The Game Analysis among Governments, the Public and Green Smart Supply Chain Enterprises in Necessity Purchase and Supply during COVID-19 Pandemic

Abstract

During the COVID-19 pandemic, panic buying, price inflation, and the pollution of production processes led to economic and social unrest. In response to the current situation, the current research takes less account of the subjective perception of public panic buying and the lack of reference to the reality of effective governance. First, this paper uses prospect theory to portray the public’s perceived value of goods in panic buying and non-panic buying situations. Then, drawing on the experience of effective governance in China, a tripartite evolutionary game model of local government, the public and green smart supply chain enterprises is constructed under the reward and punishment mechanism of the central government. Then, this paper analyzes the strategic choices of each game player and the stability of the system equilibrium. The structure of the study suggests the following. (1) Improving local government subsidies and penalties, the cost of positive response and the probability of response can lead to an evolutionary direction where the public chooses not to panic buy and green smart supply chain enterprises choose to ensure a balance between supply and demand and increase pollution control in the production process. (2) Our study yields three effective combinations of evolutionary strategies, of which an ideal combination of evolutionary strategies exists. Non-ideal evolutionary strategy combinations can occur due to improper incentives and penalties of local governments and misallocation of limited resources. However, we find four paths that can transform the non-ideal evolutionary strategy combination into an ideal evolutionary strategy combination. (3) The central government’s reward and punishment mechanism is an important tool to stabilize the tripartite strategy, but the central government cannot achieve effective governance by replacing incentives with punishment.

1. Introduction

The COVID-19 pandemic has maintained continued outbreak throughout the world since 2019, resulting in the frequently occurred problems such as public panic buying, price hikes by enterprises and contamination of the production process. This seriously threatens the stability of purchase and supply market of necessities and environmental issues. As of 2020, more than 90 countries have seen panic buying during the COVID-19 pandemic [1]. Some enterprises expect to sell at high prices by hoarding emergency supplies and necessities [2], and some have high emissions of pollutants in the COVID-19 pandemic control period [3]. However, panic buying rarely happens in China [4] because local governments have taken active measures in controlling it and guiding public opinion to prevent public panic buying [5]. The governments punished the enterprises for their illegal behaviors [6,7]. According to the data released by the National Bureau of Statistics of China, the Consumer Price Index for the whole year of 2021 increased by 0.9% only on a year-on-year basis.

The outbreak of the COVID-19 pandemic has severely disrupted the global supply chain in manufacturing, transportation, logistics, and demand shifting areas [8]. That can be explained: it is impossible to efficiently coordinate enterprises immediately, so that interruptions and shutdowns in supply chains occur [9] to exacerbate the imbalance between the supply and demand of necessities [10]. Enterprises at each node of the smart supply chain supported by a new generation of information technology play an important role in achieving price and supply stability in the necessities market and preventing the public from panic buying. For example, JD.com took advantage of its smart supply chain to immediately mobilize warehouse materials around Wuhan when the COVID-19 pandemic erupted in just two months with supplying 220 million necessities to the public across China by its established 700 warehouses. The smart supply chain is a comprehensive integrated technology and management system that combines the Internet of Things, Internet technology, modern supply chain management theory and other related methods and technologies, and it is used to realize the intelligence, networking and automation of inter-enterprise business in the smart supply chain [11], where those enterprises can easily communicate in real time in terms of information flow, logistics, and capital flow, thereby improving the operation efficiency of the supply chain [12]. However, there is also the problem of environmental pollution in the process of ensuring the supply of essential goods by smart supply chain enterprises.

With the concept of circular economy, the green transformation of the supply chain has become an inevitable trend of supply chain development. The management process of the COVID-19 pandemic requires not only the smart of the supply chain to ensure the supply of essential goods but also the greening of the supply chain to realize the coordinated development of economic benefits and environmental protection. A green supply chain is based on the basic concept of attaching importance to the low-carbon circulation of commodities, energy saving and emission reduction, and it makes people more inclined to use advanced supply chain management technology, computer science and technology, etc., to strengthen the management of the supply chain, realize the optimal allocation of supply chain resources, reduce the input of resources and energy, and achieve the purpose of energy saving and emission reduction [13]. Supply chain smartness and greening is the inevitable trend of supply chain development. A green smart supply chain is based on the traditional supply chain, incorporating environmental factors into all circulation activities of supply chain products, and realizing intelligence, digitalization, networking, and automation by integrating modern information technology and management [14] to achieve flexible management, rapid response, and intelligent collaboration [15], which can alleviate supply–demand mismatch and public panic buying with environmental factors in mind.

Due to their responsibilities, local governments need to deal with public panic buying and illegal acts such as price increases and productive pollution by green smart supply chain enterprises, while green smart supply chain enterprises are direct actors that can stabilize the market of essential goods as well as avoid environmental pollution problems. However, since the local government has limited resources and budget, its response measures may be untimely and less active; green smart supply chain enterprises, as “rational people”, make behavioral decisions in the pursuit of profit maximization and often find it difficult to take the responsibility of managing emergencies; the public will also make purchase decisions according to their own perceived expectations, which will cause panic buying by the public and the recurrence of productive pollution incidents, and the local government, green smart supply chain enterprises and the public will constantly adjust their strategic choices and play a continuous game.

Therefore, it is necessary to deeply analyze the mechanism of occurrence and evolutionary pattern behind panic buying and productive pollution events during the COVID-19 pandemic and explore how local government decisions affect the behavior of the public and green smart supply chain enterprises. How do green smart supply chain enterprises and the public react to supply, purchase and environmental pollution? What are the paths for local governments to achieve panic buying and productive pollution event management with limited resources? It is important for the fundamental governance of emergencies and can also provide some theoretical support to solve the existing dilemma while enriching the research on the governance of panic buying and enterprise pollution events in emergencies.

Based on the above analysis, this paper uses prospect theory to portray the public’s perceived value of items in panic buying and non-panic buying situations, and it puts forward relevant hypotheses. Then, it presents a game payment matrix based on the public’s perceived value, constructs an evolutionary game model for the governance of public panic buying and production pollution events, explores the strategies of local governments, green smart supply chain enterprises and the public under their limited rationality and their conflicting interests, and further reveals how to stabilize the public’s market for buying and supplying essential goods and prevent pollution in the production process.

This study has three contributions. Firstly, in recent years, public panic buying, corporate violations and the pollution of production processes caused by public emergencies such as the COVID-19 epidemic have occurred frequently, seriously threatening social and economic stability, the ecological environment and the safety of people’s lives and property, and the research content of this paper has significant social and practical significance and exploration value. Secondly, for the study of panic buying, most of the previous literature constructs two-party game subjects; this paper draws on the experience of effective governance in China and selects three major game subjects: green smart supply chain enterprises, local governments and the public, which broadens the study of evolutionary games and at the same time ensures the feasibility of our study. Thirdly, for the study of panic buying and enterprise pollution governance, previous literature lacks the consideration of a quantitative model of subjective perceived behavior as a finite rational public, and this paper uses prospect theory to portray the public’s perceived value of the items. In addition, most of them use qualitative and descriptive statistical methods. It is necessary to use evolutionary games to construct mathematical models to analyze the problems brought about by the COVID-19 pandemic and the evolution of the decision-making process of each participant from a dynamic perspective.

The rest of this paper is organized as follows. We outline the relevant literature in Section 2. We describe the problems and propose parametric assumptions and build a tripartite evolutionary game model in Section 3. We analyze the stability strategies of three subjects in Section 4. We conduct numerical simulation experiments in Section 5. We conclude with suggestions in Section 6.

2. Literature Review

At the moment, research on panic buying mostly focuses on two aspects: internal formation factors and external influencing elements, with internal formation factors primarily investigated from the viewpoint of the general population. For example, Yuen and Wang et al. [16] conducted a systematic review of the literature on panic buying events during the COVID-19 pandemic and found that the factors of panic buying included cognitive and personality–psychological factors (i.e., perceived scarcity, anxiety, fear of inaccessibility and self-control) and psychosocial factors (i.e., observational learning, normative influence and trust). Yuen and Leong et al. [17] conducted an online survey of 508 respondents and investigated the survey data by constructing structural equation models. The results showed that several constructs of normative social influence, observational learning, perceived severity, and perceived scarcity had significant effects on consumer panic buying, which were mediated by controls. Arafat et al. [18] identified the contributing factors of panic buying by analyzing media reports, and they found that the most frequently cited attributes of panic buying in online reports were perceived product scarcity, increasing demand, and expected price soar. Yuen and Tan et al. [19] synthesized various social and behavioral theories and developed a theoretical model along with an online survey to empirically study people’s perceptions of scarcity through data. It was found that perceived scarcity can directly or indirectly motivate panic buying behavior through anticipated feelings of regret. The above studies are mainly based on theoretical analysis and empirical research to explore the public’s psychological factors of panic buying, and perceived product scarcity is the main internal influencing factor; however, few scholars have quantified the public’s perceived value of items in panic buying scenarios and analyzed the internal formation factors of panic buying by constructing mathematical models.

The analysis of the external influences on panic buying is mainly studied from the perspective of external subjects such as government and enterprises. For example, Prentice et al. [4] collected data from five countries (Australia, India, China, Vietnam, and Indonesia) to explore the influence of external factors such as government, business, and social groups on panic buying during the COVID-19 pandemic, and they found that proactive government and business measures can instill a sense of security and reduce the frequency of panic buying. Chen et al. [20] used the idea of clustering dynamics to construct a model of the emergence of group panic buying behavior, quantified the internal and external factors affecting individual buying behavior, and found that government intervention plays an important role in reducing the size of group rush. Xie et al. [21] proposed an agent-based ABM model that incorporates government behavior into the risk analysis of panic buying, and they found that the higher the government’s refutation of rumors and the greater the amount of aid, the higher the consumer’s trust in the government. Dammeyer and Je˙zewska-Zychowicz et al. [22,23] found that when public confidence in the government’s ability to achieve effective governance increases, brick-and-mortar stores that ensure adequate supply can keep the public away from panic buying. The findings of the above studies were effectively demonstrated in practice in China during the COVID-19 pandemic. Most of the above studies use empirical and theoretical analyses to explore the influence of government and enterprises on public panic buying behavior; however, few scholars have studied the interaction behavior between the participating subjects during public panic buying and explored how the government and enterprises influence public panic buying behavior.

