}_{\mathrm{a}\mathrm{a}}$. When the government adopts the governance strategy of “not establishing a safety risk management system” and the chain owner enterprise adopts an “active leadership” governance strategy, the SMEs will face a penalty from the chain owner enterprise, and the total revenue will be ${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}-{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$. When the government adopts the governance strategy of “establishing a safety risk management system” and the chain owner enterprise adopts an “active leadership” governance strategy, the SMEs will face penalties from both the government and the chain owner enterprise, and the total revenue will be ${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}-{\mathrm{K}}_{\mathrm{a}\mathrm{a}}-{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$. When the SMEs upstream and downstream of the supply chain adopt the governance strategy of “strengthening digital technological innovation,” they will incur additional innovation costs, including labor costs and digital technology innovation costs, denoted as $\Delta {\mathrm{C}}_{\mathrm{c}}$. When the government adopts the governance strategy of “not establishing a safety risk management system” and the chain owner enterprise adopts a “passive leadership” governance strategy, the SMEs will not have any additional benefits, and the total revenue will be ${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}-\Delta {\mathrm{C}}_{\mathrm{c}}$. When the government adopts the governance strategy of “establishing a safety risk management system” and the chain owner enterprise adopts a “passive leadership” governance strategy, the SMEs will receive an additional reward from the government, and the total revenue will be ${\mathrm{R}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{C}}_{\mathrm{c}}-\Delta {\mathrm{C}}_{\mathrm{c}}$. When the government adopts the governance strategy of “not establishing a safety risk management system” and the chain owner enterprise adopts an “active leadership” governance strategy, the SMEs will receive a reward from the chain owner enterprise, and the total revenue will be ${\mathrm{R}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{C}}_{\mathrm{c}}-\Delta {\mathrm{C}}_{\mathrm{c}}$. When the government adopts the governance strategy of “establishing a safety risk management system” and the chain owner enterprise adopts an “active leadership” governance strategy, the SMEs will receive rewards from both the government and the chain owner enterprise, and the total revenue will be ${\mathrm{R}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{a}\mathrm{a}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{C}}_{\mathrm{c}}-\Delta {\mathrm{C}}_{\mathrm{c}}$.

The main parameters of government departments, chain owner enterprises, and small and medium-sized enterprises (SMEs) in the upstream and downstream of the supply chain are shown in

Table 1. Variables and meanings.

Variable	Variable Meaning	Variable	Variable Meaning
${\mathrm{C}}_{\mathrm{a}}$	Basic management costs of government departments	${\mathrm{R}}_{\mathrm{b}}$	Chain owner’s business operating income
R	Government sector security management gains	${\mathrm{C}}_{\mathrm{b}}$	Basic operating costs of chain-owning enterprises
${\mathrm{R}}^{\prime }$	Increased gains in security management in the government sector	$\Delta {\mathrm{R}}_{\mathrm{b}}$	Loss of earnings from chain-owning businesses
${\mathrm{R}}_{\mathrm{a}}$	Government incentives for chain owner companies	${\mathrm{R}}_{\mathrm{b}\mathrm{b}}$	Incentives for chain-owning enterprises to upstream and downstream MSMEs in the supply chain
${\mathrm{K}}_{\mathrm{a}}$	Government penalizes chain owner companies	${\mathrm{K}}_{\mathrm{b}\mathrm{b}}$	Chain owner companies penalize upstream and downstream MSMEs in the supply chain
${\mathrm{R}}_{\mathrm{a}\mathrm{a}}$	Government incentives for upstream and downstream SMEs in the supply chain	${\mathrm{R}}_{\mathrm{c}}$	Business benefits for upstream and downstream MSMEs in the supply chain
${\mathrm{K}}_{\mathrm{a}\mathrm{a}}$	Government penalties for MSMEs up and down the supply chain	${\mathrm{C}}_{\mathrm{c}}$	Basic operating costs for MSMEs upstream and downstream of the supply chain
K	Losses from reduced levels of security in the semiconductor supply chain	α	Soundness of government security risk management systems
$\Delta {\mathrm{C}}_{\mathrm{c}}$	Cost of innovation for upstream and downstream supply chain MSMEs	μ	Degree of negative dominance of chain-owning firms

.

(2)

Model building

Based on the above model assumptions and parameter settings, the evolutionary game matrix for the three parties—government departments, chain owner enterprises, and small and medium-sized enterprises (SMEs) in the upstream and downstream of the supply chain—is shown in

Table 2. Tripartite Evolutionary Game Matrix.

	Chain Owner Enterprise		MSMEs Upstream and Downstream of the Supply Chain
			Enhancing Digital Technology Innovation Z	Not Choosing to Enhance Digital Technology Innovation 1 − z
Government departments	Establishment of a safety risk management system x	Positive dominance y	$\mathrm{R}+{\mathrm{R}}^{\prime }-\mathsf{\alpha }{\mathrm{C}}_{\mathrm{a}}-{\mathrm{R}}_{\mathrm{a}\mathrm{b}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}$	$\mathrm{R}-\mathrm{K}-\mathsf{\alpha }{\mathrm{C}}_{\mathrm{a}}-{\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}$
			${\mathrm{R}}_{\mathrm{b}}-\mathsf{\mu }{\mathrm{C}}_{\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}$	${\mathrm{R}}_{\mathrm{b}}-\mathsf{\mu }{\mathrm{C}}_{\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$
			${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}-\Delta {\mathrm{C}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}$	${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}-{\mathrm{K}}_{\mathrm{a}\mathrm{b}}-{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$
		Negative dominance $1-y$	$\mathrm{R}-\mathrm{K}-\mathsf{\alpha }{\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}-{\mathrm{R}}_{\mathrm{a}\mathrm{b}}$	$\mathrm{R}-\mathrm{K}-\mathsf{\alpha }{\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+{\mathrm{K}}_{\dot{\mathrm{a}\mathrm{b}}}$
			${\mathrm{R}}_{\mathrm{b}}-\Delta {\mathrm{R}}_{\mathrm{b}}-{\mathrm{C}}_{\mathrm{b}}-{\mathrm{K}}_{\mathrm{a}}$	${\mathrm{R}}_{\mathrm{b}}-\Delta {\mathrm{R}}_{\mathrm{b}}-{\mathrm{C}}_{\mathrm{b}}-{\mathrm{K}}_{\mathrm{a}}$
			${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}-\Delta {\mathrm{C}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}$	${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}-{\mathrm{K}}_{\mathrm{a}\mathrm{b}}$
	No safety risk management system in place $1-x$	Positive dominance y	${\mathrm{R}}^{\prime }-{\mathrm{C}}_{\mathrm{a}}$	$-\mathrm{K}-{\mathrm{C}}_{\mathrm{a}}$
			${\mathrm{R}}_{\mathrm{b}}-\mathsf{\mu }{\mathrm{C}}_{\mathrm{b}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}$	${\mathrm{R}}_{\mathrm{b}}-\mathsf{\mu }{\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$
			${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}-\Delta {\mathrm{C}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}$	${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}-{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$
		Negative dominance $1-y$	$-\mathrm{K}-{\mathrm{C}}_{\mathrm{a}}$	$-\mathrm{K}-{\mathrm{C}}_{\mathrm{a}}$
			${\mathrm{R}}_{\mathrm{b}}-\Delta {\mathrm{R}}_{\mathrm{b}}-{\mathrm{C}}_{\mathrm{b}}$	${\mathrm{R}}_{\mathrm{b}}-\Delta {\mathrm{R}}_{\mathrm{b}}-{\mathrm{C}}_{\mathrm{b}}$
			${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}-\Delta {\mathrm{C}}_{\mathrm{c}}$	${\mathrm{R}}_{\mathrm{c}}-{\mathrm{C}}_{\mathrm{c}}$

.

