Healthcare Supply Chain Resilience Investment Strategy Analysis Based on Evolutionary Game

Abstract

Healthcare is considered one of the necessities for sustaining life. However, frequent emergencies raise the risk of supply chain disruption, seriously threatening people’s lives and health security. Therefore, building a resilient healthcare supply chain is an important initiative to manage the healthcare crisis effectively. Based on the secondary supply chain formed by medical supply manufacturers and retailers, this paper constructs an evolution game model of resilience investment decisions under the non-disruption and disruption symmetry scenarios of the supply chain and analyzes the stabilization strategies employed by both parties based on their asymmetry strategy choices. Subsequently, the numerical simulation is used to analyze the impact of various parameters on the evolutionary results and their evolutionary trends. The results of the study show that additional benefits from resilience investment, potential costs, disruption losses, market encroachment revenue, “free-rider” benefits, additional benefit increase coefficient, resilience investment reduction coefficient, disruption loss reduction coefficient, additional unit cost reduction coefficient, and market encroachment revenue coefficient all influence the resilience investment decisions. Finally, based on the simulation results, specific recommendations are formulated to improve the resilience of the healthcare supply chain.

1. Introduction

The term “supply chain” (SC) refers to a complex network system that connects customers with diverse products or services following their demand. This process entails managing and regulating logistics, information flow, and financial flow from the product or service supplier to the retailer. Nevertheless, the SC network has evolved into a more complex SC ecosystem due to economic globalization, specialized division of labor, digital intelligence, and the upgrading of personalized customer demand. This complexity increases the likelihood of unexpected events affecting the SC [1]. Statistics indicate that over 75% of organizations encounter SC disruptions yearly [2], which are frequently caused by risk factors such as natural disasters, conflicts, and policy changes. These disruptions can result in significant losses to organizations.

The healthcare supply chain (HCSC) is a vital network that is dedicated to preserving lives and delivering high-quality healthcare to people. It aims to provide patients with high-quality products and efficient services promptly and at affordable prices. This is crucial for guaranteeing the security and well-being of humans. According to statistics, healthcare expenditures in the U.S. hit USD 3.5 trillion in 2017, with USD 25.4 billion explicitly allocated to the HCSC [3]. In 2023, healthcare organizations accounted for approximately 11% of global gross domestic product [4]. Healthcare expenses are expensive and consistently increasing, resulting in unprecedented government spending. With the increasing impact of disasters on human life, there has been a higher demand for services in the SC, further disrupting healthcare delivery. The COVID-19 pandemic has placed significant and sustained pressure on the HCSC, resulting in shortages of essential healthcare resources [5,6]. As a result, healthcare expenses have increased across all sectors. Numerous hospitals cannot provide medical care due to a shortage of medical supplies [7]. The HCSC plays a critical role in ensuring the well-being of patients and healthcare workers. It provides patients with necessary medicines and equipment and supports healthcare workers by providing them with the required equipment to deliver their services [8]. Therefore, the importance of the HCSC has become more critical in light of the major disasters that have led to a surge in demand for and scarcity of medical equipment. Enhancing healthcare supply chain resilience (HCSCRES) means improving the adaptability of the healthcare system, enabling it to reconfigure its resources and increasing the availability of healthcare resources [9]. As it is critical to ensure the availability of medical supplies during disruption, the HCSC must be as resilient as possible during any event that could lead to a disruption. In other words, constructing a resilient HCSC is a solution to the healthcare crisis [10].

An analysis of the literature indicates that scholars have studied the basic concepts, key elements, antecedents, and consequences of HCSCRES [11,12,13]. Mandal [14] used structural equation modeling to explore how organizational culture impacts HCSCRES, with technological orientation playing a moderating role. Tortorella et al. [15] utilized an empirical approach to collect quantitative data and found that digitization enhances HCSCRES. Betto and Garengo [7] employed a case study to define HCSCRES as a third-order capability. They identified a circular path for developing HCSCRES in response to uncertain events. Manufacturers produce pharmaceuticals and medical equipment, while retailers handle distribution. Due to differing interests, information asymmetry, and bounded rationality, improving the HCSCRES depends on their strategies. To achieve HCSC sustainability, it is essential to explore the behavioral strategies of manufacturers and retailers in various situations. However, there is a lack of understanding from an evolutionary game theory perspective regarding building a resilient HCSC and the decision-making behaviors of both parties in different scenarios, despite scholars’ qualitative and quantitative research on enhancing HCSCRES. In addition, free-riding behavior is also prevalent among SC member firms. The basic meaning of free-riding behavior is the speculative behavior of enjoying the benefits of others without paying the cost [16]. To cope with SC disruption, medical supply manufacturers can take HCSCRES measures to secure the SC, such as increasing the inventory of medical supplies, improving the production capacity of medical supplies, and sourcing from multiple sources. While these measures improve HCSCRES, they also create conditions for free-riding behavior by medical supply retailers since manufacturers secure the supply of medical supplies for retailers. Therefore, a major challenge is how to actively induce HCSC members to invest in costs to enhance HCSCRES. To address this research gap, this study aims to analyze the resilience investment behaviors and interaction mechanisms of medical supply manufacturers and retailers in both non-disruption and disruption symmetry scenarios of the HCSC, based on evolutionary game theory. Specifically, this study systematically explains the following questions: What are the stable states and corresponding conditions for enhancing the HCSCRES? How do the strategy choices of manufacturers and retailers and related factors influence the evolution of stable states? We developed an evolutionary game model and conducted numerical simulations to achieve these objectives. The main research findings are as follows: (1) The proposed evolutionary game model involving manufacturers and retailers effectively describes both parties’ behavioral strategies’ influencing factors and interaction mechanisms; (2) The effects of parameters such as “free-rider” benefits, market encroachment revenue coefficient, disruption loss reduction coefficient, and additional unit cost reduction coefficient on the resilience investment are illustrated in numerical simulations; (3) Following supply chain management theory, corresponding suggestions are proposed.

Potential innovations in this paper: The models consider free-rider behavior. The research highlights the risk that healthcare retailers’ free-riding behavior could lead to failure in collaborating to enhance HCSCRES. Therefore, free-riding behavior needs to be taken into account. The research also analyzes resilience investment strategies under two scenarios: SC non-disruption and disruption. Two separate models were constructed to discuss these scenarios, acknowledging that SC disruption may or may not occur.

This paper is structured as follows: The next section provides a literature review, which introduces the terms and research relevant to this paper. That is followed by the game analysis, which constructs a game model of resilience investment decisions under the non-disruption and disruption scenarios and conducts system stability analysis. The fourth section performs numerical simulation analysis. The last section is a summary, which reviews the paper and suggests possible improvements.

2. Literature Review

Healthcare supply chain management (HCSCM) is critical to providing adequate and timely essential healthcare resources to healthcare organizations and is integral to delivering quality healthcare services. The HCSC must ensure the availability of essential medical supplies and effectively manage the distribution of medicines, equipment, and other critical resources [17]. This section reviews relevant aspects of HCSC and HCSCRES.

2.1. Healthcare Supply Chain

The SC is a complex network that connects suppliers, manufacturers, distributors, and end-users into a whole around the core enterprise, starting from the procurement of raw materials, going through the process of making intermediate products as well as final products, and ultimately delivering the products to the consumers through the sales network. The HCSC has attracted extensive attention from scholars, government officials, and healthcare providers recently as a tool to manage healthcare costs and improve service quality effectively; in contrast to the general SC, the HCSC is distinguished by high complexity, high value of goods movement, and, most importantly, human lives [18]. It is characterized by complexity, life support focus, urgency, and time sensitivity [19]. Given the crucial responsibility of healthcare organizations to provide healthcare services, Senna et al. [12] define the HCSC as a SC whose primary mission is to ensure the provision of high-quality healthcare services to the populace and preserve lives. The HCSC comprises an external chain (suppliers, manufacturers, and distributors) and an internal chain (patient care units, hospital warehouses, and patients) [20]. Kitsiou et al. [21] describe a typical HCSC structure: the focal entities are healthcare providers (e.g., hospitals), which are various departments that manage complex information and product flow. Next are the backward entities, including manufacturers, purchasing groups, and transporters. Finally, the forward entities may include private entities, insurance companies, and government agencies. The main processes of the chain include product flows (e.g., pharmaceuticals, medical devices), information flows (e.g., orders, invoices, requisitions), and financial flows (e.g., medical fees, registration fees).

Over the past decade, the healthcare industry has experienced significant changes and has become increasingly competitive. Patients now play a more significant role in healthcare decisions, forcing providers to deliver healthcare services more efficiently and effectively [22]. Additionally, emerging environmental risks and changing disease realities are posing new challenges to the current models of healthcare sustainability [23]. With the aging of the population, changes in the disease spectrum, and the widespread use of new medical technologies, the demand for healthcare services is growing, and the healthcare services industry is gradually becoming a more significant part of the gross domestic product. The global healthcare system faces growing demands to minimize resource wastage and eliminate unnecessary expenses while enhancing the quality and consistency of healthcare services delivered to patients [24]. Consequently, researchers have started implementing supply chain management (SCM) methods to improve healthcare services, lower healthcare expenses, and enhance consumer satisfaction.

SCM integrates and coordinates logistics, information, and financial flows across different sectors and firms, aiming to optimize the value chain between raw material suppliers and final customers while efficiently transforming and utilizing SC resources [25]. Over the years, scholars have begun introducing SCM theories into the healthcare field, and there has been a growing interest in research on HCSCM [26]. SCM focuses on collaboration and interaction between stakeholders, and the extensive expertise of SCM offers a unique opportunity to comprehend, evaluate, and improve healthcare systems [27]. HCSCM differs significantly from general industrial SCM. This is because the healthcare field deals with tangible goods such as drugs and medical equipment, as well as the management of patient flow, the establishment of relationships, and the allocation of power and accountability [20]. In order to ensure the safety of human life, the HCSC must maintain an extremely high level of service, approaching 100%. Additionally, HCSCM must respond effectively to unexpected events such as widespread disease outbreaks, chemical/biological attacks, and pandemics [28]. An optimized HCSC ensures timely medical supplies and equipment availability, contributing to efficient patient care and effective response to healthcare crises [29]. Due to these specific attributes, HCSCM often deviates from conventional SCM procedures and requires unique management practices. It can be described as the reorientation of SC thinking in healthcare that encompasses business activities and operations to achieve a smooth and continuous flow of healthcare materials and services. The HCSC is typically associated with the procuring and logistics of medical supplies and services [30]. Betcheva et al. [27] defined HCSCM as the efficient management of individuals, procedures, information, and finances to provide healthcare goods and services to consumers, improving clinical outcomes and user experience while controlling costs.