In addition, Wang and Li [24] structured a description of the snatch-and-grab event in a truck accident, and the article used prospect theory to construct a two-sided evolutionary game between the government and the public to investigate the evolutionary law of the event. The study found that the evolutionary outcome of the event was closely related to the perceived value of the public and the government for their respective gains and losses. Later, Wang and Nie et al. [25] used prospect theory to describe the publics’ perceived value of items in the benchmark and panic buying situation, and they constructed an evolutionary game model between the public and the government to explore public panic buying. Although the above literature considers the evolutionary process among subjects affecting public panic buying, it only considers the game between two subjects, the government and the public. Zhao et al. [26] constructed an evolutionary game model of small and medium-sized enterprises and large enterprises to analyze consumers’ purchase intentions under the situation of rumor spreading and demand disruption to maintain stable and sustainable market development. Although it considers firms as subjects influencing public panic buying and the scenario of demand disruption due to unexpected events, it does not consider the government and public participation process.

Regarding the impact of enterprises on public panic buying, previous studies have not defined the types of enterprises. However, the outbreak of the COVID-19 pandemic has caused a large-scale shutdown of enterprises and supply chain disruptions [27], resulting in an imbalance between supply and demand in the necessities market [28]. It is difficult for traditional companies to reduce panic buying by the public through aggressive measures. Some scholars have discussed from the perspective of smart supply chain. For example, Chitrakar et al. [29] studied the application and impact of smart technologies in the food supply chain during the COVID-19 pandemic. These technologies make food processing activities more intelligent and solve the problem of insufficient manpower in the food supply chain. Papadopoulos et al. [30] explored the deployment of digital technologies by SMEs to ensure business continuity in response to extreme disruptions such as COVID-19 and global social shocks. Gupta et al. [31] constructed a game-theoretic model to analyze the strategic combinations of all possible actions of different stakeholders in the food supply chain and explored the use of traceability technology in the food supply chain to reduce food losses. It can be seen that smart supply chain enterprises can connect their systems together to share information, reduce response time, and make effective decisions in the market [32], thus effectively responding to supply chain disruptions and shutdowns; however, the rapid response of smart supply chain enterprises may also lead to untimely pollution prevention and contamination of the production process. Under the pressure of COVID-19 pandemic management, enterprises are likely to deviate from the original sustainable development track in the process of ensuring the balance between the supply and demand of essential goods. Zhang [33] found that a blocked circular economy will lead to more serious global plastic pollution. Chen et al. [3] established an AERMOD-based steel enterprise pollution forecast model, simulated the impact on the atmosphere of a steel company in Hebei province during the COVID-19 pandemic control period and the late decommissioning period, and found that the polluting emissions were worse during the COVID-19 pandemic control period. Therefore, in the process of public panic buying, intelligent supply chain enterprises are effective subjects to deal with public panic buying. However, most of the previous studies only considered the application of intelligent technologies by enterprises during the COVID-19 pandemic to solve the problems of supply chain disruptions and production shutdowns, and few scholars have considered the problem of productive pollution by smart supply chain enterprises.

With the development concept of the circular economy, the transformation to green supply chains has become an inevitable trend of supply chain development, and green supply chain management can effectively alleviate the pollution problem of enterprises. In recent years, the application of game theory to study green supply chain management is a current research hotspot. Zhang and Su [34] analyzed the main influencing factors of green behavior of supply chain enterprises by constructing a game model of green behavior of supply chain enterprises. Liu et al. [35] applied the evolutionary game model to study a two-level green supply chain consisting of green suppliers and green manufacturers, and they analyzed various internal and external factors affecting the emission reduction behaviors of both sides of the game. Zhou et al. [36] used a game model to analyze the optimal innovation strategy choice of a recycling supply chain among two innovation paths: green autonomous innovation and green imitation innovation. Majeed et al. [37] constructed a game-theoretic model to study the effect of social preferences on supply chain management performance. Some other scholars have studied the evolutionary game process among the participants of corporate pollution events based on green supply chain management. For example, Zuo et al. [38] used evolutionary game theory to construct an evolutionary game model of green operation model of a pig supply chain, and they analyzed the evolutionary path and influence mechanism of a green operation model of the pig supply chain for the problems of environmental surface source pollution brought by the pig farming industry in China. Barari et al. [39] studied sustainability theory in combination with supply chain management and coordination in order to ensure the sustainability of ecosystems, constructing an evolutionary game approach that seeks synergistic alliances between environmental and commercial benefits by establishing coordination between producers and retailers to judge their strategies for triggering green practices. Mahmoudi et al. [40] modeled the contrast between government goals and producer goals using two swarm evolutionary game theory approaches to study government policies and the implementation of incentives to influence producers’ pollution activities. From the above study, we found that the implementation of smart supply chain and green supply chain management can be a good solution to the imbalance of supply and demand in the market of essential goods and the pollution problem of enterprises during the COVID-19 pandemic, which provides the theoretical support for this paper to select the enterprise type of green smart supply chain enterprises. However, most scholars have studied the evolutionary process among participants in enterprise pollution events in non-emergency situations, and fewer studies have studied the evolution of participants in enterprise pollution events in emergency situations such as the COVID-19 pandemic. In addition, few scholars have considered the game process among participants in enterprise pollution events in both public panic buying and green smart supply chains.

To summarize the above, existing studies can provide some theoretical and methodological support for the study of public panic buying and enterprise pollution problems during the COVID-19 pandemic. However, there are some shortcomings. (1) For the study of panic buying, on the one hand, most previous studies lacked a consideration of quantitative models of subjective perceived behavior as a finite rational public [16,17,18,19]. In recent years, prospect theory has been mostly used to portray the public’s perceived value of items [24,25]. In the evolution of public panic buying, information asymmetry tends to motivate the finite rational public to form behavioral motives through the subjective perception of event triggers, which is consistent with the application basis of prospect theory to portray the subject’s decision-making behavior. On the other hand, most previous studies consider the evolutionary game between the government and the public [24,25] (on one hand) and the enterprise and the enterprise [26] as two subjects. However, in panic buying events, the government, the public and the enterprise are direct stakeholders, and few scholars consider the evolutionary process among the government, the public and the enterprise at the same time. (2) For the study of enterprise pollution, there are few studies related to the evolutionary process among the participants of enterprise pollution events under the scenarios of emergencies such as the COVID-19 pandemic, and few scholars have studied green smart supply chain enterprises as the subjects of evolutionary games. In this sense, this paper uses an evolutionary game model to analyze the conflict of interests, decision influencing factors and stable equilibrium of each subject in panic buying and enterprise pollution events, so as to provide a reference for public panic buying, for market fluctuations of essential goods during the COVID-19 pandemic and for enterprise production pollution prevention. The relevant literature for this study is summarized in

Table 1. Literature Review.

Research Perspectives		Research Content	Literature Sources
Factors affecting panic buying	In terms of internal factors	Perceived scarcity, anxiety, trust, and observational learning influence the public’s panic buying. (Literature review method)	Yuen and Wang et al. (2020) [16]
		Observational learning, perceived severity, and perceived scarcity have significant effects on consumer panic buying. (Survey method and empirical analysis)	Yuen and Leong et al. (2021) [17]
		Perceived scarcity stimulates panic buying behavior directly or indirectly through an anticipated sense of regret. (Survey method and empirical analysis)	Yuen and Tan et al. (2022) [19]
	In terms of external factors	Proactive government and enterprise measures can instill a sense of security and reduce the frequency of panic buying.	Prentice et al. (2021) [4]
		Interventions such as the intensity of government epidemic information play an important role in reducing the size of the group rush.	Chen et al. (2022) [20]
		The more the government refutes rumors and the more aid is available, the more trust consumers will have in the government, thus reducing panic buying.	Xie et al. (2022) [21]
Evolutionary interactions of the panic buying process		The article uses cumulative prospect theory to construct a two-sided evolutionary game between the government and the public, and it investigates the evolutionary law of panic buying. (Government and public)	Wang and Li. (2017) [24]
		The article uses prospect theory to describe the public’s perceived value of goods, while the study constructs an evolutionary game model between the public and the government to explore public panic buying. (Government and public)	Wang and Nie et al. (2020) [25]
		The article constructs an evolutionary game model for small and medium-sized enterprises and large enterprises, and it analyzes consumers’ purchase intention under rumor propagation and demand disruption. (Small and medium-sized enterprises and large enterprises)	Zhao et al. (2021) [26]
Smart supply chain responds to supply chain disruptions		COVID-19 pandemic period intelligent technology can enable the operation in the food supply chain.	Chitrakar et al. (2021) [29]
		Small and medium-sized enterprises deploy digital technologies to ensure business continuity in response to extreme disruptions such as COVID-19 and global social shocks.	Papadopoulos et al. (2020) [30]
Green supply chain management tackles productive pollution	Green supply chain management with game theory	The article applies the evolutionary game model to analyze the various internal and external factors that affect the abatement behavior of both sides of the game.	Liu et al. (2021) [35]
		The article uses a game model to analyze the optimal innovation strategy choice of recycling supply chain in the green innovation path.	Zhou et al. (2023) [36]
	The evolutionary game of productive pollution	The article analyzes the evolutionary path and influence mechanism of a green operation model of a pig supply chain in view of the environmental surface source pollution and other problems brought by pig farming. (Non-emergency)	Zuo et al. (2017) [38]
		The article constructs an evolutionary game approach to study the strategies of producers and retailers to trigger green practices. (Non-emergency)	Barari et al. (2012) [39]

.

3. Problem Description and Parametric Assumptions

3.1. Problem Description

This paper constructs a tripartite game model of local governments, green smart supply chain enterprises and the public under the central government’s mechanism of incentives and punishments. The logical relationships among the three subjects are shown in Figure 1.