3.3. Strategy Stability Analysis

(1)

Government

The expected payoff for the government department in “establishing a safety risk management system” is $\mathrm{E}{\mathrm{F}}_1$, while the expected payoff for “not establishing a safety risk management system” is $\mathrm{E}{\mathrm{F}}_2$, and the average expected payoff is EF.

$$\begin{array}{ll}\mathrm{E}{\mathrm{F}}_1=& \mathrm{y}\mathrm{z}(\mathrm{R}+{\mathrm{R}}^{\prime }-\mathsf{\alpha }{\mathrm{C}}_{\mathrm{a}}-{\mathrm{R}}_{\mathrm{a}\mathrm{b}}-{\mathrm{R}}_{\mathrm{a}})+\mathrm{y}\left(1-\mathrm{z}\right)\left(\mathrm{R}-\mathrm{K}-\mathsf{\alpha }{\mathrm{C}}_{\mathrm{a}}-{\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}\right)\\ & +\left(1-\mathrm{y}\right)\mathrm{z}\left(\mathrm{R}-\mathrm{K}-\mathsf{\alpha }{\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}-{\mathrm{R}}_{\mathrm{a}\mathrm{b}}\right)\\ & +\left(1-\mathrm{y}\right)\left(1-\mathrm{z}\right)\left(\mathrm{R}-\mathrm{K}-\mathsf{\alpha }{\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}\right)\end{array}$$

(1)

$$\begin{array}{ll}\mathrm{E}{\mathrm{F}}_2=& \mathrm{y}\mathrm{z}({\mathrm{R}}^{\prime }-{\mathrm{C}}_{\mathrm{a}})+\mathrm{y}\left(1-\mathrm{z}\right)\left(-\mathrm{K}-{\mathrm{C}}_{\mathrm{a}}\right)+\left(1-\mathrm{y}\right)\mathrm{z}\left(-\mathrm{K}-{\mathrm{C}}_{\mathrm{a}}\right)\\ & +\left(1-\mathrm{y}\right)\left(1-\mathrm{z}\right)\left(-\mathrm{K}-{\mathrm{C}}_{\mathrm{a}}\right)\end{array}$$

(2)

$$\mathrm{E}\mathrm{F}=\mathrm{x}\mathrm{E}{\mathrm{F}}_1+\left(1-\mathrm{x}\right)\mathrm{E}{\mathrm{F}}_2$$

(3)

Based on the Malthusian replication dynamic equation, the government’s replication dynamic equation $\mathrm{F}\left(\mathrm{x}\right)$ can be expressed as:

$$\begin{gathered} \mathrm{F}\left(\mathrm{x}\right)=\mathrm{d}\mathrm{x}/\mathrm{d}\mathrm{t} \\ =\mathrm{x}(\mathrm{E}{\mathrm{F}}_1-\mathrm{E}\mathrm{F}) \\ =\mathrm{x}\left(1-\mathrm{x}\right)\left[\mathrm{R}-\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}-\mathrm{y}\left({\mathrm{K}}_{\mathrm{a}}+{\mathrm{R}}_{\mathrm{a}}\right)-\mathrm{z}\left({\mathrm{K}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}\right)\right] \end{gathered}$$

(4)

According to the theorem of differential equations, for the government to reach a stable state, the following condition must be satisfied:

$$\begin{gathered} \mathrm{F}\left(\mathrm{x}\right)=0 \\ {\mathrm{F}}^{\prime }\left(\mathrm{x}\right)=\left(1-2\mathrm{x}\right)\left[\mathrm{R}-\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}-\mathrm{y}\left({\mathrm{K}}_{\mathrm{a}}+{\mathrm{R}}_{\mathrm{a}}\right)-\mathrm{z}\left({\mathrm{K}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}\right)\right]<0 \end{gathered}$$

Let $\mathrm{F}\left(\mathrm{x}\right)=0$, and solve to obtain x = 0 and x = 1. At this point, $\mathrm{y}*$ can be expressed as:

$$\mathrm{y}*=[\mathrm{R}-(\mathsf{\alpha }-1){\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}-\mathrm{z}\left({\mathrm{K}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}\right)]/\left({\mathrm{K}}_{\mathrm{a}}+{\mathrm{R}}_{\mathrm{a}}\right)$$

(5)

When $\mathrm{R}-\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}-\mathrm{z}\left({\mathrm{K}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}\right)>{\mathrm{K}}_{\mathrm{a}}+{\mathrm{R}}_{\mathrm{a}}$, it is always true that $\mathrm{y}<\mathrm{y}*$. If and only if x = 1, $\mathrm{F}\left(\mathrm{x}\right)=0$ and ${\mathrm{F}}^{\prime }\left(\mathrm{x}\right)<0$, the government’s governance strategy reaches a stable state, and the government will choose to “Establish a security risk management system.” When $\mathrm{R}-\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}-\mathrm{z}\left({\mathrm{K}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}\right)<0$, it is always true that $\mathrm{y}>\mathrm{y}*$, and x = 0 is the evolutionarily stable strategy, meaning the government will choose the “Do not establish a security risk management system” governance strategy.

When $0\le \mathrm{R}-(\mathsf{\alpha }-1){\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}-\mathrm{z}\left({\mathrm{K}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}\right)\le {\mathrm{K}}_{\mathrm{a}}+{\mathrm{R}}_{\mathrm{a}}$, $\mathrm{y}=\mathrm{y}*$, there are the following three cases: (1) When $\mathrm{y}=\mathrm{y}*$, regardless of the value of x, the government’s strategy of “Establishing a security risk management system” will reach an evolutionarily stable state; (2) When $\mathrm{y}<\mathrm{y}*$, the government will adopt the “Establish a security risk management system” governance strategy; (3) When $\mathrm{y}>\mathrm{y}*$, the government will adopt the “Do not establish a security risk management system” governance strategy. The evolution of the government’s governance strategy is shown in Figure 2. It can be observed that the governance strategies of chain-chain owner enterprises y and upstream and downstream small and medium-sized enterprises in the supply chain z influence the government’s choice of governance strategy. Meanwhile, the government’s safety management benefits, safety management costs, and rewards and penalties for chain-chain owner enterprises and small and medium-sized enterprises in the supply chain also affect the government’s governance strategy.