The literature on the healthcare industry from a SCM perspective is inadequate [31]. While healthcare practitioners recognize the significance of implementing SCM practices, the distinct characteristics of the healthcare industry make it unsuitable to adapt industrial SC approaches directly [22]. A SC typically encompasses logistics, information, and financial flows. The architecture of the SC is primarily impacted by the requirements, limitations, and opportunities related to the physical flow of products. In the healthcare industry, financial and information flows are crucial factors in determining the design decisions of the HCSC [28].

Table 1. Research related to the healthcare supply chain.

Author	Main Contribution
Hussain et al. [28]	This paper, based on stakeholder theory, identifies the incentives, barriers, and enablers of social sustainability in the HCSC.
Aldrighetti et al. [18]	This paper argues that enabling alternate suppliers is the most effective mitigation strategy for long-term HCSC disruption.
Scavarda et al. [32]	This paper analyzes the HCSC in emerging countries and proposes a management framework from a sustainability perspective.
Marques et al. [33]	This paper utilizes a systematic literature review approach to synthesize 74 empirical studies (2006–2016) to map the latest HCSC research.
Alizadeh et al. [34]	This paper considers biological risks and investigates the design of forward and reverse SC networks for medical consumer products through a programming approach.
Sazvar et al. [35]	This paper presents a scenario-based model of a closed-loop pharmaceutical SC network designed to improve pharmaceutical waste’s social and environmental impacts.
Senna et al. [12]	This paper explores the impact of supply chain risk management on HCSC performance.
Saha and Rathore [4]	This paper explores the impact of Healthcare 4.0 technologies on HCSC performance.

briefly summarizes recent research findings on the HCSC. Scholars have used qualitative and quantitative approaches to study different aspects of the HCSC, such as sustainability, research mapping, network design, and performance.

2.2. Healthcare Supply Chain Resilience

The demand for supply chain resilience (SCRES) is based on the fundamental premise that it is impossible to eliminate all risks [36]. However, organizations can reduce the disruption risks that can affect the SC by improving its resilience, which is a prerequisite for the demand for resilience [37]. According to Christopher and Peck [38], SCRES refers to the capability of a system to recover to its original or better state after the disturbance. Williams et al. [39] consider SCRES as the ability of a SC to respond to unexpected disruptions and resume normal operations. Dubey et al. [40] define SCRES as the capability of a supply system to recover to its original state within an acceptable period after a disruption. The above definition of SCRES only focused on post-event response, which is reactive. To prevent disruptions and mitigate their impact, SCRES should also consider the concept of disruption prevention. Ponomarov and Holcomb [41] consider SCRES as the adaptive capacity to cope with unforeseen events, respond to disruptions, and recover from them. Hohenstein et al. [42] argue that SCRES is the SC’s capability to be prepared for unexpected risk events, responding and recovering quickly to potential disruptions to return to its original situation or grow by moving to a new, more desirable state, which somehow affirms the SC’s capability to learn after disruptions and to turn threats into opportunities. Chowdhury and Quaddus [43] identified SCRES as the ability of a SC to cope with disruptive events through both proactive and reactive forms. A review of definitions reveals no standardized definition of SCRES, but scholars are progressively gaining a more comprehensive knowledge of this concept. It has evolved from involving only post-disruption reactive responses to pre-disruption proactive prevention and post-disruption reactive responses. SCRES embodies a learning capability that enables the SC to recover to a higher level of performance. In addition, most scholars view SCRES as a capability that includes absorption, adaptation, and recovery capabilities [44,45,46,47]. In summary, this study defines SCRES as a capability that can absorb disturbance events before disruption, respond rapidly to adapt to the environment after the disruption, and recover the SC to its original level or even higher.

Healthcare has always been one of the most critical industries, and protecting lives is vital to every government. However, the HCSC has been taken seriously in the last 20 years due to several different disasters. As the complexity of managing globalized operations increases, SCRES emerges as an essential capability [48]. Service companies require resilience to effectively manage the growing complexity of their operations, mitigate the risk of disruptions, and achieve optimal performance. Healthcare organizations must strategically allocate their resources to ensure the continuity of services during disruption. The resilience requirement in the healthcare services industry is more urgent than in the manufacturing industry. This is due to the potential lethality of not promptly providing patient treatment and related services [49,50]. Timely access to medical supplies becomes even more critical during healthcare crises such as epidemics or natural disasters [51]. Therefore, we extend the concept of resilience to the HCSC.

We have seen several essential definitions in the literature that pertain to HCSCRES. Zamiela [11] defines resilience as a dynamic capability that enables firms to prepare for uncertainty through adequate planning with SC partners. According to Berke et al. [52], disaster resilience is the capacity to restructure, adapt, and modify in response to stress. In the context of the HCSC, this necessitates the coordination and consolidation of the resources and abilities of SC entities to guarantee sufficient readiness, efficient recovery and response, and, above all, robust service provision to healthcare workers and patients in the event of a disruption. According to Mandal [14], resilience is a dynamic capability, and HCSCRES is the capability of HCSC entities to collaborate effectively to ensure continuous healthcare provision to patients during disruption. Additionally, Alemsan et al. [53] defined healthcare resilience as the capability of a healthcare system to adjust its functioning before, during, or after changes and disturbances to maintain the required performance under both expected and unexpected conditions. The concepts discussed are directly relevant to HCSC due to the interconnected networks that can be affected during a prolonged catastrophe like COVID-19. The current definitions of HCSCRES are limited to when disruptions occur, disregarding the absorptive capacity before disruptions and its capacity to recover after disruptions. Therefore, this study considers HCSCRES as a capability that includes the capability to absorb disturbance events before disruption, the capability to adapt to the environment by responding rapidly after the disruption, and the capability to recover the HCSC to its original level or even higher to ensure that healthcare entities can provide reliable and continuous healthcare services to patients in an uncertain environment.

3. Evolutionary Modeling and Analysis of Stabilization Strategies

Disruptions in the HCSC can threaten patients’ lives and impose additional costs on healthcare providers. Participants must allocate resources to many aspects of improving SCRES. These include increasing drug redundancy, enhancing HCSC flexibility and agility, and actively fostering the SC risk culture. This study considers a secondary HCSC consisting of a medical supply manufacturer (MSM) and a medical supply retailer (MSR) and assumes that both are finite rationality. Initially, their strategies are not optimal, and they learn, experiment, and adjust until they reach a steady state. There is a symmetry strategy: investment and non-investment. Healthcare entities can reduce losses caused by SC disruption by implementing resilience investment. The HCSC is analyzed independently in symmetry scenarios: non-disruption and disruption, as the SC disruption may or may not occur.

3.1. Healthcare Supply Chain Non-Disruption Scenario

3.1.1. Basic Hypothesis

Hypothesis 1. 

The MSM will choose either a “resilience investment” strategy or a “resilience non-investment” strategy due to its resilience investment costs, benefits, and synergistic benefits. The probability of choosing the “resilience investment” strategy is x, and the probability of choosing the “resilience non-investment” strategy is 1 − x;

Hypothesis 2. 

The MSR will choose either a “resilience investment” strategy or a “resilience non-investment” strategy due to its resilience investment costs, benefits, and“free-rider” benefits. The probability of choosing the “resilience investment” strategy is y, and the probability of choosing the “resilience non-investment” strategy is 1 − y;

Hypothesis 3. 

The healthcare entity’s daily operations create revenue, with inherent revenue R_m for the MSM and inherent revenue R_r for the MSR;

Hypothesis 4. 

The unilateral resilience investment has an additional benefit for the MSM, which is r_m. This means that the MSM can respond to customer demand and develop new medical supplies to capture revenue. However, this investment also incurs costs that are named C_1m. These costs include maintaining a redundant inventory of medical supplies and procuring from multiple sources, which increases the unit price of medical supplies purchases. Moreover, the MSR’s benefits from the MSM’s development of various medical products to meet the sales needs of retailers through a “free-rider” behavior is θr_r.

Hypothesis 5. 

The additional benefits obtained by the MSR after the unilateral resilience investment are r_r, such as the MSR adopting the big data analytics technology to predict the demand for medical supplies; the cost of the investment is C_1r, which is for the acquisition of big data analytics equipment and the training of big data analytics technicians. However, a portion of the MSM’s profits will reduce because of the MSR’s resilience investment; the reduced benefits are named $r^{*}$. For instance, if the retailer looks for a new medical supplies supplier, the profit of the original supplier will be reduced.

Hypothesis 6. 

The additional benefits to the MSM and the MSR from the simultaneous resilience investment are $\left(1+\alpha \right)r_m$ and $\left(1+\beta \right)r_r$, and the investment costs are $\left(1-a\right)C_{1m}$ and $\left(1-b\right)C_{1r}$, $\alpha >0,\beta >0,0<a<1,0<b<1$.

The payment matrix for the MSM and MSR is constructed based on the above hypothesis, as shown in

Table 2. Payment matrix in healthcare supply chain non-disruption scenarios.

MSM	MSR
	Resilience Investment $\mathit{y}$	$\mathbf{Resilience}\mathbf{Non}\text{-}\mathbf{Investment}1-\mathit{y}$
resilience investment $x$	$R_m+\left(1+\alpha \right)r_m-\left(1-a\right)C_{1m},$ $R_r+\left(1+\beta \right)r_r-\left(1-b\right)C_{1r}$	$R_m+r_m-C_{1m}$, $R_r+\theta r_r$
resilience non-investment $1-x$	$R_m-r^{*}$, $R_r+r_r-C_{1r}$	$R_m$, $R_r$

.