When faced with public panic buying, as well as green smart supply chain enterprises that drive up prices and reduce pollution prevention measures during the COVID-19 pandemic, local governments choose to actively respond with probability z and to negatively respond with probability 1−z. The strategies of local governments affect green smart supply chain enterprises and the public; when local governments choose to actively respond, they need to coordinate green smart supply chain enterprises to actively respond and monitor their illegal behavior through contractual agreements. For example, local governments need to coordinate green smart supply chain enterprises to carry out emergency production, warehousing and the allocation of necessities, and the preparation of logistics supply. They also need to actively guide public opinion information during the COVID-19 pandemic and take corresponding measures to prevent the spread of bad public opinion among the public as well as prevent pollution from the production process of companies. Considering the balance between benefits and costs, green smart supply chain enterprises choose to actively respond with a probability of x, and they choose to negatively respond with a probability of 1−x (assuming that green smart supply chain enterprises have illegal behaviors when they choose to respond negatively, including driving up prices and reduce pollution prevention measures). The strategies of green smart supply chain enterprises affect the supply and prices of market necessities. The public chooses to panic buy with probability y, and they choose not to panic buy with probability 1−y. x, y, z∈[0,1]. If the COVID-19 pandemic situation worsens, local governments will be punished by the central government, and they will be rewarded by the central government if they are effectively governed.

3.2. Parametric Assumptions

To formulate the problem, several assumptions are made.

Assumption 1.

When local governments choose to actively respond, they need to actively guide public opinion and supervise the illegal behavior of green smart supply chain enterprises [41] and offer them subsidies for active responses and penalties for negative responses. If the local government actively responds and the public chooses not to panic buy, at this time, the problem will be effectively managed, and the local government will receive incentives from the central government and positive social utility (such as reputation, credibility enhancement). If the local government’s negative response causes public panic buying and green smart supply chain enterprises to choose illegal behaviors, the local government not only needs to bear the negative effects brought about by public panic buying and green smart supply chain enterprises’ illegal behavior (such as the decline of reputation and credibility) but will also be punished by the central government for unfavorable responses.

Assumption 2.

When green smart supply chain enterprises choose to actively respond, they need to use information platforms to cooperate with each other and perform their own duties, such as market demand forecasting, emergency production and procurement, coordination of warehousing materials, logistics coordination and distribution to achieve the stable operation of the supply chain of necessities, and actively address pollution in the production process, in order to increase the supply of necessities in the market to stabilize prices, and its active response will be rewarded by the local government. When the public chooses to panic buy, if green smart supply chain enterprises choose to respond negatively, they will obtain illegal benefits, while the green intelligent supply chain enterprises will reduce the pollution prevention measures of the production process, which will further increase the illegal benefits.

Assumption 3.

During the COVID-19 pandemic, information asymmetry tends to prompt the bounded rational public to decide their own strategies through subjective perception, assuming that there is no difference between each individual, with the same perceptual and psychological effects. Drawing on the model assumptions of Wang et al. [25], this study uses the public’s perceived value to describe the public’s gains and losses, and the zero-value reference point of the perceived value is the public’s spending when they choose not to panic purchase. When the public chooses not to panic buy, the public’s demand for necessities tends to be normal, and the purchase volume is $M_0$; if the price of necessities in the market rises, it is a waste of money for the public at this time, the public’s perceived value is a loss, and the perceived value function is $V_N=-\alpha {(M_0{P}_M-M_0{P}_0)}^{\gamma }$, where $\alpha$($\alpha >1$) is the loss aversion coefficient, $\gamma$is the sensitivity of the public to the loss, $P_0$ is the price of necessities under normal circumstances, and $P_M$ is the market price of necessities. In the situation where the public chooses to panic buy necessities (that is, to meet the demand value of a single commodity under a sense of psychological security), the public’s psychological expected value of necessities will become higher, and the public’s psychological expected total value of all the necessities purchased is greater than the actual total value. At this time, the public’s perceived value is profit [42], and the perceived value function is $V_R=\beta {(M{P}_M-M_0{P}_0)}^{\theta }$, where $\beta$ ($\beta >0$) is the psychological expectation of income, $\theta$ is the sensitivity of income, $M$ is the purchase amount of necessities when the public chooses to panic buy, $M_0,M$ is an invariant and $M>M_0$.

Assumption 4.

When green smart supply chain enterprises choose to actively respond, it can ensure a sufficient supply of daily necessities and ensure the normal purchase demand of the public [43,44]; at this time, the price of necessities is $P_0$. If the public chooses to panic buy, the perceived value of the public is $V_{AB}=\beta {(M{P}_0-M_0{P}_0)}^{\theta }$. If the public chooses not to panic buy, the public’s perceived value is $V_{AN}=-\alpha {(M_0{P}_0-M_0{P}_0)}^{\gamma }=0$. When green smart supply chain enterprises choose to negatively respond, the supply of necessities in the market is in short supply, green smart supply chain enterprises have illegal acts, and the price of necessities rises to $P$; at this time, the perceived value of the public when they choose to panic buy is $V_{PB}=\beta {(MP-M_0{P}_0)}^{\theta }$. If the public choose not to panic buy, it will not cause a surge in demand for necessities. According to the theory of supply and demand, it is assumed that when the public choose not to panic buy, it will not lead to non-market changes in the prices of necessities, because stable demand inhibits the illegal behavior of green smart supply chain enterprises, so that the price of necessities is stabilized as $P_0$; at this time, the perceived value of the public is $V_{PN}=-\alpha {(M_0{P}_0-M_0{P}_0)}^{\gamma }=0$. It is assumed that the government’s credibility (the public’ trust in the local government’s ability to stabilize the supply of necessities and prices) is 0 when the local government passively guides public opinion, and the credibility of the local government under the active guidance of public opinion is ${\omega }_1$; it is assumed that credibility is positively related to the cost of active response by local governments [45]. Referring to the model assumptions of Wang et al. [25], the public’s perceived benefit is equal to the weighted value of the local government’s credibility and the public’s perceived value. According to the “principle of rational man considering marginal quantities”, when local governments choose to negatively respond, the public’s perceived benefits are greater than their panic buying costs, $V_{PB}>V_{AB}>C_P$.

The parameter symbols in Assumptions 1–4 are shown in

Table 2. Variables symbol descriptions in models.

Entities	Variables	Meaning
Local Governments	$C_G^{}$	Coping costs incurred when local governments choose to actively respond.
	$R_G$	Incentives from the central government when local governments respond effectively.
	$R_U$	The positive effects of the local government’s effective response.
	$R_{-U}$	$\mathrm{Negative}\mathrm{effects}\mathrm{local}\mathrm{governments}\mathrm{receive}\mathrm{when}\mathrm{problems}\mathrm{worsen}.(R_{-U}>R_U$)
	$C_G^G$	$\mathrm{Central}\mathrm{government}\mathrm{punishment}\mathrm{for}\mathrm{local}\mathrm{governments}\mathrm{when}\mathrm{problems}\mathrm{worsen}.(C_G^G>R_G$)
	${\omega }_1$	$\mathrm{The}\mathrm{credibility}\mathrm{of}\mathrm{the}\mathrm{local}\mathrm{government}\mathrm{when}\mathrm{it}\mathrm{actively}\mathrm{responds}.(0\le {\omega }_1\le 1$)
Green Smart Supply Chain Enterprises	$R_S^G$	Local government subsidies when green smart supply chain enterprises choose to actively respond.
	$C_S$	Costs when green smart supply chain enterprises choose to actively respond.
	$R_{SS}$	Illegal gains generated when green smart supply chain enterprises choose to negatively respond.
	$C_S^G$	Green smart supply chain enterprises suffer illegal penalties from local governments when they choose to negatively respond.
Public	$C_P$	Costs incurred when the public choose to panic buy.
	$V_{AB}$	The perceived value of the public choosing to panic buy when green smart supply chain enterprises choose to actively respond.
	$V_{AN}$	The perceived value of the public choosing not to panic buy when green smart supply chain enterprises choose to actively respond.
	$V_{PB}$	The perceived value of the public choosing to panic buy when green smart supply chain enterprises choose to negatively respond.

, respectively.

Based on the above assumptions, the payoff matrix of green smart supply chain enterprises, the public, and local governments is shown in

Table 3. The payoff matrix of the three-way game.

Green Smart Supply Chain Enterprises	Public	Local Governments
		Actively Respond z	Negatively Respond 1-z
Actively Respond x	Panic Buying y	$R_S^G-C_S,(1-{\omega }_1)V_{AB}-C_P,-R_S^G-C_G^{}$	$-C_S,V_{AB}-C_P,-C_G^G-R_{-U}$
	No Panic Buy1−y	$R_S^G-C_S,0,R_G+R_U-R_S^G-C_G^{}$	$-C_S,0,0$
Negatively Respond 1−x	Panic Buying y	$R_{SS}-C_S^G,(1-{\omega }_1)V_{PB}-C_P,C_S^G-C_G^{}$	$R_{SS},V_{PB}-C_P,-C_G^G-R_{-U}$
	No Panic Buy1−y	$-C_S^G,0,R_G+R_U+C_S^G-C_G^{}$	$0,0,0$

. The values of the strategy combinations in the payment matrix, from left to right, represent the benefits to the smart supply chain companies, the public and the local government when they choose the strategy.

4. Analysis of the Stability Strategy of Each Game Subject

4.1. Stability Analysis of Green Smart Supply Chain Enterprises

The expected payoffs of green smart supply chain enterprises when they choose to actively respond ($U_x$) and negatively respond ($U_{1-x}$) are as follows:

$$\begin{array}{c}{U}_x=yz(R_S^G-C_S)+y(1-z)(-C_S)+(1-y)z(R_S^G-C_S)+(1-y)(1-z)(-C_S)\\ U_{1-x}=yz(R_{SS}-C_S^G)+y(1-z)(R_{SS})+(1-y)z(-C_S^G)\end{array}$$

(1)

.