(2)

Chain owner enterprise

The chain owner’s expected return for “positive dominance” is EG₁ the expected return for “negative dominance” is EG₂, and the average expected return is EG.

The replicator dynamic equation for the lead firm is as follows:

$$\begin{gathered} \mathrm{F}\left(\mathrm{y}\right)=\mathrm{d}\mathrm{y}/\mathrm{d}\mathrm{t} \\ =\mathrm{y}\left(\mathrm{E}{\mathrm{G}}_1-\mathrm{E}\mathrm{G}\right) \\ =\mathrm{y}(1-\mathrm{y})[-(\mathsf{\mu }-1){\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}+\Delta {\mathrm{R}}_{\mathrm{b}}+\mathrm{x}({\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}})-\mathrm{z}({\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}\left)\right] \end{gathered}$$

(6)

Let $\mathrm{F}\left(\mathrm{y}\right)=0$, and solve to obtain y = 0 and y = 1. At this point, $\mathrm{z}*$ can be expressed as:

$$\mathrm{z}*=[-(\mathsf{\mu }-1){\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}+\Delta {\mathrm{R}}_{\mathrm{b}}+\mathrm{x}\left({\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}\right)]/\left({\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}\right)$$

(7)

When $-\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}+\Delta {\mathrm{R}}_{\mathrm{b}}+\mathrm{x}\left({\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}\right)>{\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$, it is always the case that $\mathrm{z}<\mathrm{z}*$. Only when y = 1, $\mathrm{F}\left(\mathrm{y}\right)=0$ and ${\mathrm{F}}^{\prime }\left(\mathrm{y}\right)<0$, the governance strategy of the lead firm reaches a stable state, and the lead firm will choose “active leadership.” When $-(\mathsf{\mu }-1){\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}+\Delta {\mathrm{R}}_{\mathrm{b}}+\mathrm{x}\left({\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}\right)<0$, it is always the case that $\mathrm{z}>\mathrm{z}*$, and the governance strategy of the lead firm reaches a stable state when y = 0, where the lead firm adopts a “passive leadership” governance strategy.

When $0\le -(\mathsf{\mu }-1){\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}+\Delta {\mathrm{R}}_{\mathrm{b}}+\mathrm{x}\left({\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}\right)\le {\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$, $\mathrm{z}*\in \left[\mathrm{0,1}\right]$, there are three possible scenarios: (1) When $\mathrm{z}=\mathrm{z}*$, regardless of the value of y, the lead firm will adopt the “active leadership” governance strategy and the system will reach an evolutionary stable state. (2) When $\mathrm{z}<\mathrm{z}*$, the lead firm will adopt the “active leadership” governance strategy;. (3) When $\mathrm{z}>\mathrm{z}*$, the lead firm will choose the “passive leadership” governance strategy. The evolution of the lead firm’s governance strategy is shown in Figure 3. It can be observed that the government’s governance strategy x and the governance strategies of the upstream and downstream small and medium-sized enterprises in the supply chain z both influence the governance strategy choice of the lead firm. The basic operational costs, expected revenue loss, the government’s rewards and punishments toward the lead firm, and the lead firm’s rewards and punishments toward the upstream and downstream small and medium-sized enterprises all affect the governance strategy of the lead firm.

(3)

MSMEs upstream and downstream of the supply chain

The expected payoff for upstream and downstream small and medium-sized enterprises in the supply chain adopting “digital technology innovation” is $\mathrm{E}{\mathrm{H}}_1$, the expected payoff for not adopting “digital technology innovation” is $\mathrm{E}{\mathrm{H}}_2$, and the average expected payoff is EH.

The replicator dynamic equation for upstream and downstream small and medium-sized enterprises in the supply chain is given by:

$$\begin{array}{ll}\mathrm{F}\left(\mathrm{z}\right)& =\mathrm{d}\mathrm{z}/\mathrm{d}\mathrm{t}\\ & =\mathrm{z}(\mathrm{E}{\mathrm{H}}_1-\mathrm{E}\mathrm{H})\\ & =\mathrm{z}(1-\mathrm{z})[-\Delta {\mathrm{C}}_{\mathrm{c}}+\mathrm{x}({\mathrm{R}}_{\mathrm{a}\mathrm{b}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}})+\mathrm{y}({\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}\left)\right]\end{array}$$

(8)

Let $\mathrm{F}\left(\mathrm{z}\right)=0$, and solve to obtain z = 0 and z = 1. At this point, $\mathrm{x}*$ can be expressed as:

$$\mathrm{x}*=[\Delta {\mathrm{C}}_{\mathrm{c}}-\mathrm{y}\left({\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}\right)]/\left({\mathrm{R}}_{\mathrm{a}\mathrm{b}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}\right)$$

(9)

When $\Delta {\mathrm{C}}_{\mathrm{c}}-\mathrm{y}\left({\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}\right)>{\mathrm{R}}_{\mathrm{a}\mathrm{b}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}$, it is always true that $\mathrm{x}<\mathrm{x}*$, and when z = 0, $\mathrm{F}\left(\mathrm{z}\right)=0$ and ${\mathrm{F}}^{\prime }\left(\mathrm{z}\right)<0$; thus, z = 0 is the stable strategy for upstream and downstream small and medium-sized enterprises in the supply chain, which will adopt the “no digital technology innovation” governance strategy. When $\Delta {\mathrm{C}}_{\mathrm{c}}-\mathrm{y}\left({\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}\right)<0$, it is always true that $\mathrm{x}>\mathrm{x}*$, and z=1 is the evolutionarily stable strategy, meaning the upstream and downstream small and medium-sized enterprises will adopt the “strengthen digital technology innovation” governance strategy.

When $0\le \Delta {\mathrm{C}}_{\mathrm{c}}-\mathrm{y}\left({\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}\right)\le {\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$, $\mathrm{x}*\in \left[\mathrm{0,1}\right]$, there are three possible cases: (1) When $\mathrm{x}=\mathrm{x}*$, regardless of the value of z, the upstream and downstream small and medium-sized enterprises in the supply chain will adopt the “strengthen digital technology innovation” governance strategy and reach an evolutionarily stable state. (2) When $\mathrm{x}<\mathrm{x}*$, the upstream and downstream small and medium-sized enterprises will choose the “no digital technology innovation” governance strategy. (3) When $\mathrm{x}>\mathrm{x}*$, the upstream and downstream small and medium-sized enterprises will choose the “strengthen digital technology innovation” governance strategy. The evolution of governance strategies for upstream and downstream small and medium-sized enterprises is shown in Figure 4. It can be observed that the government’s governance strategy selection x and the chain leader’s governance strategy selection y jointly affect the governance strategy evolution of upstream and downstream small and medium-sized enterprises. Furthermore, the labor and innovation costs of digital technology innovation for upstream and downstream small and medium-sized enterprises, as well as the rewards and punishments exerted by both the government and chain leader on these enterprises, will also influence the governance strategy selection of upstream and downstream small and medium-sized enterprises.