3.1.2. Evolutionary Stabilization Strategy Analysis

The expected returns to resilience investment or non-investment and the average expected returns $(E_{11},E_{11},{\overline{E}}_1)$ for the MSM are as shown in Formulas (1)–(3):

$$E_{11}=y\left[R_m+\left(1+\alpha \right)r_m-\left(1-\mathrm{a}\right)C_{1m}\right]+\left(1-y\right)\left[R_m+r_m-C_{1m}\right]$$

(1)

$$E_{12}=y\left(R_m-r^{*}\right)+\left(1-y\right)R_m$$

(2)

$${\overline{E}}_1=x{E}_{11}+\left(1-x\right)E_{12}$$

(3)

According to the Malthusian dynamic equation and Formulas (1)–(3), we obtain the replicated dynamic equation of the MSM:

$$\frac{dx}{dt}=x\left(E_{11}-{\overline{E}}_1\right)=x\left(1-x\right)\left(E_{11}-E_{12}\right)=x\left(1-x\right)\left(r_m+\alpha r_{m}y+r^{*}y-C_{1m}+a{C}_{1m}y\right)$$

(4)

Let $F_1\left(x\right)=x\left(E_{11}-{\overline{E}}_1\right)$ and perform a first-order derivation of $F_1\left(x\right)$:

$$F_1^{\prime }\left(x\right)=d{F}_1\left(x\right)/dx=\left(1-2x\right)\left(r_m+\alpha r_{m}y+r^{*}y-C_{1m}+\mathrm{a}{C}_{1m}y\right)$$

(5)

For analytical purposes, we define equations $G_1(y)$ and $y_1^{*}$:

$$G_1(y)=r_m+\alpha r_{m}y+r^{*}y-C_{1m}+a{C}_{1m}y$$

(6)

$$y_1^{*}=\frac{C_{1m}-r_m}{\alpha r_m+r^{*}+a{C}_{1m}}$$

(7)

According to Formula (6), $G_1^{\prime }\left(y\right)=\alpha r_m+r^{*}+\mathrm{a}{C}_{1m}$ and $G_1(y)$ is an increasing function on $y$.

According to the stability theorem for replicated dynamic equations proposed by Friedman [54], if $F_1\left(x\right)=0$ and $F_1^{\prime }\left(x\right)<0$, the system will converge to a stabilizing strategy.

• When $y=y_1^{*}$, the $F_1\left(x\right)\equiv 0$. At this time, for any $x(0<x<1)$ value, any probability of the MSM “resilience investment” strategy is an evolutionarily stable strategy; the probability of the system choosing the MSM’s resilience investment will not change over time, and the system is in an evolutionarily stable state.
• When $0<y<y_1^{*}<1$, the $G_1(y)<G(y_1^{*})=0$. At this time, $F_1^{\prime }\left(x\right){|}_{x=0}<0$, $F_1^{\prime }\left(x\right){|}_{x=1}>0$, $x=0$ is the evolutionary stabilization point. The costs to the MSM of choosing the resilience investment outweigh the additional benefits of the resilience investment. Therefore, the “resilience non-investment” strategy is the preferred strategy for the MSM.
• When $0<y_1^{*}<y<1$, the $G_1(y)>G(y_1^{*})=0$. At this time, $F_1^{\prime }\left(x\right){|}_{x=0}>0$, $F_1^{\prime }\left(x\right){|}_{x=1}<0$, $x=1$ is the evolutionary stabilization point. This indicates that the benefits of investing in resilience outweigh the costs, so the “resilience investment strategy” should be the priority for the MSM.

The expected returns to resilience investment or non-investment and the average expected returns $(E_{21},E_{21},{\overline{E}}_2)$ for the MSR are as shown in Formulas (8)–(10):

$$E_{21}=x\left[R_r+\left(1+\beta \right)r_r-\left(1-b\right)C_{1r}\right]+\left(1-x\right)\left(R_r+r_r-C_{1r}\right)$$

(8)

$$E_{22}=x\left(R_r+\theta r_r\right)+\left(1-x\right)R_r$$

(9)

$${\overline{E}}_2=y{E}_{21}+\left(1-y\right)E_{22}$$

(10)

According to the Malthusian dynamic equation and Formulas (8)–(10), we obtain the replicated dynamic equation of the MSR:

$$\frac{dy}{dt}=y\left(E_{21}-{\overline{E}}_2\right)=y\left(1-y\right)\left(E_{21}-E_{22}\right)=y\left(1-y\right)\left(r_r+\beta r_{r}x-\theta r_{r}x-C_{1r}+b{C}_{1r}x\right)$$

(11)

Let $F_1\left(y\right)=y\left(E_{21}-{\overline{E}}_2\right)$ and perform a first-order derivation of $F_1\left(y\right)$:

$$F_1^{\prime }\left(y\right)=d{F}_1\left(y\right)/dy=\left(1-2y\right)\left(r_r+\beta r_{r}x-\theta r_{r}x-C_{1r}+b{C}_{1r}x\right)$$

(12)

For analytical purposes, we define equations $G_1(x)$ and $x_1^{*}$:

$$G_1(x)=r_r+\beta r_{r}x-\theta r_{r}x-C_{1r}+b{C}_{1r}x$$

(13)

$$x_1^{*}=\frac{C_{1r}-r_r}{\beta r_r+b{C}_{1r}-\theta r_r}$$

(14)

According to Formula (13), the first-order derivation of $G_1(x)$ is performed.

$$G_1^{\prime }\left(x\right)=\beta r_r+b{C}_{1r}-\theta r_r$$

(15)

According to the stability theorem for replicated dynamic equations proposed by Friedman [54], if $F_1\left(y\right)=0$ and $F_1^{\prime }\left(y\right)<0$, the system will converge to a stabilizing strategy.

4.

When $x=x_1^{*}$, the $F_1\left(y\right)\equiv 0$. At this time, for any $y(0<y<1)$ value, any probability of the MSR “resilience investment strategy” is an evolutionarily stable strategy, the probability of the system choosing the MSR’s resilience investment will not change over time, and the system is in an evolutionarily stable state.

5.

If $\beta r_r+b{C}_{1r}-\theta r_r>0$, then $G_1^{\prime }\left(x\right)=\beta r_r-\theta r_r+b{C}_{1r}>0$ and $G_1\left(x\right)$ is an increasing function on $x$.

(1)

When $0<x<x_1^{*}<1$, the $G_1(x)<G_1(x_1^{*})=0$. At this time, $F_1^{\prime }\left(y\right){|}_{y=0}<0$, $F_1^{\prime }\left(y\right){|}_{y=1}>0$, $y=0$ is the evolutionary stabilization point. The costs to the MSR of choosing the resilience investment outweigh the additional benefits of the resilience investment. Therefore, the “resilience non-investment strategy” is the preferred strategy for the MSR.

(2)

When $0<x_1^{*}<x<1$, the $G_1(x)>G_1(x_1^{*})=0$. At this time, $F_1^{\prime }\left(y\right){|}_{y=0}>0$, $F_1^{\prime }\left(y\right){|}_{y=1}<0$, $y=1$ is the evolutionary stabilization point. This indicates that the benefits of investing in resilience outweigh the costs, so the “resilience investment strategy” should be the priority for the MSR.

6.

If $\beta r_r+b{C}_{1r}-\theta r_r<0$, then $G_1^{\prime }\left(x\right)=\beta r_r-\theta r_r+b{C}_{1r}<0$ and $G_1\left(x\right)$ is a decreasing function on $x$.

(1)

When $0<x<x_1^{*}<1$, $G_1(x)>G_1(x_1^{*})=0$. At this time, $F_1^{\prime }\left(y\right){|}_{y=0}>0$, $F_1^{\prime }\left(y\right){|}_{y=1}<0$, $y=1$ is the evolutionary stabilization point. This indicates that the benefits of investing in resilience outweigh the costs, so the “resilience investment strategy” should be the priority for the MSR.

(2)

When $0<x_1^{*}<x<1$, $G_1(x)<G_1(x_1^{*})=0$. At this time, $F_1^{\prime }\left(y\right){|}_{y=0}<0$, $F_1^{\prime }\left(y\right){|}_{y=1}>0$, $y=0$ is the evolutionary stabilization point. The costs to the MSR of choosing the resilience investment outweigh the additional benefits of the resilience investment. Therefore, the “resilience non-investment strategy” is the preferred strategy for the MSR.

3.1.3. Equilibrium Point and Stability Analysis

In Formulas (4) and (11), $F_1\left(x\right)$ and $F_1\left(y\right)$ are equal to 0, respectively; this leads to five equilibria points of the evolutionary game, which are as follows: (0,0), (0,1), (1,0), (1,1), and ($x_1$, $y_1$), where $x_1=\frac{C_{1r}-r_r}{b{C}_{1r}+\beta r_r-\theta r_r}$, $y_1=\frac{C_{1m}-r_m}{r^{*}+a{C}_{1m}+\alpha r_m}$.

To analyze the stability of the equilibrium point, construct the Jacobi matrix $J_1$ [54]:

$$J_1=\left[\begin{array}{cc}\frac{\partial F_1(x)}{\partial x}& \frac{\partial F_1(x)}{\partial y}\\ \frac{\partial F_1(y)}{\partial x}& \frac{\partial F_1(y)}{\partial y}\end{array}\right]=\left[\begin{array}{cc}(1-2x)(r_m+\alpha r_{m}y+r^{*}y-C_{1m}+a{C}_{1m}y)& x(1-x)(\alpha r_m+r^{*}+a{C}_{1m})\\ y\left(1-y\right)\left(\beta r_r-\theta r_r+b{C}_{1r}\right)& (1-2y)(r_r+\beta r_{r}x-\theta r_{r}x-C_{1r}+b{C}_{1r}x)\end{array}\right]$$

(16)

According to Lyapunov [55], the equilibrium point is asymptotically stable if all the eigenvalues have a negative fundamental part. On the other hand, if at least one of the eigenvalues has a positive fundamental part, then the equilibrium point is unstable. To analyze the evolutionary stabilization strategy (ESS), we bring the pure strategy equilibrium points into the Jacobi matrix $J_1$ and calculate their eigenvalues separately, as shown in

Table 3. Eigenvalues of the Jacobi matrix in the non-disruption scenario.