Thus, the average payoff of green smart supply chain enterprises (${\overline{U}}_1$) is as follows:

$${\overline{U}}_1=x{U}_x+(1-x)U_{1-x}$$

(2)

According to Equation (2), the replicator dynamics equation of green smart supply chain enterprises can be calculated as:

$$F(x)=dx/dt=x(U_x-{\overline{U}}_1)=x(1-x)[z(R_S^G+C_S^G)-y{R}_{SS}-C_S]$$

(3)

Furthermore, the first partial derivative of $F(x)$ and the set $G(y:z)$ are, respectively:

$$dF(x)/dx=(1-2x)[z(R_S^G+C_S^G)-y{R}_{SS}-C_S]$$

(4)

$$G(y,z)=z(R_S^G+C_S^G)-y{R}_{SS}-C_S$$

(5)

When $F(x)=0$ and $dF(x)/dx<0$, x is evolutionarily stable, the following analysis can be obtained:

(1) When $z=y{R}_{SS}+C_S/R_S^G+C_S^G$(Let $z\ast =y{R}_{SS}+C_S/R_S^G+C_S^G$), there is $dF(x)/dx\equiv 0$, no matter what the value of x is, it is in a stable state. At this time, the strategy selection ratio of green smart supply chain enterprises will not change with time.

(2) When $z\ne z\ast$, there are two cases:

① Because of $\partial G(y,z)/\partial z>0$, we know that $G(y,z)$ is increasing with respect to z. When $z<z\ast$, there are $dF(x)/dx{|}_{x=0}<0$ and $dF(x)/dx{|}_{x=1}>0$, so x = 0 is the evolution equilibrium point. At this point, green smart supply chain enterprises tend to choose to negatively respond.

② When $z>z\ast$, there are $dF(x)/dx{|}_{x=0}>0$, $dF(x)/dx{|}_{x=1}<0$, so x = 1 is the evolution equilibrium point. At this point, green smart supply chain enterprises tend to choose to actively respond.

The green smart supply chain enterprises replication dynamic phase diagram is shown in Figure 2.

It can be seen from Figure 2 that the volume $V_{A_1}$ of $A_1$ is the probability that green smart supply chain enterprises choose to actively respond, and the volume $V_{A_2}$ of $A_2$ is the probability that green smart supply chain enterprises choose to negatively respond, according to the calculation: $V_{A_1}={\displaystyle \underset{A_1}{\iint }(y{R}_{SS}+C_S)/(R_S^G+C_S^G)}dydx=1-(R_{SS}+2C_S)/2(R_S^G+C_S^G)$, $V_{A_2}=1-V_{A_1}$.

Proposition 1.

The probability that green smart supply chain enterprises choose to actively respond is positively related to $R_S^G$and $C_S^G$, and it is negatively related to $C_S$and$R_{SS}$.

Proof. 

According to the probability $V_{A_1}$ that green smart supply chain enterprises actively respond, the first partial derivative of each element can be obtained: $d{V}_{A_1}/d{R}_S^G>0$, $d{V}_{A_1}/d{C}_S^G>0$, $d{V}_{A_1}/d{C}_S<0$ and $d{V}_{A_1}/d{R}_{SS}<0$. Therefore, the increase in $R_S^G$ and $C_S^G$ or the decrease in $C_S$ and $R_{SS}$ can improve the probability that green smart supply chain enterprises actively respond. □

Proposition 1 shows that local governments can not only reduce the illegal gains of green smart supply chain enterprises and reduce the environmental pollution of the production process by strict supervision but also increase illegal penalties to avoid green smart supply chain enterprises choosing to negatively respond. It is also possible to increase the probability that green smart supply chain enterprises to actively respond by reducing costs and increasing financial subsidies.

Proposition 2.

In the evolution process, the probability that green smart supply chain enterprises choose to actively respond decreases with the increase in the probability of the public choosing to panic buy, and it increases with the increase in the probability that local governments choose to actively respond.

Proof. 

According to the strategic stability analysis of green smart supply chain enterprises, when $y<[z(R_S^G+C_S^G)-C_S]/R_{SS}$, there are $G(y:z)>0$ and $dF(x)/dx{|}_{x=1}<0$, so x = 1 is the evolutionary stability strategy (ESS). Conversely, when $y>[z(R_S^G+C_S^G)-C_S]/R_{SS}$, x = 0 is ESS. When $z<z\ast$, there are $\partial G(y:z)<0$ and $dF(x)/dx{|}_{x=0}<0$, so x = 1 is ESS. Conversely, when $z>z\ast$, x = 1 is ESS. Summing up, with the gradual increase in y or decrease in z, the strategy of green smart supply chain enterprises decreases from x = 1 (Actively Respond) to x = 0 (Negatively Respond). □

Proposition 2 shows that if the public can rationally treat public opinion information and maintain full trust in local governments, instead of looting necessities according to external public opinion and self-perceived judgment, at this time, if green smart supply chain enterprises choose to negatively respond, not only will they not obtain the expected benefits, but they will also suffer reputation damage and penalties from the local government. It can be seen that local governments can encourage green smart supply chain enterprises to choose to actively respond by improving their own enthusiasm and reducing the probability of panic buying by the public.

4.2. Stability Analysis of the Public

The expected payoffs of the public with panic buying ($U_y$) and not panic buying ($U_{1-y}$) are as follows:

$$\begin{array}{c}\begin{array}{l}{U}_y=xz[(1-{\omega }_1)V_{AB}-C_P]+x(1-z)(V_{AB}-C_P)+(1-x)z[(1-{\omega }_1)V_{PB}-C_P]\\ +(1-x)(1-z)(V_{PB}-C_P)\end{array}\\ U_{1-y}=0\end{array}$$

(6)

Thus, the average payoff of the public (${\overline{U}}_2$) is as follows:

$${\overline{U}}_2=y{U}_y+(1-y)U_{1-y}$$

(7)

According to Equation (7), the replicator dynamics equation of the public can be calculated as:

$$F(y)=dy/dt=y(U_y-{\overline{U}}_2)=y(1-y)[x(1-{\omega }_{1}z)(V_{AB}-V_{PB})+(1-{\omega }_{1}z)V_{PB}-C_P]$$

(8)

Furthermore, the first partial derivative of $F(y)$ and the set $G(x,z)$ are, respectively:

$$dF(y)/dy=(1-2y)[x(1-{\omega }_{1}z)(V_{AB}-V_{PB})+(1-{\omega }_{1}z)V_{PB}-C_P]$$

(9)

$$G(x,z)=x(1-{\omega }_{1}z)(V_{AB}-V_{PB})+(1-{\omega }_{1}z)V_{PB}-C_P$$

(10)

When $F(y)=0$ and $dF(y)/dy<0$, y is ESS. The following analysis can be obtained:

(1) When $x=[(1-{\omega }_{1}z)V_{PB}-C_P]/[(1-{\omega }_{1}z)(V_{PB}-V_{AB})]$

(Let $x\ast =[(1-{\omega }_{1}z)V_{PB}-C_P]/[(1-{\omega }_{1}z)(V_{PB}-V_{AB})]$), there is $dF(y)/dy\equiv 0$, no matter what the value of y is, it is in a stable state. At this time, the strategy selection ratio of the public will not change with time.

(2) When $x\ne x\ast$, there are two cases:

① Because of $\partial G(x,z)/\partial x<0$, we know that $G(x,z)$ is decreasing with respect to x. When $x<x\ast$, there are $dF(y)/dy{|}_{y=0}>0$ and $dF(y)/dy{|}_{y=1}<0$, so y = 1 is the evolution equilibrium point. At this point, the public tends to choose to panic buy.

② When $x>x\ast$, there are $dF(y)/dy{|}_{y=0}<0$ and $dF(y)/dy{|}_{y=1}>0$, so y = 0 is the evolution equilibrium point. At this point, the public tends to choose not to panic buy.

The public replication dynamic phase diagram is shown in Figure 3.

It can be seen from Figure 3 that the volume $V_{B_1}$ of $B_1$ is the probability that the public chooses to panic buy, and the volume $V_{B_2}$ of $B_2$ is the probability that the public chooses not to panic buy, according to the calculation: $\begin{array}{l}{V}_{B_1}={\displaystyle \underset{B_1}{\iint }[(1-{\omega }_{1}z)V_{PB}-C_P]/[(1-{\omega }_{1}z)(V_{PB}-V_{AB})]}dzdy=\\ V_{PB}/(V_{PB}-V_{AB})+C_{P}In(1-{\omega }_1)/{\omega }_1(V_{PB}-V_{AB})\end{array}$, $V_{B_2}=1-V_{B_1}$.

Proposition 3.

The probability that the public chooses to panic buy is positively correlated with $V_{PB}$and$V_{AB}$, and negatively correlated with${\omega }_1$and$C_P$.

Proof. 

According to the expression of panic buying probability $C_1$, the first partial derivative of each element can be obtained:$d{V}_{B_1}/d{V}_{PB}>0$ (s.t. $In(1-{\omega }_1)<-{\omega }_1{V}_{AB}/C_P$); $d{V}_{B_1}/d{V}_{AB}>0$ (s.t. $In(1-{\omega }_1)>-{\omega }_1{V}_{PB}/C_P$); $d{V}_{B_1}/d{\omega }_1<0$;$d{V}_{B_1}/d{C}_P<0$. Therefore, the increase in $V_{PB}$ and $V_{AB}$ or the decrease in ${\omega }_1$ and $C_P$ can improve the probability of the public choosing to panic buy. □

Proposition 3 shows that on the one hand, the public’s strategic choice is related to its trust in local governments and the cost of panic buying; the public may choose to panic buy when they believe that local governments cannot effectively deal with the COVID-19 pandemic or when they believe that panic buying is very convenient for them. On the other hand, a sharp increase in the price of necessities increases the perceived value of the public, thereby increasing the probability that the public chooses to panic purchase.

Proposition 4.