3.4. Stability Analysis of Equilibrium Points

In a multi-party evolutionary game, if the equilibrium solution is an evolutionarily stable state, then the equilibrium is a strict Nash equilibrium, i.e., a pure strategy equilibrium. Therefore, the asymptotic stability of the eight pure strategy equilibrium points in the system can be analyzed. From F(x) = 0, F(y) = 0, F(z) = 0, the eight pure strategy equilibrium points are obtained: E₁(0,0,0), E₂(1,0,0), E₃(0,1,0), E₄(0,0,1), E₅(1,1,0), E₆(1,0,1), E₇(0,1,1), E₈(1,1,1).

By using Equations (4) and (9), the Jacobian matrix of the evolutionary game system for the three parties—government departments, chain owner enterprises, and small and medium-sized enterprises (SMEs) in the upstream and downstream of the supply chain—is constructed. The stability of each equilibrium point is analyzed using the Lyapunov indirect method, as shown in

Table 3. Stability analysis of the equilibrium points.

Equilibrium Point	Eigenvalue	Stability
E1(0,0,0)	$\mathrm{R}-\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}$; $-\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}+\Delta {\mathrm{R}}_{\mathrm{b}}$; $-\Delta {\mathrm{C}}_{\mathrm{c}}<$0	Pending
E2(1,0,0)	$\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}-\mathrm{R}-{\mathrm{K}}_{\mathrm{a}}-{\mathrm{K}}_{\mathrm{a}\mathrm{b}}$; $-\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}+\Delta {\mathrm{R}}_{\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}$; $-\Delta {\mathrm{C}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}$	Pending
E3(0,1,0)	$\mathrm{R}-\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}-{\mathrm{R}}_{\mathrm{a}}$; $\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}-{\mathrm{K}}_{\mathrm{b}\mathrm{b}}-\Delta {\mathrm{R}}_{\mathrm{b}}$; $-\Delta {\mathrm{C}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$	Pending
E4(0,0,1)	$\mathrm{R}-\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}-{\mathrm{R}}_{\mathrm{a}\mathrm{b}}$; $-\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}+\Delta {\mathrm{R}}_{\mathrm{b}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}$; $\Delta {\mathrm{C}}_{\mathrm{c}}$ > 0	Unstable point
E5(1,1,0)	$\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}-\mathrm{R}-{\mathrm{K}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}}$; $\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}-{\mathrm{K}}_{\mathrm{b}\mathrm{b}}-\Delta {\mathrm{R}}_{\mathrm{b}}-{\mathrm{R}}_{\mathrm{a}}-{\mathrm{K}}_{\mathrm{a}}$; $-\Delta {\mathrm{C}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$	Pending
E6(1,0,1)	$\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}-\mathrm{R}-{\mathrm{K}}_{\mathrm{a}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}$; $-\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}+\Delta {\mathrm{R}}_{\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}$; $\Delta {\mathrm{C}}_{\mathrm{c}}-{\mathrm{R}}_{\mathrm{a}\mathrm{b}}-{\mathrm{K}}_{\mathrm{a}\mathrm{b}}$	Pending
E7(0,1,1)	$\mathrm{R}-\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}-{\mathrm{R}}_{\mathrm{a}}-{\mathrm{R}}_{\mathrm{a}\mathrm{b}}$; $\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}-\Delta {\mathrm{R}}_{\mathrm{b}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}$; $\Delta {\mathrm{C}}_{\mathrm{c}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$	Pending
E8(1,1,1)	$\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}-\mathrm{R}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}}$; $\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}-\Delta {\mathrm{R}}_{\mathrm{b}}-{\mathrm{R}}_{\mathrm{a}}-{\mathrm{K}}_{\mathrm{a}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}$; $\Delta {\mathrm{C}}_{\mathrm{c}}-{\mathrm{R}}_{\mathrm{a}\mathrm{b}}-{\mathrm{K}}_{\mathrm{a}\mathrm{b}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$	Pending

.

E₄(0,0,1) is not an evolutionarily stable strategy, meaning that there is no possibility for small and medium-sized enterprises (SMEs) in the upstream and downstream of the supply chain to independently and proactively “enhance digital technology innovation” to consciously improve industrial base capabilities and supply chain security levels. For E₃(0,1,0) and E₇(0,1,1), the government adopts the governance strategy of “not establishing a safety risk management system” and allows the chain owner enterprises and SMEs in the upstream and downstream of the supply chain to develop freely according to market rules. However, since the government plays a crucial role in supply chain security governance, managing and guiding the safety behavior of chain owner enterprises and SMEs in the supply chain, it is unlikely that the chain owner enterprises and SMEs will proactively incur additional operational costs to actively lead and strengthen digital technology innovation in the absence of a government reward and punishment mechanism. Therefore, these two equilibrium points are excluded. The remaining five equilibrium points are discussed below.

(1)

starting phase E₁(0,0,0)

When $\mathrm{R}-\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}<0$ occurs, the government will adopt the governance strategy of “not establishing a safety risk management system.” In this case, the chain owner enterprises, in order to pursue their own interests and development, invest significant funds to integrate digital industrial resources and innovation elements, proactively leading efforts to capture market share. However, the development levels of related small and medium-sized enterprises (SMEs) in the upstream and downstream of the supply chain are uneven, leading to occasional unsafe behaviors. At this point, the resource integration costs and guidance costs for the chain owner enterprises are relatively high, and there is a lack of guidance for unsafe behaviors by SMEs in the supply chain. As a result, $-\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}+\Delta {\mathrm{R}}_{\mathrm{b}}<0$, and the chain owner enterprises will choose the “passive leadership” governance strategy.

(2)

Government Departments Move Toward a Security Risk Management System E₂(1,0,0)

When $\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}-\mathrm{R}-{\mathrm{K}}_{\mathrm{a}}-{\mathrm{K}}_{\mathrm{a}\mathrm{b}}<0$ occurs, the government adopts the governance strategy of “establishing a safety risk management system.” If the government’s rewards for the chain owner enterprises are insufficient to offset the resource integration costs and guidance costs incurred by the chain owner enterprises in proactively taking the lead, then $-\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}+\Delta {\mathrm{R}}_{\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}<0$, the chain owner enterprises will adopt the “passive leadership” governance strategy. If the government’s rewards and punishments for small and medium-sized enterprises (SMEs) in the upstream and downstream of the supply chain are insufficient to offset the labor and innovation costs for these SMEs to strengthen digital technology innovation, i.e., $-\Delta {\mathrm{C}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}<0$, the SMEs will continue to adopt the “not strengthening digital technology innovation” governance strategy.