Equilibrium Point	Jacobi Matrix Eigenvalue			Condition
	${\mathit{\lambda }}_1$	${\mathit{\lambda }}_2$	Sign
(0,0)	$r_m-C_{1m}$	$r_r-C_{1r}$	$\left(-,-\right)$	ESS	①
(0,1)	$r^{*}-\left(1-a\right)C_{1m}+\left(1+\alpha \right)r_m$	$C_{1r}-r_r$	$\left(-,-\right)$	ESS	②
(1,0)	$C_{1m}-r_m$	$\left(1+\beta -\theta \right)r_r-\left(1-b\right)C_{1r}$	$\left(-,-\right)$	ESS	③
(1,1)	$\left(1-a\right)C_{1m}-r^{*}-\left(1+\alpha \right)r_m$	$\left(1-b\right)C_{1r}-\left(1+\beta -\theta \right)r_r$	$\left(-,-\right)$	ESS	④

Note: ① $r_m<C_{1m}, r_r<C_{1r}$; ② $C_{1r}<r_r, r^{*}+\left(1+\alpha \right)r_m<\left(1-a\right)C_{1m}$; ③ $C_{1m}<r_m, \left(1+\beta -\theta \right)r_r<\left(1-b\right)C_{1r}$; ④ $\left(1-a\right)C_{1m}<r^{*}+\left(1+\alpha \right)r_m, \left(1-b\right)C_{1r}<\left(1+\beta -\theta \right)r_r$.

.

Proposition 1. 

If $r_m<C_{1m}$ and $r_r<C_{1r}$, the evolutionary stability point of the system is (0,0).

Proposition 1 states that if the cost of implementing unilateral resilience investments exceeds the additional benefits gained by the MSR and MSM, then in the context of firms’ pursuit of profit maximization, they will not invest in resilience and instead opt to reduce profit loss.

Proposition 2. 

If $r^{*}<\left(1-a\right)C_{1m}-\left(1+\alpha \right)r_m$ and $C_{1r}<r_r$, the evolutionary stability point of the system is (0,1).

Proposition 2 suggests that if both parties make resilience investments simultaneously, the difference between the costs incurred by the MSR and the benefits gained will exceed the portion of the profits that would be lost by the resilience investment made unilaterally by the MSR, the MSR may choose to forgo the resilience investment to minimize costs. However, the MSM would opt to participate in resilience investments because the additional benefits of its unilateral resilience investment outweigh the costs.

Proposition 3. 

If $C_{1m}<r_m$ and $\left(1+\beta \right)r_r-\left(1-b\right)C_{1r}<\theta r_r$, the evolutionary stability point of the system is (1,0).

Proposition 3 indicates that the MSM will choose to participate actively in the resilience investment to maximize profits if the additional benefits of the unilateral resilience investment exceed the investment’s costs. If both parties make resilience investments simultaneously, the difference between the MSR’s additional benefits and costs is less than the “free-rider” benefits of the MSM’s unilateral resilience investment, and the MSR will choose resilience non-investment.

Proposition 4. 

If $\left(1-a\right)C_{1m}-\left(1+\alpha \right)r_m<r^{*}$ and $\theta r_r<\left(1+\beta \right)r_r-\left(1-b\right)C_{1r}$, the evolutionary stability point of the system is (1,1).

Proposition 4 demonstrates that if both parties make resilience investments simultaneously, the difference between the MSM’s costs and additional benefits is less than the portion of the profits that would be reduced if the MSR’s unilateral resilience investment and the MSM chose resilience investment to minimize its losses; in this case, the difference between the MSR’s additional benefits and cost exceeds the “free-rider” benefit of the MSM’s unilateral resilience investment, so the MSR is favored to resilience investment.

3.2. Healthcare Supply Chain Disruption Scenario

3.2.1. Basic Hypothesis

Hypothesis 7. 

When disruption occurs, healthcare entities suffer a loss of revenue, with the value of the loss for the MSM and MSR being $R_m^{-}$ and $R_r^{-}$. This loss is attributed to a decrease in sales caused by the disruption and a decrease in revenue due to market encroachment. Additionally, the disruption increases the costs of additional products, with values $C_{2m}$ and $C_{2r}$.

Hypothesis 8. 

When the MSM invests unilaterally in resilience, it can reduce the loss of revenue caused by disruptions; the loss reduction is denoted as $f{R}_m^{-}$; for example, by activating a backup supplier of raw materials for medical supplies to maintain regular operation. Additionally, the MSM can recover from the disruption faster due to the resilience investment and encroachment on the other MSM’s market share during recovery by filling in the market gaps, and this revenue is denoted as $R_m^{+}$. The disruption increases the costs of additional products, denoted as $\left(1-s\right)C_{2m}$. The MSR mitigates losses from disruptions through “free-rider” behavior, denoted as $\gamma R_r^{-}$, which includes maintaining the ability to supply during disruptions through investments in resilience. The MSM may actively search for a new MSR to enhance SCRES, resulting in a slight reduction for the original MSR, denoted as $\mu Rr$.

Hypothesis 9. 

When the MSR invests unilaterally in resilience, it can reduce the loss of revenue caused by disruptions; the loss reduction is denoted as $d{R}_r^{-}$, for example, by activating a backup supplier for medical supplies to maintain regular operation. Additionally, the MSR can recover from the disruption faster due to the resilience investment and encroachment on the other MSR’s market share during recovery by filling in the market gaps, and this revenue is denoted as $R_r^{+}$. The disruption increases the costs of additional products, denoted as $\left(1-g\right)C_{2r}$. The MSM will also suffer a loss in market share due to the MSR looking for a new supplier, which is assumed to be $h{R}_m$. This is because, during the disruption period, the MSM was unable to provide medical supplies, prompting the MSR to seek out another MSM to replace the original one.

Assumption 10. 

When the MSM and the MSR resilience investment are simultaneous, the loss reductions are $\left(f+m\right)R_m^{-}$ and $\left(d+n\right)R_r^{-}$, the additional costs are $\left(1-s-v\right)C_{2m}$ and $\left(1-g-u\right)C_{2r}$ and the gains from market capture are $\left(1+k\right)R_m^{+}$ and $\left(1+j\right)R_r^{+}$.

The payment matrix for the MSM and MSR is constructed based on the above hypothesis, as shown in

Table 4. Payment matrix in healthcare supply chain disruption scenarios.

MSM	MSR
	Resilience Investment $\mathit{y}$	$\mathbf{Resilience}\mathbf{Non}\text{-}\mathbf{Investment}1-\mathit{y}$
resilience investment $x$	$\begin{array}{l}{R}_m-\left(1-a\right)C_{1m}-\left(1-f-m\right)R_m^{-}\\ -\left(1-s-v\right)C_{2m}+\left(1+k\right)R_m^{+}\end{array}$, $\begin{array}{l}{R}_r-\left(1-b\right)C_{1r}-\left(1-d-n\right)R_r^{-}\\ -\left(1-g-u\right)C_{2r}+\left(1+j\right)R_r^{+}\end{array}$	$R_m+R_m^{+}-\left(1-f\right)R_m^{-}-C_{1m}-\left(1-s\right)C_{2m},$ $R_r-\left(1-\gamma \right)R_r^{-}-\mu R_r-C_{2r}$
resilience non-investment $1-x$	$R_m-R_m^{-}-h{R}_m-C_{2m}$, $R_r+R_r^{+}-\left(1-d\right)R_r^{-}-C_{1r}-\left(1-g\right)C_{2r}$	$R_m-R_m^{-}-C_{2m}$, $R_r-R_r^{-}-C_{2r}$

.

3.2.2. Evolutionary Stabilization Strategy Analysis

The expected returns to resilience investment or resilience non-investment and the average expected return $(E_{31},E_{32},{\overline{E}}_3)$ for the MSM are as shown in Formulas (17)–(19):

$$E_{31}=y\left[R_m-\left(1-a\right)C_{1m}-\left(1-f-m\right)R_m^{-}-\left(1-s-v\right)C_{2m}+\left(1+k\right)R_m^{+}\right]+\left(1-y\right)\left[R_m+R_m^{+}-\left(1-f\right)R_m^{-}-C_{1m}-\left(1-s\right)C_{2m}\right]$$

(17)

$$E_{32}=y\left[R_m-R_m^{-}-h{R}_m-C_{2m}\right]+\left(1-y\right)\left[R_m-R_m^{-}-C_{2m}\right]$$

(18)

$${\overline{E}}_3=x{E}_{31}+\left(1-x\right)E_{32}$$

(19)

According to the Malthusian dynamic equation and Formulas (17)–(19), we obtain the replicated dynamic equation of the MSM:

$$\frac{dx}{dt}=x\left(E_{31}-{\overline{E}}_3\right)=x\left(1-x\right)\left[\left(k{R}_m^{+}+m{R}_m^{-}+v{C}_{2m}+a{C}_{1m}+h{R}_m\right)y+R_m^{+}+f{R}_m^{-}+s{C}_{2m}-C_{1m}\right]$$

(20)

Let $F_2\left(x\right)=x\left(E_{31}-{\overline{E}}_3\right)$ and perform a first-order derivation of $F_2\left(x\right)$:

$$F_2^{\prime }\left(x\right)=d{F}_2\left(x\right)/dx=\left(1-2x\right)\left[\left(k{R}_m^{+}+m{R}_m^{-}+v{C}_{2m}+a{C}_{1m}+h{R}_m\right)y+R_m^{+}+f{R}_m^{-}+s{C}_{2m}-C_{1m}\right]$$

(21)

For analytical purposes, we define equations $G_2(y)$ and $y_2^{*}$:

$$G_2(y)=\left(k{R}_m^{+}+m{R}_m^{-}+v{C}_{2m}+a{C}_{1m}+h{R}_m\right)y+R_m^{+}+f{R}_m^{-}+s{C}_{2m}-C_{1m}$$

(22)

$$y_2^{*}=\frac{C_{1m}-R_m^{+}-f{R}_m^{-}-s{C}_{2m}}{k{R}_m^{+}+m{R}_m^{-}+v{C}_{2m}+a{C}_{1m}+h{R}_m}$$

(23)

According to Formula (22), $G_2^{\prime }\left(y\right)=k{R}_m^{+}+m{R}_m^{-}+v{C}_{2m}+a{C}_{1m}+h{R}_m$ and $G_2(y)$ is an increasing function on $y$.