In the evolution process, the probability that the public chooses to panic buy decreases with the increase in the probability of green smart supply chain enterprises and local governments choosing to actively respond.

Proof. 

According to the strategic stability analysis of the public, when $x<x\ast$ and $z<[(1-x)V_{PB}+x{V}_{AB}-C_P]/[(1-x){\omega }_1{V}_{PB}+x{\omega }_1{V}_{AB}]$, there is $dF(y)/dy{|}_{y=1}<0$, so y = 1 is the evolution equilibrium point; conversely, y = 0 is the evolution equilibrium point. Summing up, with the gradual increase in x and z, the strategy of the public decreases from y = 1 (Panic Buying) to y = 0 (Do Not Panic Buy). □

Proposition 4 shows that local governments can increase the probability of their own response to prevent the public from choosing to panic buy, and they can also prevent the public from choosing to panic buy by increasing the probability that green smart supply chain enterprises actively respond.

4.3. Stability Analysis of Local Governments

The expected payoffs of the local governments when they actively respond ($U_z$) and negatively respond ($U_{1-z}$) are as follows:

$$\begin{array}{c}{U}_z=xy(-R_S^G-C_G^{})+x(1-y)(R_G+R_U-R_S^G-C_G^{})+(1-x)y(C_S^G-C_G^{})+(1-x)(1-y)(R_G+R_U+C_S^G-C_G^{})\\ U_{1-z}=xy(-C_G^G-R_{-U})+(1-x)y(-C_G^G-R_{-U})\end{array}$$

(11)

Thus, the average payoff of the local government (${\overline{U}}_3$) is as follows:

$${\overline{U}}_3=z{U}_z+(1-z)U_{1-z}$$

(12)

According to Equation (12), the replicator dynamics equation of the local government can be calculated as:

$$F(z)=dz/dt=z(U_z-{\overline{U}}_3)=z(1-z)[y(C_G^G+R_{-U}-R_G-R_U)-x(R_S^G+C_S^G)+R_G+R_U+C_S^G-C_G^{}]$$

(13)

Furthermore, the first partial derivative of $F(z)$ and the set $G(x,y)$ are, respectively:

$$dF(z)/dz=(1-2z)[y(C_G^G+R_{-U}-R_G-R_U)-x(R_S^G+C_S^G)+R_G+R_U+C_S^G-C_G^{}]$$

(14)

$$G(y,z)=y(C_G^G+R_{-U}-R_G-R_U)-x(R_S^G+C_S^G)+R_G+R_U+C_S^G-C_G^{}$$

(15)

When $F(z)=0$ and $dF(z)/dz<0$, z is the evolution equilibrium point. The following analysis can be obtained:

(1) When $x=[y(C_G^G+R_{-U}-R_G-R_U)+R_G+R_U+C_S^G-C_G^{}]/(R_S^G+C_S^G)$

(Let $x\ast \ast =[y(C_G^G+R_{-U}-R_G-R_U)+R_G+R_U+C_S^G-C_G^{}]/(R_S^G+C_S^G)$), there is $dF(z)/dz\equiv 0$; no matter what the value of z is, it is in a stable state. At this time, the strategy selection ratio of the local government will not change with time.

(2) When $x\ne x\ast \ast$, there are two cases:

① Because of $\partial G(x,y)/\partial x<0$, we know that $G(x,y)$ is decreasing with respect to x. When $x<x\ast \ast$, there are $dF(z)/dz{|}_{z=0}>0$ and $dF(z)/dz{|}_{z=1}<0$, so z = 1 is the evolution equilibrium point. At this point, local governments tend to choose actively respond.

② When $x>x\ast \ast$, there are $dF(z)/dz{|}_{z=0}<0$ and $dF(z)/dz{|}_{z=1}>0$, so z = 0 is the evolution equilibrium point. At this point, local governments tend to choose to negatively respond.

The local governments replication dynamic phase diagram is shown in Figure 4.

It can be seen from Figure 4 that the volume $V_{C_1}$ of $C_1$ is the probability that local governments choose to actively respond, and the volume $V_{C_2}$ of $C_2$ is the probability that local governments choose to negatively respond, according to the calculation:

$$\begin{array}{l}{V}_{C_1}={\displaystyle \underset{C_1}{\iint }[y(C_G^G+R_{-U}-R_G-R_U)+R_G+R_U+C_S^G-C_G^{}]/(R_S^G+C_S^G)}dydz=\\ (R_G+R_U+C_G^G+R_{-U}+2C_S^G-2C_G^{})/2(R_S^G+C_S^G)\end{array},V_{C_2}=1-V_{C_1}$$

Proposition 5.

The probability that the local government chooses to actively respond is positively correlated with$R_G$, $C_G^G$and $R_{-U}$, and it is negatively correlated with $C_G^{}$and $R_S^G$.

Proof. 

According to the expression of actively respond probability $C_1$, the first partial derivative of each element can be obtained:$d{V}_{C_1}/d{R}_G>0$, $d{V}_{C_1}/d{C}_G^G>0$, $d{V}_{C_1}/d{R}_{-U}>0$, $d{V}_{C_1}/d{C}_G<0$, and $d{V}_{C_1}/d{R}_S^G<0$. Therefore, the increase in $R_G,C_G^G$ and $R_{-U}$ or the decrease in $C_G^{}$ and $R_S^G$ can improve the probability that the local government will actively respond. □

Proposition 5 shows that although high response costs and high subsidies will reduce the probability that local governments will respond positively, once the situation worsens, local governments will be punished by the central government and lose their reputation. For the local government, the loss of credibility and the punishment of the central government are irreversible; in reality, they often do not choose to negatively respond. Due to the functions of local governments, the process of managing the COVID-19 pandemic needs to consume a lot of social resources, and excessive costs can even cause financial difficulties for local governments, which greatly reduces the probability that local governments choose to actively respond. Incentives and penalties from the central government have played an irreplaceable role not only increasing the probability that local governments will actively respond but also improving the effectiveness of their responses.

Proposition 6.

In the evolution process, the probability that local governments choose to actively respond increases with the increase in the probability of the public choosing to panic buy, and it decreases with the increase in the probability that green smart supply chain enterprises choose to actively respond.

Proof. 

According to the strategic stability analysis of the local government, when $x<x\ast \ast$, there are $G(x:y)>0$ and $dF(z)/dz{|}_{z=1}<0$, so z = 1 is the evolution equilibrium point; conversely, when $x>x\ast \ast$, z = 0 is the evolution equilibrium point. When $y<[R_G+R_U+C_S^G-C_G^{}-x(R_S^G+C_S^G)]/(R_G+R_U-C_G^G-R_{-U})$, there are $G(x:y)<0$ and $dF(z)/dz{|}_{z=0}<0$, z = 0 is the evolution equilibrium point. Conversely, when $y>[R_G+R_U+C_S^G-C_G^{}-x(R_S^G+C_S^G)]/(R_G+R_U-C_G^G-R_{-U})$, z = 1 is the evolution equilibrium point. Summing up, with the decrease in x or the gradual increase in y, the strategy of the local government increases from z = 0 (Negatively Respond) to z = 1 (Actively Respond). □

Proposition 6 shows that the increase in the amount of misinformation or rumors will increase the probability that the public chooses to panic buy; at this time, local governments need to increase the probability that they will actively respond to increase the adjustment of crisis information; otherwise, the situation will become worse. When green smart supply chain enterprises choose to actively respond, they can avoid social problems such as panic buying by the public and wide-ranging price fluctuations to a certain extent. Due to the high financial pressure of local governments, they have the possibility of free-riding. However, the smart supply chain enterprise has the characteristics of rational people, and the government’s own responsibilities make this situation not appear in reality. On the contrary, if the smart supply chain enterprise chooses to negatively respond, it will increase the risk of deterioration of the situation; when the time comes, the local government will increase its response.

From Propositions 2, 4, and 6, we know that in evolutionary game models, x, y, and z are correlated. That is to say, there is interaction among the strategies of green smart supply chain enterprises and public and local governments, and strategic choices are mutually influenced. The evolutionary stability strategy is the result of a three-subject game. The following will conduct a systematic analysis of the evolutionary game.

4.4. Stability Analysis of Equilibrium Point of Tripartite Evolutionary Game System

According to Reinhard’s research conclusion, in an asymmetric game, if the condition of information asymmetry holds, the evolutionary stable strategy is a pure strategy. Therefore, it is only necessary to explore the eight partial equilibrium points in $O_1(0,0,0),O_2(1,0,0),O_3(0,1,0),O_4(0,0,1),O_5(1,1,0),O_6(1,0,1),O_7(0,1,1),O_8(1,1,1)$. The Jacobian matrix of the three-way evolutionary game system can be obtained by taking partial derivatives of $F(x),F(y),F(z)$ with respect to x, y and z and letting $F(x)=0,F(y)=0,F(z)=0$:

$$J=\left(\begin{array}{ccc}\frac{\partial F(x)}{\partial x}& \frac{\partial F(x)}{\partial y}& \frac{\partial F(x)}{\partial z}\\ \frac{\partial F(y)}{\partial x}& \frac{\partial F(y)}{\partial y}& \frac{\partial F(y)}{\partial z}\\ \frac{\partial F(z)}{\partial x}& \frac{\partial F(z)}{\partial y}& \frac{\partial F(z)}{\partial z}\end{array}\right)=\left(\begin{array}{ccc}\begin{array}{l}(1-2x)[z(R_S^G+\\ C_S^G)-y{R}_{SS}-C_S]\end{array}& x(1-x)(-R_{SS})& x(1-x)(R_S^G+C_S^G)\\ \begin{array}{l}y(1-y)(1-{\omega }_{1}z)\\ (V_{AB}-V_{PB})\end{array}& \begin{array}{l}(1-2y)[x(1-{\omega }_{1}z)\\ (V_{AB}-V_{PB})+\\ (1-{\omega }_{1}z)V_{PB}-C_P]\end{array}& \begin{array}{l}y(1-y)[-(1-x){\omega }_1{V}_{PB}\\ -x{\omega }_1{V}_{AB}]\end{array}\\ -z(1-z)x(R_S^G+C_S^G)& \begin{array}{l}z(1-z)(C_G^G+\\ R_{-U}-R_G-R_U)\end{array}& \begin{array}{l}(1-2z)[y(C_G^G+\\ R_{-U}-R_G-R_U)\\ -x(R_S^G+C_S^G)+R_G\\ +R_U+C_S^G-C_G^{}]\end{array}\end{array}\right)$$

The Jacobian matrix of the system at point $O_1(0,0,0)$ is

$J=\left(\begin{array}{ccc}-C_S& 0& 0\\ 0& (1-{\omega }_2)V_{PB}-C_P& 0\\ 0& 0& R_G+R_U+C_S^G-C_G^{}\end{array}\right)$, the eigenvalues of the Jacobian matrix $\lambda =\left(\begin{array}{c}-C_S\\ (1-{\omega }_2)V_{PB}-C_P\\ R_G+R_U+C_S^G-C_G^{}\end{array}\right)$. Similarly, the eigenvalues of the other seven points can be obtained, as shown in

Table 4. Stability analysis of equilibrium points.