(3)

Chain owner companies under government safety management shifting to an active lead governance strategy E₅(1,1,0)

When $\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}-\mathrm{R}-{\mathrm{K}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}}<0$, the government continues to adopt the “establishing a safety risk management system” governance strategy. Meanwhile, the lead enterprise, by continuously integrating digital industry resources and innovation elements, drives upstream and downstream small and medium-sized enterprises (SMEs) in the supply chain to enhance digital technology innovation. The resource integration and guidance costs of the proactive leadership strategy are controlled, and the lead enterprise begins to take proactive leadership in achieving the safety, stability, and autonomy of the semiconductor supply chain. When $\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}-{\mathrm{K}}_{\mathrm{b}\mathrm{b}}-\Delta {\mathrm{R}}_{\mathrm{b}}-{\mathrm{R}}_{\mathrm{a}}-{\mathrm{K}}_{\mathrm{a}}<0$, the lead enterprise switches to the “proactive leadership” governance strategy. However, due to the varying levels of digitalization and technological innovation among SMEs in the supply chain, the rewards and punishments imposed by both the government and the lead enterprise on SMEs are insufficient to fully address the human resources and innovation costs associated with enhancing digital technology innovation. This leads to the condition $-\Delta {\mathrm{C}}_{\mathrm{c}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}<0$, causing SMEs in the supply chain to tend toward choosing the “do not strengthen digital technology innovation” governance strategy.

(4)

Transformation of Micro, Small and Medium Enterprises to Enhanced Digital Technology Innovation Governance Strategies under Government Security Management E₆(1,0,1)

When $\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}-\mathrm{R}-{\mathrm{K}}_{\mathrm{a}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}<0$ occurs, the government will maintain the governance strategy of “establishing a safety risk management system.” Under this strategy, the government will penalize unsafe behaviors of small and medium-sized enterprises (SMEs) in the upstream and downstream of the supply chain that do not strengthen digital technology innovation. When $\Delta {\mathrm{C}}_{\mathrm{c}}-{\mathrm{R}}_{\mathrm{a}\mathrm{b}}-{\mathrm{K}}_{\mathrm{a}\mathrm{b}}<0$ occurs, SMEs in the upstream and downstream of the supply chain are likely to adopt the “strengthening digital technology innovation” governance strategy. However, at this point, the resource integration costs and guidance costs for the chain owner enterprises remain high, and the government’s rewards for the chain owner enterprises are insufficient to offset the increased costs from proactive leadership. Therefore, $-\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}+\Delta {\mathrm{R}}_{\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}<0$ still holds, and the chain owner enterprises will continue to adopt the “passive leadership” governance strategy.

(5)

ideal state E₈(1,1,1)

When $\left(\mathsf{\alpha }-1\right){\mathrm{C}}_{\mathrm{a}}-\mathrm{R}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}}<0$ occurs, the government will maintain the governance strategy of “establishing a safety risk management system.” Under the government’s safety management, some chain owner enterprises will be eliminated due to their passive leadership, lack of focus on building the supply chain system, and failure to coordinate the industrial and supply chains, which results in a series of supply chain security issues. The remaining chain owner enterprises, through continuous strengthening of guidance and integration of industrial resources and innovation elements, will drive the secure development of the semiconductor industry. As a result, the benefits of proactive leadership will significantly increase, making $\left(\mathsf{\mu }-1\right){\mathrm{C}}_{\mathrm{b}}-\Delta {\mathrm{R}}_{\mathrm{b}}-{\mathrm{R}}_{\mathrm{a}}-{\mathrm{K}}_{\mathrm{a}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}<0$ hold, and the chain owner enterprises will choose the “active leadership” governance strategy. The upgrading of the government’s safety management measures and the active leadership of the chain owner enterprises will greatly encourage small and medium-sized enterprises (SMEs) in the upstream and downstream of the supply chain to strengthen digital technology innovation. This satisfies the condition of $\Delta {\mathrm{C}}_{\mathrm{c}}-{\mathrm{R}}_{\mathrm{a}\mathrm{b}}-{\mathrm{K}}_{\mathrm{a}\mathrm{b}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{K}}_{\mathrm{b}\mathrm{b}}<0$, and SMEs will adopt the “strengthening digital technology innovation” governance strategy. At this point, a virtuous interaction will form among the government, chain owner enterprises, and SMEs in the supply chain, with the strategy set {establishing a safety risk management system, active leadership, strengthening digital technology innovation}. This will help promote the healthy and orderly development of the semiconductor supply chain, ensuring its security, stability, and autonomy.

4. Simulation Analysis

4.1. Parameter Assignment

To further explore the governance mechanism of semiconductor supply chain security and the impact of various parameters on the security level of the semiconductor supply chain, numerical simulation analysis will be conducted using MATLAB R2016b. Based on the current development status of semiconductor supply chain security in China, the parameters for each governance entity will be assigned. To ensure the system stabilizes with the collaborative efforts of government departments, chain owner enterprises, and small and medium-sized enterprises (SMEs) in the upstream and downstream of the supply chain, aiming for the ideal semiconductor supply chain security governance scenario (i.e., convergence at the equilibrium point E8(1,1,1), the relevant parameters need to satisfy $(\mathsf{\alpha }-1){\mathrm{C}}_{\mathrm{a}}+{\mathrm{R}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{a}}<\mathrm{R}$, $(\mathsf{\mu }-1){\mathrm{C}}_{\mathrm{b}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}<{\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+\Delta {\mathrm{R}}_{\mathrm{b}}$, and $\Delta {\mathrm{C}}_{\mathrm{c}}<{\mathrm{R}}_{\mathrm{a}\mathrm{b}}+{\mathrm{K}}_{\mathrm{a}\mathrm{b}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_{\mathrm{b}\mathrm{b}}$. The parameter values are assigned as follows: α = 1.5, ${\mathrm{C}}_{\mathrm{a}}=2.5,{\mathrm{R}}_{\mathrm{a}}=1.5$, ${\mathrm{K}}_{\mathrm{a}}=1$, ${\mathrm{R}}_{\mathrm{a}\mathrm{b}}=0.5$, ${\mathrm{K}}_{\mathrm{a}\mathrm{b}}=1$, R = 4.5, μ = 1.5, ${\mathrm{C}}_{\mathrm{b}}=4$, $\Delta {\mathrm{R}}_{\mathrm{b}}=1.5$, ${\mathrm{R}}_{\mathrm{b}\mathrm{b}}=1.5$, ${\mathrm{K}}_{\mathrm{b}\mathrm{b}}=0.5$ and $\Delta {\mathrm{C}}_{\mathrm{c}}=1$. Next, the stability of government departments, chain owner enterprises, and SMEs in the upstream and downstream of the supply chain under different initial probabilities will be systematically simulated. The initial probability values (x = 0.3, y = 0.6, z = 0.2) will be used as the baseline model, and the impact of parameter changes on the stability of the evolutionary game system will be explored.