According to the stability theorem for replicated dynamic equations proposed by Friedman [54], if $F_2\left(x\right)=0$ and $F_2^{\prime }\left(x\right)<0$, the system will converge to a stabilizing strategy.

• When $y=y_2^{*}$, the $F_2\left(x\right)\equiv 0$. At this time, for any $x(0<x<1)$ value, any probability of the MSM “resilience investment” strategy is an evolutionarily stable strategy; the probability of the system choosing the MSM’s resilience investment will not change over time, and the system is in an evolutionarily stable state.
• When $0<y<y_2^{*}<1$, the $G_2(y)<G(y_2^{*})=0$. At this time, $F_2^{\prime }\left(x\right){|}_{x=0}<0$, $F_2^{\prime }\left(x\right){|}_{x=1}>0$, $x=0$ is the evolutionary stabilization point. The costs to the MSM of choosing the resilience investment outweigh the additional benefits of the resilience investment. Therefore, the “resilience non-investment” strategy is the preferred strategy for the MSM.
• When $0<y_2^{*}<y<1$, the $G_2(y)>G(y_2^{*})=0$. At this time, $F_2^{\prime }\left(x\right){|}_{x=0}>0$, $F_2^{\prime }\left(x\right){|}_{x=1}<0$, $x=1$ is the evolutionary stabilization point. This indicates that the benefits of investing in resilience outweigh the costs, so the “resilience investment” strategy should be the priority for the MSM.

The expected returns to resilience investment or non-investment and the average expected return $(E_{41},E_{42},{\overline{E}}_4)$ for the MSR are as shown in Formulas (24)–(26):

$$E_{41}=x\left[R_r-\left(1-b\right)C_{1r}-\left(1-d-n\right)R_r^{-}-\left(1-g-u\right)C_{2r}+\left(1+j\right)R_r^{+}\right]+\left(1-x\right)\left[R_r-\left(1-d\right)R_r^{-}+R_r^{+}-C_{1r}-\left(1-g\right)C_{2r}\right]$$

(24)

$$E_{42}=x\left[R_r-\left(1-\gamma \right)R_r^{-}-\mu R_r-C_{2r}\right]+\left(1-x\right)\left[R_r-R_r^{-}-C_{2r}\right]$$

(25)

$${\overline{E}}_4=y{E}_{41}+\left(1-y\right)E_{42}$$

(26)

According to the Malthusian dynamic equation and Formulas (24)–(26), we obtain the replicated dynamic equation of the MSR:

$$\begin{array}{ll}\frac{dy}{dt}=& y\left(E_{41}-{\overline{E}}_4\right)=y\left(1-y\right)\left(E_{41}-E_{42}\right)\\ & =y\left(1-y\right)\left[\left(j{R}_r^{+}+n{R}_r^{-}+u{C}_{2r}+\mu R_r+b{C}_{1r}-\gamma R_r^{-}\right)x+R_r^{+}+d{R}_r^{-}+g{C}_{2r}-C_{1r}\right]\end{array}$$

(27)

Let $F_2\left(y\right)=y\left(E_{41}-{\overline{E}}_4\right)$ and perform a first-order derivation of $F_2\left(y\right)$:

$$F_2^{\prime }\left(y\right)=d{F}_2\left(y\right)/dy=\left(1-2y\right)\left[\left(j{R}_r^{+}+n{R}_r^{-}+u{C}_{2r}+\mu R_r+b{C}_{1r}-\gamma R_r^{-}\right)x+R_r^{+}+d{R}_r^{-}+g{C}_{2r}-C_{1r}\right]$$

(28)

For analytical purposes, we define equations $G_2(x)$ and $x_2^{*}$:

$$G_2(x)=\left(j{R}_r^{+}+n{R}_r^{-}+u{C}_{2r}+\mu R_r+b{C}_{1r}-\gamma R_r^{-}\right)x+R_r^{+}+d{R}_r^{-}+g{C}_{2r}-C_{1r}$$

(29)

$$x_2^{*}=\frac{C_{1r}-R_r^{+}-d{R}_r^{-}-g{C}_{2r}}{j{R}_r^{+}+n{R}_r^{-}+u{C}_{2r}+\mu R_r+b{C}_{1r}-\gamma R_r^{-}}$$

(30)

According to Formula (29), $G_2^{\prime }\left(x\right)=j{R}_r^{+}+n{R}_r^{-}+u{C}_{2r}+\mu R_r+b{C}_{1r}-\gamma R_r^{-}$ and $G_2(x)$ is an increasing function on $x$.

According to the stability theorem for replicated dynamic equations proposed by Friedman, if $F_2\left(y\right)=0$ and $F_2^{\prime }\left(y\right)<0$, the system will converge to a stabilizing strategy.

4.

When $x=x_2^{*}$, the $F_2\left(y\right)\equiv 0$. At this time, for any $y(0<y<1)$ value, any probability of the MSR “resilience investment” strategy is an evolutionarily stable strategy; the probability of the system choosing the MSR’s resilience investment will not change over time, and the system is in an evolutionarily stable state.

5.

When $0<x<x_2^{*}<1$, the $G_2(x)<G_2(x_2^{*})=0$. At this time, $F_2^{\prime }\left(y\right){|}_{y=0}<0$, $F_2^{\prime }\left(y\right){|}_{y=1}>0$, $y=0$ is the evolutionary stabilization point. The costs to the MSR of choosing the resilience investment outweigh the additional benefits of the resilience investment. Therefore, the “resilience non-investment strategy” is the preferred strategy for the MSR.

6.

When $0<x_2^{*}<x<1$, the $G_2(x)>G_2(x_2^{*})=0$. At this time, $F_2^{\prime }\left(y\right){|}_{y=0}>0$ and $F_2^{\prime }\left(y\right){|}_{y=1}<0$, $y=1$ is the evolutionary stabilization point. This indicates that the benefits of investing in resilience outweigh the costs, so the “resilience investment strategy” should be the priority for the MSR.

3.2.3. Equilibrium Point and Stability Analysis

In Formulas (20) and (27), $F_2\left(x\right)$ and $F_2\left(y\right)$ are equal to 0, respectively; this leads to five equilibria points of the evolutionary game, which are (0,0), (0,1), (1,0), (1,1), and ($x_2$,$y_2$). $x_2=\frac{C_{1r}-R_r^{+}-g{C}_{2r}-d{R}_r^{-}}{b{C}_{1r}+u{C}_{2r}+j{R}_r^{+}+\mu R_r-\left(\gamma -n\right)R_r^{-}}$, $y_2=\frac{C_{1m}-R_m^{+}-s{C}_{2m}-f{R}_m^{-}}{\mathrm{a}{C}_{1m}+v{C}_{2m}+h{R}_m+k{R}_m^{+}+m{R}_m^{-}}$.

To analyze the stability of the equilibrium point, construct the Jacobi matrix $J_2$ [54]:

$$J_2=\left[\begin{array}{cc}\frac{\partial F_2(x)}{\partial x}& \frac{\partial F_2(x)}{\partial y}\\ \frac{\partial F_2(y)}{\partial x}& \frac{\partial F_2(y)}{\partial y}\end{array}\right]=\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]$$

(31)

$$a_{11}=(1-2x)[(1+ky)R_m^{+}+(f+my)R_m^{-}+(ay-1)C_{1m}+(s+vy)C_{2m}+h{R}_{m}y]$$

$$a_{12}=x(1-x)(a{C}_{1m}+v{C}_{2m}+h{R}_m+k{R}_m^{+}+m{R}_m^{-})$$

$$a_{21}=y\left(1-y\right)\left(b{C}_{1r}+u{C}_{2r}+\mu R_r+(n-\gamma )R_r^{-}+j{R}_r^{+}\right)$$

$$a_{22}=(1-2y)[(1+jx)R_r^{+}+(d+nx-\gamma x)R_r^{-}+(bx-1)C_{1r}+(g+ux)C_{2\mathrm{r}}+\mu R_{r}x]$$

According to Lyapunov [55], the equilibrium point is asymptotically stable if all the eigenvalues have a negative fundamental part. On the other hand, if at least one of the eigenvalues has a positive fundamental part, then the equilibrium point is unstable. To analyze the evolutionary stabilization strategies, we bring the pure strategy equilibrium points into the Jacobi matrix $J_2$ and calculate their eigenvalues separately, as shown in

Table 5. Eigenvalues of the Jacobi matrix in the disruption scenario.