Equilibrium Point O		Eigenvalues		Stable Situation
	${\mathit{\lambda }}_1$	${\mathit{\lambda }}_2$	${\mathit{\lambda }}_3$
$O_1(0,0,0)$	$-C_S$	$V_{PB}-C_P$	$R_G+R_U+C_S^G-C_G^{}$	Unstable Point
$O_2(1,0,0)$	$C_S$	$V_{AB}-C_P$	$R_G+R_U-R_S^G-C_G^{}$	Unstable Point
$O_3(0,1,0)$	$-R_{SS}-C_S$	$C_P-V_{PB}$	$C_S^G-C_G^{}+C_G^G+R_{-U}$	ESS (Condition 1)
$O_4(0,0,1)$	$R_S^G+C_S^G-C_S$	$(1-{\omega }_1)V_{PB}-C_P$	$C_G^{}-R_G-R_U-C_S^G$	ESS (Condition 2)
$O_5(1,1,0)$	$R_{SS}+C_S$	$C_P-V_{AB}$	$C_G^G+R_{-U}-R_S^G-C_G^{}$	Unstable Point
$O_6(1,0,1)$	$C_S-R_S^G-C_S^G$	$(1-{\omega }_1)V_{AB}-C_P$	$R_S^G+C_G^{}-R_G-R_U$	ESS (Condition 3)
$O_7(0,1,1)$	$R_S^G+C_S^G-R_{SS}-C_S$	$C_P-(1-{\omega }_1)V_{PB}$	$-(C_S^G-C_G^{})-C_G^G-R_{-U}$	ESS (Condition 4)
$O_8(1,1,1)$	$R_{SS}+C_S-R_S^G-C_S^G$	$C_P-(1-{\omega }_1)V_{AB}$	$R_S^G+C_G^{}-C_G^G-R_{-U}$	ESS (Condition 5)

.

The stability conditions for the equilibrium points in Table 4 are as follows:

$\begin{array}{l}\mathrm{Condition}1:-C_G^G-R_{-U}>C_S^G-C_G^{},\\ \mathrm{Condition}2:C_G^{}<R_G+R_U+C_S^G,R_S^G+C_S^G<C_S,(1-{\omega }_1)V_{PB}<C_P,\\ \mathrm{Condition}3:(1-{\omega }_1)V_{AB}<C_P,C_S<R_S^G+C_S^G,R_S^G+C_G^{}<R_G+R_U,\\ \mathrm{Condition}4:-C_G^G-R_{-U}<C_S^G-C_G^{},R_S^G-C_S<R_{SS}-C_S^G,C_P<(1-{\omega }_1)V_{PB},\\ \mathrm{Condition}5:-R_S^G-C_G^{}>-C_G^G-R_{-U},C_P<(1-{\omega }_1)V_{AB},R_S^G-C_S>R_{SS}-C_S^G\end{array}$.

When the eigenvalues of the Jacobian matrix are all negative, the equilibrium point is the evolutionary stability strategy (ESS) of the system. The analysis of the system stability point can be discussed by Scenarios 1, 2 and 3 as follows:

In Scenario 1: When $-C_G^G-R_{-U}>C_S^G-C_G^{}$, it means that the loss of the local government choosing to negatively respond is less than the loss of choosing to actively respond. At this point, the local government’s strategy is to respond negatively, and the system only has a stable point, $O_3(0,1,0)$.

Proof. 

When $-C_G^G-R_{-U}>C_S^G-C_G^{}$, there are $C_G^{}>R_G+R_U+C_S^G$, $R_S^G+C_G^{}>R_G+R_U$ and $R_S^G+C_G^{}>C_G^G+R_{-U}$. According to Table 4, it can be seen that Condition 1 is satisfied, while Conditions 2, 3, 4 and 5 are not satisfied. □

It can be seen from Scenario 1 that when the central government’s punishment and the negative effects of the deterioration of the situation are small, or when the local government’s punishment on green smart supply chain enterprises is small and the local government’s active response cost is large, the local government actively responds and negatively responds. The returns of all are negative, and the strategy portfolio evolution is stable at (0, 1, 0). It can be seen that if the emergency response rules and regulations of the central government are not perfect, the local governments will choose to respond negatively, which will lead to the deterioration of the situation. The central government can prevent local governments from choosing to respond negatively by increasing penalties and incentives, which will be reflected in Scenarios 2 and 3. Based on China’s governance during the COVID-19 pandemic, we can find that for local governments, the damage of poor governance is huge and irreversible. In reality, the local government does not choose to respond negatively, so the equilibrium point $O_3(0,1,0)$ in Scenario 1 has no research value.

In Scenario 2: When $-R_S^G-C_G^{}>-C_G^G-R_{-U}$ and $C_P<(1-{\omega }_1)V_{AB}$, it means that the loss of the local government choosing to negatively respond is greater than the loss of choosing to actively respond. While local government’s strategy is to respond negatively, and the public’s strategy is to panic buy, the reason for this is the lack of credibility of the local government due to its weak response, and the system may have two stable points $O_7(0,1,1)$ and $O_8(1,1,1)$. (a) If the condition $R_S^G-C_S<R_{SS}-C_S^G$ is added, the system achieves a unique stable point, $O_7(0,1,1)$; (b) If the condition $R_S^G-C_S>R_{SS}-C_S^G$ is added, the system realizes a unique stable point, $O_8(1,1,1)$.

Proof. 

When $-R_S^G-C_G^{}>-C_G^G-R_{-U}$ and $C_P<(1-{\omega }_1)V_{AB}$, there are $-C_G^G-R_{-U}<C_S^G-C_G^{}$ and $C_P<(1-{\omega }_1)V_{PB}$. According to Table 4, it can be seen that Conditions 1, 2 and 3 are not satisfied. If condition $R_S^G-C_S<R_{SS}-C_S^G$ is added, Condition 4 is satisfied; if condition $R_S^G-C_S>R_{SS}-C_S^G$ is added, Condition 5 is satisfied. □

From Scenario 2, it can be seen that when the central government’s punishment and negative effects are large and the local government’s coping cost and subsidies to green smart supply chain enterprises are small, it can effectively prevent the local government in Scenario 1 from choosing a negative coping strategy. Since the public’s perceived benefits outweigh its panic buying costs, in the stable strategy combination of Scenario 2(a) and (b), the public will choose to panic buy. Scenario 2(a) is manifested in the fact that it often occurs in the misallocation of limited resources and funds of local governments, resulting in a strategic combination (0, 1, 1). Scenario 2(b) is quite different from reality, when local governments and green smart supply chain enterprises choose to actively respond. According to China’s experience, the public’s panic buying has been effectively suppressed at this time. Therefore, the equilibrium point, $O_8(1,1,1)$ in Scenario 2(b) should be discarded. It can be seen that when the local government chooses to actively respond, improper allocation of its resources may still lead to the failure of governance, and increasing the degree and effectiveness of active response measures such as public opinion guidance can effectively prevent the public from panic buying. This situation will be reflected in Scenario 3.

In Scenario 3: When $(1-{\omega }_1)V_{PB}<C_P$ and $R_S^G+C_G^{}<R_G+R_U$, the local government has greater coping costs and its own credibility. At this point, the public’s strategy is not panic buying, and the system may have two stable points $O_4(0,0,1)$ and $O_6(1,0,1)$. (a) If the condition $R_S^G+C_S^G<C_S$ is added, the system only has a unique stable point $O_4(0,0,1)$; (b) If the condition $C_S<R_S^G+C_S^G$ is added, the system only has a unique stable point $O_6(1,0,1)$.

Proof. 

When $(1-{\omega }_1)V_{PB}<C_P$ and $R_S^G+C_G^{}<R_G+R_U$, there are $(1-{\omega }_1)V_{AB}<C_P$, $C_G^{}<R_G+R_U+C_S^G$ and $-C_G^G-R_{-U}<C_S^G-C_G^{}$; according to Table 4, it can be seen that Conditions 1, 4 and 5 are not satisfied, Conditions 2 and 3 need more conditions to judge; if condition $R_S^G+C_S^G<C_S$ is added, Condition 2 is satisfied; if condition $C_S<R_S^G+C_S^G$ is added, Condition 3 is satisfied. □

It can be seen from Scenario 3 that when the local government effectively responds, the sum of central government incentives and positive utility is greater than the sum of its coping costs and subsidies to green smart supply chain enterprises. At this time, if the local government imposes more illegal penalties and positive response subsidies for green smart supply chain enterprises, the strategy portfolio evolution will be stable at (1,0,1). If the local government’s illegal penalties and active response subsidies for green smart supply chain enterprises are small, the strategy portfolio evolution will be stable at (0,0,1). Local governments need to ensure that the sum of aggressive subsidies and illegal penalties is strictly greater than their coping costs to avoid a stable strategy mix of (0,0,1).