4.2. Analysis of Different Initial Probabilities

To examine the impact of different initial probability strategy choices by government departments, chain owner enterprises, and small and medium-sized enterprises (SMEs) in the upstream and downstream of the supply chain on the stability of the evolutionary game system, the initial conditions at time t = 0 are set as follows: the government adopts the “establishing a safety risk management system” governance strategy, chain owner enterprises choose the “active leadership” governance strategy, and SMEs in the upstream and downstream of the supply chain opt for the “strengthening digital technology innovation” governance strategy with the probabilities (0.3,0.6,0.2), (0.5,0.5,0.5) and (0.7,0.4,0.8), respectively. The simulation results are shown in Figure 5. As seen in Figure 5, different initial probabilities do not affect the evolutionary path of governance strategy choices for the government, chain owner enterprises, and SMEs, but they do influence the speed at which the system reaches a stable state. The closer the initial probabilities are to the proportions of the evolutionarily stable strategies, the faster the system converges to a stable state. Therefore, to promote the stable and healthy development of semiconductor supply chain security, government departments should actively establish a safety risk management system, enhance safety management for chain owner enterprises and SMEs in the supply chain, guide the governance strategy choices of both, and create a favorable environment for effective supply chain security governance.

4.3. Parametric Analysis

This section investigates the impact of the government’s safety management benefits and rewards and penalties on the stability of the evolutionary game system, with the initial probabilities set as (0.3, 0.6, 0.2).

(1)

Government security management benefit analysis

In this section, the government’s safety management benefits R are set to 2 and 6, with the simulation results shown in Figure 6.

By comparing the baseline model, it can be observed that the government’s security management benefits significantly affect the system’s stability. If the chain owner enterprises and SMEs in the upstream and downstream of the supply chain have a higher evaluation of government security management, the probability that the government adopts the “establishing a safety risk management system” governance strategy, chain owner enterprises choose the “active leadership” governance strategy, and SMEs adopt the “strengthening digital technology innovation” governance strategy will be higher than in the initial model, leading to a reduced time for the government, chain owner enterprises, and SMEs to reach a stable state.

If the government’s security management benefits are low, it will face a trade-off between security management benefits and costs. When the government observes that chain owner enterprises actively take the lead in integrating digital industrial resources and innovation elements, it might relax its management. Upon noticing this, chain owner enterprises will gradually adopt the “passive leadership” governance strategy, which leads to a decline in the efficiency of semiconductor supply chain security governance and insufficient security levels. At this point, the government is likely to revert to the “establishing a safety risk management system” governance strategy, and the continual evolution of governance strategies by both the government and the chain owner enterprises will put them in a state of strategic dilemma, preventing the system from reaching a stable state. It is evident that increasing the government’s security management benefits can enhance the likelihood of the government choosing the “establishing a safety risk management system” strategy, thus accelerating the achievement of semiconductor supply chain security governance goals and improving the supply chain security level. Therefore, the government should strengthen its security management, enhance its security management image, and adopt a variety of measures such as risk prevention, monitoring and early warning, risk assessment, and risk response to manage chain owner enterprises and SMEs in the supply chain. This will also improve the evaluation of the government by chain owner enterprises and SMEs, contributing to the achievement of semiconductor supply chain security and stability.

(2)

Analysis of government incentives and penalties for chain-owning companies

This section considers the impact mechanism of the government’s reward intensity for chain owner enterprises on the stability of the system. The government’s reward intensity for chain owner enterprises is denoted as $R_a$ = 0.3, 3, and the simulation results are shown in Figure 7a,b.

From Figure 7a,b, it can be observed that the relationship between the government’s reward intensity for chain owner enterprises choosing the “active leadership” governance strategy and the system’s stability is not linear. When the government’s reward intensity is relatively low, the cost of the government choosing the “establishing a safety risk management system” governance strategy is lower, and the probability of selecting this strategy increases faster compared to Figure 5a. However, when the government’s reward intensity is lower than the resource integration and guidance costs of the chain owner enterprises’ “active leadership,” this results in $(\mathsf{\mu }-1){\mathrm{C}}_{\mathrm{b}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}>{\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+\Delta {\mathrm{R}}_{\mathrm{b}}$. At this point, chain owner enterprises will reduce the probability of choosing “active leadership,” causing the system to evolve into the ineffective state {establish safety risk management system, passive leadership, strengthen digital technology innovation}. When the government’s reward intensity ${\mathrm{R}}_{\mathrm{a}}$ is relatively high, this implies higher security management costs. At this point, the government faces a trade-off between security management benefits and costs. When chain owner enterprises tend to choose the “active leadership” governance strategy, the government may choose to adopt the “no safety risk management system” strategy to reduce operational costs. As a result, chain owner enterprises will adopt a “passive leadership” governance strategy, and the strategies of both the government and chain owner enterprises will fluctuate, preventing the system from reaching a stable state. Increasing the government’s reward intensity can accelerate the chain owner enterprises’ adoption of the “active leadership” strategy, but at the cost of lower security management efficiency. Therefore, the government should select an appropriate reward intensity based on the current state of semiconductor supply chain governance to balance the incentives and management costs effectively.

This section considers the impact mechanism of the government’s punishment intensity for chain owner enterprises on the stability of the system. Let the government’s punishment intensity be denoted as ${\mathrm{K}}_{\mathrm{a}}$ = 0.2, 2, and the simulation results are shown in Figure 7c,d.

When the government’s punishment intensity ${\mathrm{K}}_{\mathrm{a}}$ for chain owner enterprises is low, the penalty cost for “passive leadership” is also low, and it is not enough to offset the increased resource integration and guidance costs associated with the “active leadership” strategy. As a result, chain owner enterprises adopt the “passive leadership” governance strategy, leading to an ineffective situation {establish safety risk management system, passive leadership, strengthen digital technology innovation}. When the government’s punishment intensity ${\mathrm{K}}_{\mathrm{a}}$ increases to 2, the three-party evolutionary game model involving the government, chain owner enterprises, and SMEs in the upstream and downstream of the supply chain reaches a stable state, and the evolution speed of chain owner enterprises choosing the “active leadership” strategy increases. Therefore, when formulating the reward and punishment mechanisms, the government should increase the punishment intensity for chain owner enterprises choosing the “passive leadership” strategy. Based on the current state of semiconductor supply chain governance, the government should also select an appropriate reward intensity to ensure that the system converges to a stable state and promotes the desired governance outcomes.

(3)

Analysis of government incentives and penalties for upstream and downstream SMEs in the supply chain

To verify how the government’s reward intensity for SMEs in the upstream and downstream of the supply chain influences the evolution of the governance strategies in the evolutionary game system, let the government’s reward intensity for SMEs be denoted as ${\mathrm{R}}_{\mathrm{a}\mathrm{b}}$ = 0.2, 3, and the simulation results are shown in Figure 8a,b.

When the government’s reward intensity for SMEs in the upstream and downstream of the supply chain ${\mathrm{R}}_{\mathrm{a}\mathrm{b}}$ is low, the government, chain owner enterprises, and SMEs tend toward the ideal scenario of {establishing a safety risk management system, active leadership, strengthening digital technology innovation}. However, due to the low reward intensity ${\mathrm{R}}_{\mathrm{a}\mathrm{b}}$, reducing the reward intensity does not significantly promote the system’s convergence to a stable state, and the time it takes to reach stability is similar to that in Figure 5a. When the government’s reward intensity ${\mathrm{R}}_{\mathrm{a}\mathrm{b}}$ for SMEs is sufficiently high, SMEs will accelerate the adoption of the “strengthening digital technology innovation” governance strategy. However, an excessively high reward intensity forces the government to make a trade-off between safety management costs and safety management benefits. As the supply chain security governance approaches a stable state, the government may choose to relax safety management in order to save on costs. In response, chain owner enterprises, aiming to reduce resource integration and guidance costs, may switch to a “passive leadership” governance strategy. This creates a situation where the governance strategies of both the government and chain owner enterprises oscillate. Therefore, there exists an effective range for the government’s reward intensity for SMEs.