Equilibrium Point	Jacobi Matrix Eigenvalue			Condition
	${\mathit{\lambda }}_1,{\mathit{\lambda }}_2$		Sign
(0,0)	$R_r^{+}+g{C}_{2r}+d{R}_r^{-}-C_{1r}$	$R_m^{+}+s{C}_{2m}+f{R}_m^{-}-C_{1m}$	$\left(+,+\right)$	Instability	\
(0,1)	$C_{1r}-R_r^{+}-g{C}_{2r}-d{R}_r^{-}$	$\begin{array}{l}\left(1+k\right)R_m^{+}+\left(m+f\right)R_m^{-}\\ +\left(s+v\right)C_{2m}+h{R}_m-\left(1-a\right)C_{1m}\end{array}$	$\left(-,+\right)$	Instability	\
(1,0)	$C_{1m}-R_m^{+}-s{C}_{2m}-f{R}_m^{-}$	$\begin{array}{l}\left(1+j\right)R_r^{+}-\left(\gamma -d-n\right)R_r^{-}\\ +\left(g+u\right)C_{2r}-\left(1-b\right)C_{1r}+\mu R_r\end{array}$	$\left(-,-\right)$	ESS	⑤
(1,1)	$\begin{array}{l}\left(1-a\right)C_{1m}-\left(1+k\right)R_m^{+}-\\ \left(s+v\right)C_{2m}-\left(m+f\right)R_m^{-}-h{R}_m\end{array}$	$\begin{array}{l}\left(1-b\right)C_{1r}-\left(g+u\right)C_{2r}-\left(1+j\right)R_r^{+}\\ -\left(d+n-\gamma \right)R_r^{-}-\mu R_r\end{array}$	$\left(-,-\right)$	ESS	⑥

Note: $⑤\left(1+j\right)R_r^{+}+\left(g+u\right)C_{2r}+\left(d+n\right)R_r^{-}+\mu R_r<\left(1-b\right)C_{1r}+\gamma R_r^{-};$ ⑥ $\left(1-b\right)C_{1r}+\gamma R_r^{-}<\left(1+j\right)R_r^{+}+\left(g+u\right)C_{2r}+\left(d+n\right)R_r^{-}+\mu R_r$.

.

Proposition 5. 

If $\left(1+j\right)R_r^{+}+\left(g+u\right)C_{2r}+\left(d+n\right)R_r^{-}+\mu R_r<\left(1-b\right)C_{1r}+\gamma R_r^{-}$, the evolutionary stability point of the system is (1,0).

Proposition 5 proves that the sum of the gains from market capture when both parties make simultaneous resilience investments, the reduction in additional costs, the reduction in disruption losses, and the reduction in the MSR’s gains when the MSM makes a unilateral resilience investment is less than the sum of the costs reduced by the MSR when both parties engage in resilience investment and the disruption losses reduced by the MSR when the MSM engages in resilience investment unilaterally, the MSR because of the low benefits of resilience investment tend to choose to forgo resilience investment, while the MSM decides to participate in resilience investment actively.

Proposition 6. 

If $\left(1+j\right)R_r^{+}+\left(g+u\right)C_{2r}+\left(d+n\right)R_r^{-}+\mu R_r>\left(1-b\right)C_{1r}+\gamma R_r^{-}$, the evolutionary stability point of the system is (1,1).

Proposition 6 indicates that the sum of the gains from market capture when both parties make simultaneous resilience investments, the reduction in additional costs, the reduction in disruption losses, and the reduction in the MSR’s gains when the MSM makes a unilateral resilience investment is more than the sum of the costs reduced by the MSR when both parties engage in resilience investment and the disruption losses reduced by the MSR when the MSM engages in resilience investment unilaterally, both parties will choose to participate in resilience investment actively.

4. Numerical Simulation Analysis

The limited rationality of the game parties may prevent them from always choosing a completely rational strategy. Over time, the two parties influence each other, continuously adjust their strategies, and eventually reach a steady state. This section further explores the evolution rules of resilience investment for medical supplies suppliers and retailers under SC disruption and non-disruption scenarios. We use Matlab software to conduct numerical simulations to explore stabilization strategies by adjusting parameters and observing the simulation process.

4.1. Numerical Simulation of Supply Chain Non-Disruption Scenarios

Based on the analysis of the non-disruption scenario game played by the two parties of the HCSC, the ideal evolutionary stable state that the system can reach is (resilience investment, resilience investment). In order to reach this state, numerical simulations were conducted using Matlab software to explore the impact of relevant factors on the strategic behavior of each participant. The simulation model parameters were assigned based on satisfying the model’s hypothesis and reasonable and logical relationships. The parameters were assigned as follows: $R_m=1,R_r=1,$ $r_m=0.4,$ $r_r=0.25,C_{1m}=0.2,$ $C_{1r}=0.15,$ $\theta =0.1,r^{*}=0.05,\alpha =0.3,\beta =0.2,a=0.3,b=0.4$

4.1.1. Initial State Simulation Analysis

Based on the analysis of the game of resilience investment evolution, there are four possible combinations of initial pure strategy choices for both retailers and manufacturers, respectively (0,0), (0,1), (1,0), and (1,1). When the initial behavioral strategies of both parties are pure, the game system will reach a relative equilibrium state. We further investigate the impact of the initial probability of resilience investment strategies on the final evolutionary outcome.

The initial points of system evolution are set as (0.1,0.1), (0.3,0.3), (0.5,0.5), (0.7,0.7), (0.9,0.9), (0.9,0.1), (0.8,0.2), (0.7,0.3), (0.1,0.9), (0.2,0.8), and (0.3,0.7), and explore the willingness of both parties to invest in resilience, as well as the evolution results when the unilateral resilience investment is strong. The simulation results are shown in Figure 1 and Figure 2.

Upon analyzing Figure 1, it becomes apparent that when the MSM and MSR exhibit similar levels of willingness to invest in resilience, they will gradually converge toward the resilience investment despite a decrease in their willingness. This convergence will ultimately lead to the evolutionary stability equilibrium state of (1,1), where both parties will reach a common ground. Figure 2 shows that when the MSM chooses the “resilience investment” strategy to improve SCRES with high initial probability, although the initial probability of the MSR choosing the “resilience investment” strategy is small, after adjusting and optimizing their behavioral strategies, the MSR’s probability of choosing the “resilience investment” strategy increases continuously. The two parties finally reach an evolutionary stable equilibrium (1,1). The above shows that under the constraint of condition ④, if the MSM’s and MSR’s resilience investment willingness is positive, negative, or unilaterally positive, both parties continuously adjust and optimize their strategies to pursue profit maximization. They will ultimately evolve into choosing a resilience investment strategy (1,1). This further proves the correctness of the eigenvalue analysis above that the system will evolve to (1,1) under the constraint of condition ④.

4.1.2. Parametric Simulation Analysis

Based on the previous analysis of the stability of the evolutionary game between the MSM and MSR, it is evident that several factors influence the equilibrium state of the evolutionary game and the strategy choices of both parties. Therefore, the subsequent action is to give different initial values to each influencing factor to explore the influence of different factors on the strategy choices of both parties. The initial probability of the MSM and MSR choosing the resilience investment strategy is assumed to be (0.5,0.5).

• Analysis of the influence of r_m and r_r on the evolutionary stability results

When $r_m$ increases from 0 to 0.5 while other parameters remain unchanged, it can be seen from Figure 3 that when $r_m=0$, the MSM chooses the “resilience non-investment” strategy, and condition ② is satisfied. The system evolves to (0,1). As $r_m$ increases, the MSM chooses “resilience investment” at an increasing rate, and the system evolves to (1,1). This implies that a higher value of $r_m$ encourages the MSM to participate in resilience investment activities, which ultimately helps in building a more resilient SC.

When $r_r$ is increased from 0 to 0.5 while other parameters remain unchanged, it can be seen from Figure 4 that when $r_r=0$, the MSR chooses the “resilience non-investment” strategy, and condition ③ is satisfied. The system evolves to (1,0). As $r_r$ increases, the MSR chooses “resilience investment” at an increasing rate, and the system evolves to (1,1). This implies that a higher value of $r_r$ encourages the MSR to participate in resilience investment activities, which ultimately helps in building a more resilient HCSC.

2.

Analysis of the influence of θ on the evolutionary stability results

Holding all other parameters constant, Figure 5 displays the simulation results when $\theta$ increases from 0 to 1. When $\theta =1$, the MSR obtains extra revenue $r_r$ by “free-riding” and does not need to pay resilience investment costs. Condition ③ is satisfied at this point, and the system evolves to (1,0). As $\theta$ decreases, the MSR’s probability of choosing the “resilience investment” strategy increases and becomes faster, and the system evolves (1,1). This suggests that the decrease in $\theta$ prevents the MSR from obtaining the desired return through “free-riding” behavior, incentivizing the MSR to participate in resilience investment activities. Therefore, appropriately reducing the proportion of additional gains from “free-riding” by the MSR can help enhance HCSCRES.

3.

Analysis of the influence of a and b on the evolutionary stability results

When $a$ increases from 0 to 0.4 and $b$ also increases from 0 to 0.4, the simulation results are shown in Figure 6, holding all other parameters constant. When $a=0\mathrm{and}b=0$, constraint ④ is satisfied, and both parties simultaneously make resilience investments to improve the SCRES. When $a=0$ and $b$ increase from 0 to 0.4, the MSR accelerates in selecting the “resilience investment” strategy. When $b=0$ and $a$ increase from 0 to 0.4, the MSM chooses the “resilience investment” strategy more quickly. This indicates that when the resilience investment reduction coefficient increases, investment costs decrease due to the collaboration resulting from information and knowledge sharing, the motivation of both parties to engage in resilient investment increases, and the “resilience investment” strategy evolves as a priority for the MSM and MSR, thus promotes the realization of the SCRES.

4.

Analysis of the influence of α and β on the evolutionary stability results

When $\alpha$ and $\beta$ are increased from 0 to 0.5 while other parameters remain unchanged, it can be seen from Figure 7 that when $\alpha =0$ and $\beta =0$, the MSM and MSR both choose the “resilience investment “ strategy, and condition ④ is satisfied. When $\alpha =0$ and $\beta$ increase from 0 to 0.4, the MSR accelerates in selecting the “resilience investment” strategy. When $\beta =0$ and $\alpha$ increase from 0 to 0.4, the MSM chooses the “resilience investment” strategy more quickly. As the additional benefit increase coefficient increases, the resilience investment becomes more effective in generating more additional benefits. This investment can lead to greater synergistic overall benefits, such as sharing information on medical needs and the inventory of medical supplies. The more additional benefits gained through resilience investment, the faster the evolution of the MSM and MSR select “resilience investment” strategy. This suggests that more significant additional benefit coefficients motivate resilience investment. Therefore, healthcare entities with high coefficients of additional benefits will be more willing to invest in resilience.