To sum up, $O_4(0,0,1)$, $O_6(1,0,1)$, and $O_7(0,1,1)$ are effective equilibrium points for the three-way evolutionary game system. However, the evolution strategy combination $O_6(1,0,1)$ is an ideal equilibrium point.

5. Numerical Simulations

In order to visually observe the dynamic evolution process of the tripartite strategy, this paper used MATLABR2020b to simulate the dynamic evolution trajectory from the steady state to the ideal state, analyzed the influence of key parameters on the game evolution results of all subjects, and verified the validity of the evolutionary stability analysis. Using reference [27], the choice of the initial strategy selected in this paper was $x=0.5,y=0.5,z=0.5$.

This section refers to the numerical simulation analysis ideas in Ref. [46]; it is worth noting that the numerical simulations such as sensitivity analysis in this study are only graphical descriptions of our model, and the source of the initial values has no influence on the conclusions of this study.

5.1. Effects of Parameter Changes on Evolutionary Stable Strategy Combinations

5.1.1. Transformation from Steady State $O_4(0,0,1)$ to Ideal Steady State $O_6(1,0,1)$ and Sensitivity Analysis of Related Parameters

The parameters are set as follows when Scenario 3(a) is satisfied (the parameter satisfies the $O_4$ equilibrium point condition):$R_S^G=3.5,C_S^G=6,R_{SS}=3,V_{AB}=6,V_{PB}=8,C_S=10$ $C_G^{}=15,{\omega }_1=0.6,C_P=5,C_G^G=10,R_U=12,$ $R_{-U}=15,R_G=9$. The initial parameter settings satisfy the following three conditions mentioned in Scenario 3(a): $(1-{\omega }_1)V_{PB}<C_P$, $R_S^G+C_G^{}<R_G+R_U$ and $R_S^G+C_S^G<C_S$. Its stabilization condition from the equilibrium condition of Scenario 3(a) to the ideal equilibrium point can be achieved by adjusting the parameters. (1) Considering the effect of $R_S^G$, realizing the transition from $O_4(0,0,1)$ to $O_6(1,0,1)$, and studying the effect of $R_S^G$ on the evolution of each subject’s strategy, at this point, keeping the other parameters constant and letting $R_S^G=\left\{3.5,5.5:8\right\}$, we obtain Figure 5. (2) Considering the effect of $C_S^G$, realizing the transition from $O_4(0,0,1)$ to $O_6(1,0,1)$, and studying the effect of $C_S^G$ on the evolution of each subject’s strategy, at this point, keeping the other parameters constant and letting $C_S^G=\left\{6,6.6,8\right\}$, we obtain Figure 6.

As can be seen from Table 4, from satisfying Condition 2 to satisfying Condition 3, $R_S^G\uparrow$ or $C_S^G\uparrow$ can be transformed from stable state $O_4(0,0,1)$ to ideal stable state $O_6(1,0,1)$, and the evolutionary stability strategy of green smart supply chain enterprises is from x = 0 to x = 1, as shown in Figure 5 and Figure 6.

It is worth noting that the meanings of the abbreviations in the graphs are as follows: SSCE is the abbreviation for green smart supply chain enterprises, and lg is the abbreviation for local governments. The meanings in Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14 are the same.

From Figure 5, it can be seen that the low subsidy given by the local government to green smart supply chain enterprises will cause them to choose to respond negatively, while the lack of relief from high pollution prevention funds will also inhibit them from choosing to respond positively. With the increase in subsidies for positive responses, the strategy of green smart supply chain enterprises will change from passive response to active response, and at the same time, it can speed up the evolution of their choice to the actively respond strategy, prompting green smart supply chain enterprises to actively respond in the early stage of the COVID-19 pandemic. However, the excessive subsidies have caused fluctuations in the strategies of local governments, and the decisions of supply chain enterprises change with those of the local governments. In reality, in order to effectively manage the problems arising from the COVID-19 pandemic, local governments often need to take various emergency measures, and excessive financial subsidies will lead to high fiscal deficits of local governments, making it difficult to make decisions that are conducive to epidemic prevention and control due to financial pressure. For relaxed supervision, as the local government’s response weakens, some green smart supply chain enterprises have the opportunity to speculate and change their response measures, leading to fluctuations in the strategies of green smart supply chain enterprises. Meanwhile, it further demonstrates the influence of $R_S^G$ in Propositions 1 and 5 on the strategies of local governments and green smart supply chain enterprises. We can also find that changes in local government subsidies have a smaller impact on the public’s strategies, which is inconsistent with the conclusion of Proposition 3. However, for Propositions 2, 4, and 6, we know that the strategies between green smart supply chain enterprises, the public and the other government will affect each other. Therefore, changes in local government subsidies will indirectly affect the public’s strategy. The following parameter analysis still has the same conclusion and will not be repeated.

It can be seen from Figure 6 that the lower illegal punishment by the local government will also cause green smart supply chain enterprises to choose to respond negatively. With the increase in illegal punishment, green smart supply chain enterprises will choose to actively respond, and the evolution speed will increase. It can be seen that the response of green smart supply chain enterprises to punishment is positive; punishment is not the ultimate goal of the local government, the government’s expected goal is to mobilize the enthusiasm of green smart supply chain enterprises and the public. However, too mild punishment may worsen the situation and cause deadweight loss of social welfare, while excessive punishment will lead to the inaction of green smart supply chain enterprises, resulting in an insufficient supply of market necessities. It can be seen that local governments can accurately grasp the thresholds of punishment and subsidy in different periods, and they can achieve better governance effects in the process of emergency management.

5.1.2. Transformation from Steady State $O_7(0,1,1)$ to Ideal Steady State $O_6(1,0,1)$ and Sensitivity Analysis of Related Parameters

The parameters are set as follows when Scenario 2(a) is satisfied (the parameter satisfies the $O_7$ equilibrium point condition):$R_S^G=6,C_S^G=6,R_{SS}=3,V_{AB}=5.2,V_{PB}=8,C_S=10$ $C_G^{}=4,{\omega }_1=0.2,C_P=5,C_G^G=10,R_U=12,R_{-U}=15,R_G=9$. The initial parameter settings satisfy the following three conditions mentioned in Scenario 2(a): $-R_S^G-C_G^{}>-C_G^G-R_{-U}$, $C_P<(1-{\omega }_1)V_{AB}$ and $R_S^G-C_S<R_{SS}-C_S^G$. Its stabilization condition from the equilibrium condition of Scenario 2(a) to the ideal equilibrium point can be achieved by adjusting the parameters. (1) Considering the effect of $C_G^{}$ and ${\omega }_1$, realizing the transition from $O_7(0,1,1)$ to $O_6(1,0,1)$, and studying the effect of $C_G^{}$ and ${\omega }_1$ on the evolution of each subject’s strategy, at this point, keeping the other parameters constant and letting $C_G^{}=\left\{4,8,15\right\}:{\omega }_1=\left\{0.2,0.39,0.6\right\}$, we obtain Figure 7. (2) Considering the effect of $R_{SS}$ and $V_{PB}$, realizing the transition from $O_7(0,1,1)$ to $O_6(1,0,1)$, and studying the effect of $R_{SS}$ and $V_{PB}$ on the evolution of each subject’s strategy, at this point, keeping the other parameters constant and letting $R_{SS}=\left\{3,2,1\right\}:V_{PB}=\left\{8,6,5.5\right\}$, we obtain Figure 8.

As can be seen from Table 4, from satisfying Condition 4 to satisfying Condition 3, $C_G^{}\uparrow$ and ${\omega }_1\uparrow$ or $R_{SS}\downarrow$ and $V_{PB}\downarrow$ can be transformed from stable state $O_7(0,1,1)$ to ideal stable state $O_6(1,0,1)$, the evolutionary stability strategy of green smart supply chain enterprises is from x=0 to x=1, and the evolutionary stability strategy of the public is from y = 1 to y = 0, as shown in Figure 7 and Figure 8.

From the evolution process in Figure 7, it can be seen that the improper allocation of effective resources of local governments will also lead to the deterioration of the situation. For example, compared with Scenario 2(a), although the subsidies of green smart supply chain enterprises have increased, less investment in public opinion guidance and illegal supervision causes the public to choose panic buying and green smart supply chain enterprises to choose negative responses. This is because the local government took a fluke, reduced the cost of the response and relaxed the supervision of the vicious evolution of the situation, which eventually led to the lack of local government credibility and the increase in the expectation of illegal behavior of green smart supply chain enterprises. However, with the increase in the local government’s response cost input and intensity, the strategy portfolio evolution is stable at (1,0,1). In addition, the rising cost of local governments can accelerate the evolution of green smart supply chain enterprises choosing to actively respond and the public not choosing panic buying, further demonstrating the impact of $C_G^{}$ and ${\omega }_1$ in Propositions 3 and 5 on the strategies of the public and the local government.

It can be seen from Figure 8 that the higher illegal income of green smart supply chain enterprises will cause the public to have higher perceived value, which will lead to panic buying by the public and green smart supply chain enterprises choosing to respond negatively. With the reduction in illegal income of green smart supply chain enterprises, the time for green smart supply chain enterprises to choose to actively respond is shortened, which further demonstrates the influence of $R_{SS}$ and $V_{PB}$ in Propositions 1 and 3 on the strategies of green smart supply chain enterprises and the public.

5.2. Influence of $R_G$ and $C_G^G$ on Each Subject’s Evolution Strategy under Scenario 2(a), Scenario 3(a), and Scenario 3(b)

The parameters are set as follows when Scenario 3(b) is satisfied (the parameter satisfies the $O_6$ equilibrium point condition):$R_S^G=5.5,C_S^G=6,R_{SS}=3,V_{AB}=6,V_{PB}=8,C_S=10$ $C_G^{}=15,{\omega }_1=0.6,C_P=5,C_G^G=10,R_U=12,R_{-U}=15,R_G=5$. We get Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14.