To assess the impact of the government’s punishment intensity for SMEs that do not strengthen digital technology innovation, the government’s punishment intensity for such behavior is denoted as ${\mathrm{K}}_{\mathrm{a}\mathrm{b}}$ = 0.2, 1.5, and the simulation results are shown in Figure 8c,d. From Figure 8c,d, it is evident that when ${\mathrm{K}}_{\mathrm{a}\mathrm{b}}$ is 0.2 and 1.5, the governance strategies of the government, chain owner enterprises, and SMEs stabilize at {establishing a safety risk management system, active leadership, strengthening digital technology innovation}. As the government’s punishment intensity for SMEs increases, SMEs will accelerate the adoption of the “strengthening digital technology innovation” governance strategy, and the time for chain owner enterprises to adopt the “active leadership” strategy is shortened. However, the government’s punishment intensity for SMEs has a relatively small impact on the system’s stability. Given the varying levels of digitalization and technological innovation among SMEs in the upstream and downstream of the supply chain, as well as the improvement in the government’s safety management benefits, the government should implement a range of punishment measures—such as warnings, fines, and temporary suspension of operations—against behaviors that threaten semiconductor supply chain security. These measures can effectively guide the behavior of SMEs in the supply chain, contributing to enhanced supply chain security.

4.4. Parametric Analysis of Chain-Owning Enterprises

Chain owner enterprises primarily guide SMEs in the upstream and downstream of the supply chain to strengthen digital technology innovation by integrating digital industrial resources and innovation elements, thereby achieving the innovative development of SMEs in the supply chain and better ensuring the security, stability, and autonomy of the semiconductor supply chain. This section discusses the loss of benefits when chain owner enterprises adopt a passive leadership strategy, as well as the impact of the reward and punishment mechanisms for SMEs in the upstream and downstream of the supply chain on the stability of the evolutionary game system. At this point, the initial probabilities are also (0.3, 0.6, 0.2).

(1)

Analysis of Losses in Chain Leader Enterprises’ Earnings

Under the condition that other parameters remain unchanged, the loss of benefits from passive leadership is varied, with $\Delta {\mathrm{R}}_{\mathrm{b}}$ = 0.5, 4.5, respectively. The simulation results are shown in Figure 9.

As shown in Figure 9, the loss of benefits influences the governance strategies of chain owner enterprises, as well as the evolutionary speed of the government and SMEs in the upstream and downstream of the supply chain. When $\Delta {\mathrm{R}}_{\mathrm{b}}$ is large, chain owner enterprises, in an effort to compensate for the loss of benefits, reach a stable state faster compared to the baseline model, and the speed at which the government and SMEs in the supply chain reach stability is also accelerated. When $\Delta {\mathrm{R}}_{\mathrm{b}}$ is sufficiently small, such that $(\mathsf{\mu }-1){\mathrm{C}}_{\mathrm{b}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}>{\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+\Delta {\mathrm{R}}_{\mathrm{b}}$ occurs, the external driving force for active leadership from the chain owner enterprises weakens, and they gradually adopt a “passive leadership” governance strategy. As a result, the time for SMEs in the supply chain to converge to a stable governance strategy is extended, ultimately leading to the ineffective state of {establishing a security risk management system, passive leadership, strengthening digital technology innovation}. Therefore, increasing the loss of benefits from passive leadership for chain owner enterprises can reduce the time required for the system to reach the ideal stable state.

(2)

Analysis of chain-owning enterprises’ rewards and punishments for upstream and downstream SMEs in the supply chain

First, we discuss the impact mechanism of the reward intensity of chain owner enterprises on SMEs in the upstream and downstream of the supply chain on the system’s stability. The reward intensity of chain owner enterprises for SMEs is set as ${\mathrm{R}}_{\mathrm{b}\mathrm{b}}$ = 0.2, 2, with the simulation results shown in Figure 10a,b.

It can be observed that ${\mathrm{R}}_{\mathrm{b}\mathrm{b}}$ not only affects the evolutionary speed of the government, chain owner enterprises, and SMEs in the upstream and downstream of the supply chain, but also influences the governance strategies of the chain owner enterprises. When ${\mathrm{R}}_{\mathrm{b}\mathrm{b}}$ is relatively small, the time for the chain owner enterprises to choose the “active leadership” governance strategy shortens, while the external driving force for SMEs in the upstream and downstream of the supply chain is weaker, which slows down the time for the evolutionary game system to reach a stable state. As the chain owner enterprises gradually increase the reward intensity for SMEs, until $(\mathsf{\mu }-1){\mathrm{C}}_{\mathrm{b}}+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}>{\mathrm{R}}_{\mathrm{a}}+{\mathrm{K}}_{\mathrm{a}}+\Delta {\mathrm{R}}_{\mathrm{b}}$, the resource integration costs and guidance costs of the chain owner enterprises’ active leadership strategy become high, leading them to gradually lean towards the “passive leadership” governance strategy. Therefore, there is a reasonable range for the reward intensity of chain owner enterprises for SMEs in the supply chain.

Next, we explore the effect of the punishment intensity imposed by the chain owner enterprises on SMEs in the upstream and downstream of the supply chain on the stability of the evolutionary game system. Under the condition that other parameters remain unchanged, we set the punishment intensity ${\mathrm{K}}_{\mathrm{b}\mathrm{b}}$ of the chain owner enterprises for SMEs in the upstream and downstream of the supply chain to 0.2 and 1, respectively. The simulation results are shown in Figure 10c,d. From Figure 10c,d, it can be observed that the punishment intensity of the chain owner enterprises for SMEs does not affect the governance strategies of the government, chain owner enterprises, and SMEs in the upstream and downstream of the supply chain. Increasing the punishment intensity accelerates the time for the chain owner enterprises and SMEs in the upstream and downstream of the supply chain to reach a stable state, but the effect is relatively small. In the face of prominent supply chain security issues, when guiding the innovation development of SMEs in the supply chain, chain owner enterprises should primarily rely on reward measures rather than imposing excessive punishment. Excessive punishment not only weakens the enthusiasm of SMEs to strengthen digital technology innovation but also results in less effective governance outcomes.

4.5. Parametric Analysis of Upstream and Downstream MSMEs in the Supply Chain

This section examines the effect of the labor costs and innovation costs of SMEs in the upstream and downstream of the supply chain, strengthening digital technology innovation on the stability of the system. The initial probabilities are the same as before, i.e., (0.3, 0.6, 0.2). Let the labor cost and innovation cost of SMEs in the upstream and downstream of the supply chain for strengthening digital technology innovation be $\Delta {\mathrm{C}}_{\mathrm{c}}$ = 0.5, 4, respectively. The simulation results are shown in Figure 11.