4.2. Numerical Simulation of Supply Chain Disruption Scenarios

Based on the analysis of the disruption scenario game played by the two parties of the HCSC, the ideal evolutionary stable state that the system can reach is (resilience investment, resilience investment). In order to reach this state, numerical simulations were conducted using Matlab software to explore the impact of relevant factors on the strategic behavior of each participant. The simulation model parameters were assigned based on satisfying the model’s hypothesis and reasonable and logical relationships. The parameters were assigned as follows: $R_m=1,R_r=1,r_m=0.4,r_r=0.25,C_{1m}=0.2,C_{1r}=0.15,\theta =0.1,$ $r^{*}=0.05,\alpha =0.3,\beta =0.2,a=0.3,b=0.4,R_m^{+}=0.3,R_r^{+}=0.2,R_m^{-}=0.6,R_r^{-}=0.5,C_{2m}=0.7,$ $C_{2r}=0.6,f=0.5,d=0.3,s=0.4,g=0.4,\gamma =0.1,\mu =0.1,h=0.2,m=0.2,n=0.2,v=0.1,$ $u=0.1,k=0.2,j=0.2$.

4.2.1. Initial State Simulation Analysis

The initial willingness of both parties to invest in resilience significantly impacts the final evolutionary outcome of the system. The initial points of system evolution are set as (0.1,0.1), (0.3,0.3), (0.5,0.5), (0.7,0.7), (0.9,0.9), (0.9,0.1), (0.8,0.2), (0.7,0.3), (0.1,0.9), (0.2,0.8), and (0.3,0.7), and explore the willingness of both parties to invest in resilience, as well as the evolution results when the unilateral resilience investment is strong. The simulation results are shown in Figure 8 and Figure 9.

Upon analyzing Figure 8, in SC disruption scenarios, it becomes apparent that when the MSM and MSR exhibit similar levels of willingness to invest in resilience, they will gradually converge toward the resilience investment despite a decrease in their willingness. Figure 9 shows that when the MSM chooses the “resilience investment” strategy to improve SCRES with high initial probability, although the initial probability of the MSR choosing the “resilience investment” strategy is low, after adjusting and optimizing behavioral strategies, the MSR’s probability of choosing the “resilience investment” strategy increases continuously. The two parties finally reach an evolutionary stable equilibrium (1,1). The above shows that under the constraint of condition ⑥, if the MSM’s and MSR’s resilience investment willingness is positive, negative, or unilaterally positive and unilaterally negative, both parties continuously adjust and optimize their strategies to pursue profit maximization, and both of them will ultimately evolve into the resilience investment strategy (1,1). This further proves the correctness of the eigenvalue analysis above that the system will evolve to (1,1) under the constraint of condition ⑥.

4.2.2. Parametric Simulation Analysis

In SC disruption scenarios, based on the previous analysis of the stability of the evolutionary game between the MSM and MSR, it is evident that several factors influence the equilibrium state of the evolutionary game and the strategy choices of both parties. Therefore, the subsequent action is to give different initial values to each influencing factor to explore the influence of different factors on the strategy choices of both parties. The initial probability of the MSM and MSR choosing the resilience investment strategy is assumed to be (0.5,0.5).

• Analysis of the influence of $R_m^{-}$ and $R_r^{-}$ on the evolutionary stability results

When $R_m^{-}$ and $R_r^{-}$ are increased from 0 to 0.6 while other parameters remain unchanged, it can be seen from Figure 10 that when $R_m^{-}=0$ and $R_r^{-}=0$, the MSM chooses the “resilience investment” strategy, the MSR chooses the “resilience non-investment” strategy, condition ⑤ is satisfied. When $R_m^{-}=0.1$ and $R_r^{-}=0.1$, the MSR’s willingness to resilience investment starts to rise but is below 0.5. When $R_m^{-}$ and $R_r^{-}$ increase from 0.1 to 0.6, the probability of the MSR selecting the “resilience investment” strategy increases from convergence to 0 to convergence to 1, with the convergence rate becoming faster. The larger the disruption losses $R_m^{-}$ and $R_r^{-}$ are, the greater the willingness to invest in resilience and the faster the evolutionary speed will be. This indicates that high disruption losses can negatively impact the operations of the MSM and MSR, thereby increasing their motivation to make resilience investments.

2.

Analysis of the influence of d and f on the evolutionary stability results

When all other parameters are held constant, Figure 11 displays the simulation results when $d$ and $f$ are increased from 0 to 0.5. When $d=0$ and $f=0$, the probability that the MSR will choose the “resilience investment” strategy is approximately 0.6. As $d$ and $f$ increase to 0.5, both parties choose the resilience investment strategy, and the system evolves to (1,1), which satisfies the constraint condition ⑥. When $d=0.3$ and $f$ increase from 0.3 to 0.5, the MSM accelerates in selecting the “resilience investment” strategy. When $f=0$ and $d$ increase from 0.3 to 0.5, the MSR chooses the “resilience investment” strategy faster. This indicates that the disruption loss reduction coefficients $d$ and $f$ incentivize healthcare entities to participate in resilience investment activities, as resilience investment provides better protection for HCSC operations.

3.

Analysis of the influence of $R_m^{+}$ and $R_r^{+}$ on the evolutionary stability results

When $R_m^{+}$ increases from 0 to 0.25 while other parameters remain unchanged, Figure 12 shows that as the value of $R_m^{+}$ increases, the MSM chooses resilience investment gradually and more quickly. This indicates that more market encroachment revenue gained through resilience investment leads to a faster evolution of the MSM select “resilience investment” strategy.

The simulation results are shown in Figure 13 when $R_r^{+}$ increases from 0 to 0.25 while other parameters remain unchanged. When $R_r^{+}$ = 0 or 0.03, the MSR chooses the “resilience non-investment” strategy due to the minimal benefits of encroaching on other retailers’ market share during the SC disruption. At this point, the system satisfies constraint ⑤, and the system will eventually evolve to (1,0). When $R_r^{+}=0.07$ and 0.08, the MSR’s probability of choosing “resilience investment” increases from below 0.5 to above 0.5. When $R_r^{+}$ increases from 0.1 to 0.15, the probability of the MSR adopting the “resilience investment” strategy increases rapidly and reaches a value of 1, eventually leading the system to evolve to (1,1). These statements imply that retailers who generate higher revenue from resilience investment are less likely to participate in resilience non-investment activities and more likely to prioritize resilience investment. Therefore, the MSR’s capability to identify an alternative SC during a disruption, promptly resume operations, and seize additional revenue from the market share of other retailers can enhance retailers’ motivation to invest in resilience. This, in turn, contributes to the overall achievement of HCSCRES.

4.

Analysis of the influence of s and g on the evolutionary stability results

Holding all other parameters constant, Figure 14 displays the simulation results when $s$ increases from 0.1 to 0.4. The additional unit cost reduction coefficient affects the rate at which the MSM chooses the resilience investment strategy during the disruption period. A larger value of $s$ leads to faster convergence of the probability of choosing the resilience investment.

The simulation results are shown in Figure 15 when $g$ increases from 0 to 0.25 while other parameters remain unchanged. When $g$ = 0, the MSR chooses the “resilience non-investment” strategy due to the minimal benefits of reducing additional costs during the SC disruption. At this point, the system satisfies constraint ⑤, and the system will eventually evolve to (1,0). When $g$ increases from 0.1 to 0.16, the MSR’s probability of choosing “resilience investment” increases from below 0.5 to above 0.5. When $g$ increases from 0.2 to 0.25, the probability of the MSR adopting the “resilience investment” strategy increases rapidly and reaches a value of 1, leading the system to evolve to (1,1). These statements imply that retailers who benefit more from reducing additional costs from resilience investment are less likely to participate in non-investment activities and more likely to prioritize resilience investment. Hence, by identifying alternative suppliers during disruptions and promptly resuming operations, the MSR mitigates the financial loss caused by the inability to deliver goods and prevents loss of market share due to product unavailability, which helps to increase retailers’ incentives to participate in resilience investment, thus contributing to HCSCRES.

5.

Analysis of the influence of m and n on the evolutionary stability results

Array 1: $R_m^{-}=0.6,R_r^{-}=0.5$. In the case when $m$ increases from 0 to 0.2 while other parameters remain unchanged, Figure 16 shows that as the value of $m$ increases, the MSM chooses resilience investment more quickly. When $n$ increases from 0 to 0.2, as the value of $n$ increases, the MSR accelerates in selecting the “resilience investment” strategy. This indicates that the larger the disruption loss reduction coefficient is when both parties make resilience investments, the faster the resilience investment evolves.

Array 2: $R_m^{-}=0.2,R_r^{-}=0.1$. Holding all other parameters constant, Figure 16 displays the simulation results when m and n increase from 0.2 to 0.4. When $m$ = 0.2 and $n$ = 0.2, the probability of the MSR choosing the “resilience investment” strategy evolves toward a value less than 0.5 because the loss of SC disruption decreases, and the reduction of disruption losses due to resilience investment decreases. When $m$ = 0.3 and $n$ = 0.3, the MSR has a probability of choosing a “resilience investment” strategy near 0.6. When $m$ = 0.4 and $n$ = 0.4, the probability of the MSR choosing the “resilience investment” strategy evolves toward a value greater than 0.6 as the degree of reduction in disruption losses caused by resilience investment rises. Therefore, the degree of reduction in disruption losses from resilience investment directly impacts the motivation of the MSR to engage in resilience investment.

6.

Analysis of the influence of v and u on the evolutionary stability results

Array 1: $R_m^{-}=0.6,R_r^{-}=0.5$. When $v$ is increased from 0 to 0.1 while other parameters remain unchanged, it can be seen from Figure 17 that as the value of $v$ increases, the rate at which the MSM chooses the resilience investment strategy to evolve is affected by the additional unit cost reduction coefficient when both parties make resilience investments, but it is not effective. When $u$ increases from 0 to 0.1, the MSR accelerates in selecting the “resilience investment” strategy. This indicates that the larger the additional unit cost reduction coefficient is when both parties make resilience investments, the faster the resilience investment evolves.