From Figure 11, it can be observed that $\Delta {\mathrm{C}}_{\mathrm{c}}$ not only affects the evolution speed of the governance subjects, including the government, chain leader enterprises, and upstream and downstream SMEs, but also influences the governance strategy selection of the SMEs themselves. As labor costs and innovation costs increase, the stable strategy of SMEs in the upstream and downstream of the supply chain shifts from “strengthening digital technology innovation” to “not strengthening digital technology innovation,” leading to insufficient digitalization and lower supply chain security levels. In contrast, reducing the labor costs and digital technology innovation costs for SMEs in the upstream and downstream of the supply chain can accelerate the convergence of the game system towards the ideal equilibrium point {establishing a security risk management system, active leadership, strengthening digital technology innovation}. Therefore, enhancing the safety awareness of SMEs in the upstream and downstream of the supply chain and minimizing the additional costs of strengthening digital technology innovation is of significant importance for semiconductor supply chain security governance.

5. Conclusions

This study, based on evolutionary game theory, constructs a semiconductor supply chain security governance model involving three key stakeholders: government departments, chain owner enterprises, and upstream/downstream SMEs. MATLAB simulations reveal the dynamic evolutionary paths of multi-agent collaborative governance and its driving mechanisms. The findings indicate that semiconductor supply chain security is not driven by a single entity but is achieved through a complex equilibrium formed by the interplay of policy incentives, cost constraints, and risk perceptions among multiple governance actors. The main conclusions are as follows:

(1) The multi-agent collaborative governance mechanism serves as the core framework for enhancing supply chain resilience. From the perspective of governance actors, the governance of semiconductor supply chain security is led by chain owner enterprises, with active participation from government entities and upstream and downstream SMEs. The study demonstrates that the policy guidance of government departments, the resource integration of chain owner enterprises, and the technological innovation of SMEs are all indispensable. The government’s risk management system regulates the strategic choices of chain owner enterprises through incentives (e.g., targeted tax incentives, digital innovation funds, and stricter intellectual property protection) and penalty mechanisms (e.g., fines), while chain owner enterprises reduce the innovation costs of SMEs through technological spillover effects. It is therefore essential to strengthen the digital capabilities of upstream and downstream SMEs in the supply chain and leverage artificial intelligence to empower their digital transformation, thereby fostering a virtuous cycle of “policy-driven—resource integration—technology diffusion.” This finding aligns with the theories proposed by Nagata et al. [7] and Sami et al. [8] regarding “localized innovation networks in the context of deglobalization,” emphasizing the need for governments and enterprises to establish a dynamic balance between digitalization and security objectives. The government establishes a security risk management system, chain owner enterprises integrate resources and innovation elements, and SMEs enhance their digital technology capabilities, collectively ensuring the security and stability of the supply chain. Through AI-enabled digital innovation, SMEs can better integrate into the industrial ecosystem, enhance their risk resistance, and make positive contributions to the overall security and stability of the supply chain.

(2) The evolutionary path of governance strategies exhibits significant threshold effects and path dependence. The evolution mechanism of semiconductor supply chain security governance involves the collaborative actions of multiple actors [33]. In the initial stage, governance strategy combinations are weak, but as the government strengthens security management, chain owner enterprises take the lead, and SMEs enhance technological innovation, ultimately achieving the ideal equilibrium state. Simulation results indicate that when government security management revenue exceeds a certain threshold, it tends to establish a risk management system; meanwhile, the strategic choices of chain owner enterprises are constrained by the game between marginal costs and external incentives. Notably, SMEs’ innovation behavior is highly sensitive to cost fluctuations, and even a slight increase in innovation costs may trigger strategic reversals, leading the system into a “low-security equilibrium.”

(3) Parameter optimization can accelerate the realization of the ideal equilibrium, but excessive policy intervention should be avoided. The governance of semiconductor supply chain security is significantly influenced by the benefit parameters of governance actors. Proper adjustments to government revenue, penalty intensity, and SMEs’ innovation costs can expedite the achievement of the ideal equilibrium. However, it is crucial to balance the interests of all parties, avoiding excessively high incentive costs or punitive measures that could negatively impact governance actors. Increasing government management revenue and chain owner enterprises’ responsibility costs effectively shortens the convergence time, but excessive rewards may induce “free-riding” behavior, weakening the long-term leadership willingness of chain owner enterprises. Furthermore, the marginal effect of penalties on SMEs’ strategic stability diminishes over time, suggesting that a “primarily incentive-based, supplemented by penalties” flexible governance model is more sustainable. This conclusion complements the “cascading risk control” theory proposed by Dolgui et al. [27], emphasizing the need for governance tools to balance efficiency and fairness.

(4) Against the backdrop of intensified global competition in the semiconductor industry, the US CHIPS and Science Act has increased external pressure on China’s semiconductor supply chain through measures such as financial subsidies, supply chain restructuring, and technology blockades. Based on the governance model of this study, it can be seen that the key to addressing this challenge lies in forming a collaborative mechanism among the government, chain owner enterprises, and small and medium-sized enterprises (SMEs): The government needs to establish a more complete security risk management system and enhance the incentives and constraints on chain owner enterprises and SMEs; chain owner enterprises should strengthen their functions of resource integration and technology diffusion to guide upstream and downstream SMEs to reduce innovation costs; SMEs should enhance their digital innovation capabilities with the empowerment of AI to increase their resilience and adaptability in the supply chain system. Through this collaborative governance under multi-agent games, China’s semiconductor industry can achieve the dual goals of self-reliance and innovation-driven development while responding to external policy shocks. Although this paper takes China’s semiconductor industry as the research object, the constructed tripartite evolutionary game model is universal and can provide a reference for other countries when facing semiconductor supply chain security challenges.

The theoretical contributions and practical implications of this study lie in its extension of the theoretical framework for supply chain security governance through an evolutionary game model, shifting the traditional risk management perspective to a dynamic strategic interaction level and providing a methodological innovation for policy simulation. On a practical level, it is recommended that the government establish a “tiered” incentive and penalty mechanism, tailoring innovation subsidies based on enterprise scale differences. Simultaneously, chain owner enterprises should leverage open innovation platforms to reduce technology diffusion costs and avoid the “innovation lock-in” effect.

Nevertheless, this study has some limitations. For instance, it does not fully incorporate external variables such as geopolitical factors (e.g., technological blockades) and ecological sustainability. Future research could integrate complex network theory to quantify the impact of multi-tier supply chain topologies on security thresholds and introduce cross-national comparative case studies to further validate the universality of the governance mechanisms.

In conclusion, the essence of semiconductor supply chain security governance is a dynamic game among multiple actors constrained by the “security-efficiency-cost” trade-off. Only through institutional design that optimizes incentive-compatible mechanisms can the dual goals of “autonomous controllability” and “innovation-driven development” be achieved, providing a strategic foundation for China’s semiconductor industry to break through under the backdrop of global supply chain restructuring.