Array 2: $R_m^{-}=0.2,R_r^{-}=0.1$. Holding all other parameters constant, Figure 17 displays the simulation results when $v$ and $u$ increase from 0 to 0.1. When $v$ = 0.1 and $u$ = 0.1, the probability of the MSR choosing the “resilience investment” strategy evolves toward a value less than 0.5 because the loss of SC disruption decreases, and the reduction of additional unit cost due to resilience investment decreases. When $v$ = 0.116 and $u$ = 0.116, the MSR has a probability of choosing a “resilience investment” strategy near 0.6. When $v$ = 0.2 and $u$ = 0.2, the MSR chooses the “resilience investment” strategy as the degree of reduction in additional unit cost caused by resilience investment rises, condition ⑥ is satisfied. Therefore, the degree of reduction in additional unit cost from resilience investment directly impacts the motivation of the MSR to engage in resilience.

7.

Analysis of the influence of k and j on the evolutionary stability results

Array 1: $R_m^{-}=0.6,R_r^{-}=0.5$. In the case when $k$ increases from 0 to 0.2 while other parameters remain unchanged, it can be seen from Figure 18 that as the value of $k$ increases, the MSM chooses the resilience investment more quickly, but it is not significant. When $j$ increases from 0 to 0.2, as the value of $j$ increases, the MSR accelerates in selecting the “resilience investment” strategy. This indicates that the larger the market encroachment revenue coefficient is when both parties choose the “resilience investment” strategy, the faster the resilience investment evolves.

Array 2: $R_m^{-}=0.2,R_r^{-}=0.1$. Holding all other parameters constant, Figure 18 displays the simulation results when $k$ and $j$ increase from 0.2 to 0.3. When $k$ = 0.2 and $j$ = 0.2, the probability of the MSR choosing the “resilience investment” strategy evolves toward a value less than 0.5 because the loss of SC disruption decreases. When $k$ = 0.25 and $j$ = 0.25, the probability of the MSR choosing a “resilience investment” strategy is near 0.6 because the market encroachment revenue increases. When $k$ = 0.3 and $j$ = 0.3, the probability of the MSR choosing the “resilience investment” strategy evolves toward a value greater than 0.6 as the degree of market encroachment revenue coefficient caused by resilience investment rises. Therefore, the market encroachment revenue coefficient from resilience investment by both parties positively impacts the motivation of the MSR to engage in resilience.

8.

Analysis of the influence of μ and γ on the evolutionary stability results

In the case when $\gamma$ increases from 0.2 to 0.5 while other parameters remain unchanged, the simulation results are shown in Figure 19. When $\gamma$ = 0.5, the MSR chooses the “resilience non-investment” strategy due to the higher “free-rider” benefits and decreased disruption losses that can be achieved through unilateral resilience investment by the MSM. At this point, the system satisfies constraint ⑤ and will eventually evolve to (1,0). When $\gamma$ = 0.4, the probability of the MSR choosing the resilience investment strategy evolves to around 0.6; when $\gamma$ = 0.3 or 0.2, as the “free-rider” benefits decrease, the MSR gradually abandons the “free-rider” strategy and prefers the “resilience investment” strategy. The system eventually evolves to (1,1). This suggests that reductions in “free-rider” benefits steer retailers toward resilience investment strategies. In the case when $\mu$ increases from 0.2 to 0.4, it can be seen from Figure 19 that as the value of $\mu$ increases, the MSR chooses the resilience investment more quickly. This indicates that more potential costs gained through the MSM’s unilateral resilience investment lead to a faster evolution of the MSR select “resilience investment” strategy. When the MSM engages in unilateral resilience investment, replacing the original MSR with a new MSR enhances the motivation for the original MSR to invest in resilience.

5. Summary

5.1. Conclusions

Healthcare is considered one of the necessities for sustaining life. However, frequent emergencies raise the risk of SC disruption, seriously threatening people’s lives and health security. Therefore, constructing a resilient HCSC is a solution to effectively cope with the healthcare crisis. This study utilizes evolutionary game theory to analyze the strategies of the MSM and MSR for resilience investment under symmetric SC scenarios: non-disruption and disruption. Subsequently, a numerical simulation is used to analyze the impact of different parameters on the evolutionary results and their evolutionary trends. The results of the study show that additional benefits from resilience investment, potential costs, disruption losses, market encroachment revenue, “free-rider” benefits, additional benefit increase coefficient, resilience investment reduction coefficient, disruption loss reduction coefficient, additional unit cost reduction coefficient, and market encroachment revenue coefficient all influence the resilience investment decisions.

5.2. Suggestion

The decision-making behavior of healthcare entities on SCRES investment affects the HCSCRES. Therefore, this study uses evolutionary game theory to construct a game model of resilience investment of the MSM and MSR in disruption and non-disruption symmetry scenarios. The evolutionary game outcomes provide suggestions for enhancing HCSCRES, including macro and micro viewpoints.

• Developing a resilient HCSC security system is crucial. First, in order to minimize the impact on healthcare services, it is essential to conduct a comprehensive assessment of the security of the HCSC system and develop a comprehensive and integrated SC security strategy that encompasses various levels, such as the government, industry, and individual enterprises. This strategy aims to efficiently address a range of changing threats and disasters, ensure the rapid recovery of the medical logistics and SC system following disruptions, and mitigate the effects of SC issues on healthcare services, industries, and enterprises to protect the uninterrupted and steady functioning of healthcare services. Furthermore, building a comprehensive HCSC risk assessment, early warning, and emergency response system is imperative. This system should be managed by a national-level organization that oversees the healthcare industry chain and guarantees the security of the SC. Simultaneously, the system should also evaluate HCSC risks and create adaptable SCRES plans based on the assessment findings to ensure that SC strategies can be promptly modified in response to different threats and disasters to protect the continuous operation of healthcare services.
• Governments should establish mechanisms to subsidize resilience investment by healthcare entities. Suppose healthcare entities are reluctant to invest in resilience due to the perceived lack of significant benefits. In that case, the government should provide subsidies to ensure that the overall benefits of resilience investment outweigh the benefits of “free-riding”. Through this mechanism, the government can provide financial assistance to evaluate the ability of the HCSC to withstand and recover from disruptions. Additionally, the government can promote and incentivize the implementation of advanced technologies like blockchain and artificial intelligence to enhance the effectiveness and transparency of the SC. This initiative helps healthcare entities strategize and efficiently equip themselves for forthcoming difficulties. Governments can also promote collaboration among HCSC stakeholders to create and execute resilience strategies. Facilitate cross-organizational cooperation by offering financial assistance to strengthen the overall resilience of the HCSC system.
• The government sets up penalty mechanisms to curb “free-riding” behavior on resilience investment. In cases where one participant in an HCSC invests in building resilience while another participant takes “free-rider” behavior, it becomes essential to establish a penalty mechanism. This mechanism ensures that the benefit received by the “free-rider” is less than the total benefit derived from the resilience investment. The penalty mechanism aims to prevent opportunistic behavior in the HCSC and ensures that all parties actively participate in enhancing the HCSCRES. Specifically, it is necessary to clearly define the responsibilities and obligations of each party involved in the SC contract, including resilience investment. Simultaneously, contractual terms should incorporate sanctions for “free-rider” behavior, enhancing members’ accountability for investing in resilience. By implementing a resilience investment penalty mechanism, members can foster a cooperative atmosphere in the HCSC that promotes collective growth and safeguards the overall SCRES. This will also help to ensure that all members fulfill their responsibility to enhance SCRE, ultimately ensuring the stability of HCSC system operations.
• Healthcare entities upgrade information technology and develop big data analytics capabilities. HCSC members are caught in a game of resilience investment due to mutual distrust, low returns, high expenses of resilience investment, and “free-rider” behavior. The significance of information transparency in the HCSC cannot be exaggerated. The extensive utilization of information technology enables the gathering of healthcare-related data, the integration of information processing and big data analytics capabilities, and SC visibility. This enhances the healthcare entities’ capacity to perceive and respond to environmental changes promptly during disruptions. Healthcare entities can gain insight into actual healthcare demands and market situations through demand visibility, while supply visibility relies on-demand visibility to assess perceived market conditions. With the assistance of information technology and big data analytics, healthcare organizations can digitize their production and delivery processes. This enables them to monitor data closely throughout the production and delivery stages, promptly respond to order demands, adjust flexibly for process optimization and efficiency improvement, and minimize losses during disruptions.
• Restructuring SC structure and optimizing partnerships. Cooperative gaming among healthcare entities tends to bring more benefits than non-cooperative gaming, favoring overall HCSC performance. During disruptions, it is advisable to modify the design of SC structures, reconfigure and improve relationships between SC partners, and establish incentives to encourage cooperation. Simultaneously, an effective communication mechanism should be implemented to facilitate the sharing of healthcare knowledge and information, enhance the visibility of the SC, monitor the operational state of the HCSC promptly, identify issues, and limit losses caused by disruptions. Inadequate collaborations might lead to logistics and information flow disruptions in the HCSC. Therefore, it is imperative to establish a close collaborative partnership, develop a reliable trust mechanism, jointly formulate production plans and demand forecasts, foster close cooperation among SC partners, enhance the extent of information sharing, and improve the responsiveness of the SC in order to safeguard people’s lives.

5.3. Research Limitations and Perspectives

The environment exerts an influence on the subject’s behavior. This study focuses solely on the game between micro-entities within the HCSC. The analysis fails to account for the potential impact of government regulations that might enhance resilience, such as offering incentives for investing in resilience, punishing free-riding behavior, and improving SC infrastructure. Information and communication technology can be used as a research factor in the future as it can improve the quality and efficiency of healthcare services while reducing costs and improving patient outcomes. Additionally, the coordination and cooperation issues between manufacturers and retailers in the HCSC are not considered in this study. In order to reduce opportunistic behavior and the risk of default resulting from information asymmetry, the core firms in the SC tend to incentivize the members by designing a contractual mechanism of “benefit sharing and risk sharing” to promote information sharing and reduce the default rate. Therefore, future research will explore the impact of government regulatory actions on improving HCSCRES and how to design rational contracts to incentivize HCSC entities to work together on resilience investment.