From Figure 9 and Figure 10, the larger central government incentive and punishment under Scenario 2(a) does not achieve a shift in the strategy mix. From Figure 11 and Figure 12, it shows that in Scenario 3(a), the increase in the central government’s incentive and punishment changes the equilibrium point $O_7(0,1,1)$ to the ideal equilibrium point $O_6(1,0,1)$, but the central government needs to set larger incentives and punishments. From Figure 13 and Figure 14, it can be seen that in an ideal equilibrium state, lower incentives from the central government will not only cause fluctuations in the strategies of local governments but also indirectly affect the evolution strategies of green smart supply chain enterprises. However, as the incentive increases, the strategy of the game subject tends to be stable, which further demonstrates the influence of $R_G$ in Proposition 5 on the local government strategy. It is impossible for the central government to stabilize the strategy combination by aggravating the punishment under the lower incentive. On the contrary, the larger punishment increases the range of strategy fluctuation. It can be seen that the central government can reduce the financial pressure of local governments and prevent the extension of regional events or the adverse effects of events by increasing incentives, but it is impossible to achieve effective governance by replacing incentives with punishments.

6. Conclusions and Suggestions

Drawing on the experience of effective governance in China during the COVID-19 epidemic, this study constructed a subject evolutionary game model of local governments, the public, and green smart supply chain enterprises under the central government’s incentives and punishments. This paper not only analyzed the strategic stability of individual players but also analyzed the entire system stability, explored how to prevent the public from opting for panic buying and the illegal behavior of green smart supply chains enterprises during the COVID-19 pandemic, and ensured the stability of the supply, price of necessities and preventing pollution of the production process. This paper also used MATLAB2020b software to conduct numerical simulations to explore the influence of main parameters on the decision making of each subject and the system. The path from other equilibrium states to the ideal equilibrium state further verified the proposition of stability analysis. The specific conclusions were as follows:

6.1. Conclusions

1. We find that the strategies of green smart supply chain enterprises, the public, and local governments will affect each other. First, the probability that the public choose to panic buy will decrease as the probability that local governments and green smart supply chain enterprises choose to actively respond increases. Second, the probability that green smart supply chain enterprises choose to actively respond is positively correlated with the probability that local governments choose to actively respond. This is because during the evolution of events, the probability of a game subject’s strategy choice reflects its tendency to act, and this tendency to act is transmitted to other participating subjects, thus influencing the direction of evolution. Therefore, increasing the probability of local government response can lead to an evolutionary direction where the public chooses not to panic buy and green smart supply chain enterprises choose to ensure supply and demand balance and increase pollution governance in the production process.

2. From the stability analysis of the strategies of individual subjects, we find that the higher response costs and pollution treatment costs of green smart supply chain enterprises inhibit the probability that they will choose to respond aggressively. However, local governments can increase the probability of green smart supply chain enterprises choosing to actively respond by increasing subsidies and penalties and reducing their illegal gains. In reality, due to the uncertainty and urgency of emergencies, the cost for green smart supply chain enterprises to actively respond is often very high. As a “rational person”, it is difficult for them to actively manage the productive pollution and ensure the balance of supply and demand of essential goods; at this time, the local government increases subsidies and penalties by reducing the response cost of green smart supply chain enterprises and increasing the illegal cost of green smart supply chain enterprises to promote active response. However, for local governments, the occurrence of the COVID-19 pandemic will often lead to large fiscal deficits, and large subsidies will cause instability in their own strategies, causing fluctuations in the strategies of green smart supply chain enterprises. Excessive penalties by local governments can lead to the inaction of green smart supply chain enterprises. It can be seen that local governments can accurately grasp the threshold of penalties and subsidies in different periods and can achieve better governance results in the emergency management process. For the public, the local government can improve its own credibility by increasing its input in the supervision and guidance of public opinion on emergencies so that the public believes that the local government can effectively handle emergencies and reduce the possibility of panic buying by the public.

3. From the stability analysis of the system equilibrium, our study yields three effective combinations of evolutionary strategies, among which an ideal combination of evolutionary strategies exists. We find that for local governments, both costs and benefits can motivate them to respond positively. For example, higher penalties from the central government make the costs of local governments to respond negatively greater than their costs to respond positively, and higher subsidies from the central government make the benefits of local governments to respond positively greater than their costs to respond positively. This is because, for the sake of maximum benefit, local governments have the least to lose when they choose to respond positively. When the local government chooses to respond positively, the smaller subsidies and penalties and higher illegal gains of the local government to the green smart supply chain enterprises will also lead the green smart supply chain enterprises to choose to respond negatively, because there are higher opportunities for illegal gains and speculation of the green smart supply chain enterprises, and also the subsidies of the local government cannot cover the cost of their response. If the local government has low investment in the supervision and guidance of public opinion, etc., while the higher illegal income of green smart supply chain enterprises increases the perceived value of the public, it will cause the public to choose panic buying. At this time, the combination of green smart supply chain enterprises, the public and the local government evolutionary strategy is stable (negative response, panic buying, positive response). If the local government invests more in the supervision and guidance of public opinion and other aspects, it can effectively improve its own credibility to prevent the public from choosing panic buying; at this time, the combination of green smart supply chain enterprises, the public and the local government evolutionary strategy is also stable (negative response, no panic buying, positive response). It is evident that improper incentives and penalties by local governments and the misallocation of limited resources can worsen the situation.

Among the non-ideal evolutionary strategy combinations, we find four paths to reach the ideal evolutionary strategy combination, and there are multiple transformation paths on the same equilibrium point transition. For example, there are two paths from the steady state $O_4(0,0,1)$ to the ideal steady state $O_6(1,0,1)$, which the local government can achieve by increasing either $R_S^G$ or $C_S^G$. It can be seen that when there is an evolutionary result that green smart supply chain enterprises respond negatively, local governments can prompt green smart supply chain enterprises to choose to respond positively by increasing subsidies and penalties, and they can finally achieve the governance of the deterioration of the situation. There are also two paths from the steady state $O_7(0,1,1)$ to the ideal steady state $O_6(1,0,1)$, which can be achieved by the local government by increasing $C_G^{}$ and ${\omega }_1$ or decreasing $R_{SS}$ and $V_{PB}$. It can be seen that when there is an evolutionary result that green smart supply chain enterprises respond passively and the public chooses panic buying, local governments can change their strategic choices and finally achieve the governance of the deterioration of the situation by increasing the investment in the supervision and guidance of public opinion and reducing the illegal gains of green smart supply chain enterprises.

4. Our findings are that under non-ideal strategy combinations, it is difficult for the central government’s incentive and punishment mechanism to realize the transformation of the strategy combination; even if a shift in strategy mix is achieved, the shift is costly. It can be seen that at this time, it is difficult for the central government to indirectly achieve the governance of the deterioration of the event through the local government. This is because once there has been the deterioration of the unexpected event, for example, the public chooses panic buying, enterprises choose to reduce pollution treatment and increase the price of products, there is a continuous game process between the game subjects in the process of the governance of the event, which increases the difficulty of the governance of the event. Under the ideal combination of strategies, the central government’s increase in incentives can increase the probability that local governments choose to actively respond and prevent fluctuations in the stability of the game strategy. However, when the central government’s incentive is small, it is impossible to stabilize the strategy combination by increasing the punishment instead of the incentive. On the contrary, the larger penalty increased the amplitude of the strategy fluctuation. Therefore, the central government cannot achieve effective governance by replacing incentives with penalties.

6.2. Suggestions

Based on the above research, this paper proposes the following recommendations from four perspectives: strategic interaction among evolving subjects, digital and intelligent construction, local government governance and central government governance, respectively.

1. In the early days of the COVID-19 pandemic, local governments need to strengthen interactions with the public and enterprises, send them a signal that they can govern effectively and actively, build trust with them, and provide evidence-based prevention and response methods so that the public and enterprises can control their own behavior according to government measures rather than local governments taking countermeasures quietly. It is easy to cause panic among the public and enterprises, causing the situation to worsen. Local governments must convey and take measures to require enterprises to do a good job of ecological and environmental protection during the period of supply assurance and to solidify the main responsibility of enterprises, which should not make a choice between protecting the environment and ensuring supply, and ensuring supply while preventing and controlling environmental pollution. For the public, they need to be rational, because panic buying will not bring benefits to themselves but will lead to shortages of necessities and price fluctuations, resulting in loss of social benefits and self-interest.

2. Local governments and green smart supply chain enterprises need to focus on their own digital and intelligent level construction. For green smart supply chain enterprises, through intelligence and digitization, they can quickly respond to the market and reduce response costs and the pollution control cost of the production process. Through intelligent and digital applications, local governments can solve the information barrier with green smart supply chain enterprises, realize comprehensive and seamless supervision, reduce their own response costs and capital pressure, and realize multiple means to collaboratively supervise the pollution situation of enterprises.

3. During the COVID-19 pandemic, when setting the incentive and punishment mechanism, local governments must meet the condition that the sum of subsidies and punishments for enterprises is greater than their costs. Due to the different situations in different regions, they need to be based on their own circumstances in the process of incident governance, effectively allocate scarce resources and implement incentive and punishment mechanisms under limited resources, avoid governance in the form of punishment instead of incentive, and balance the interests of participating subjects to achieve long-term effective governance of events. How to effectively allocate resources by local governments has become an important condition for effectively controlling the public’s panic buying and illegal corporate behaviors. Local governments must also take into account the rational use of subsidies, punishment and supervision. For example, when the local government is under great financial pressure, punishment can be used as an effective means to prevent green smart supply chain enterprises from choosing to respond negatively, but lax supervision will also weaken the punishment. At this time, the means of punishment and supervision need to exist at the same time. Local governments must also always pay attention to the strategic choices of the public and green smart supply chain enterprises. Once the strategic combination deviates from the ideal state, the local government needs to adjust according to the situation to stabilize the balanced strategy combination in the ideal equilibrium state. In response to public panic buying during the COVID-19 pandemic, local governments should pay close attention to public opinion information and changes in the supply, demand and prices of necessities. For some emerging and potential problems, they should be stopped in a timely manner, and they should pay attention to the construction of their own trust system and increase the trust of the public and enterprises in the local government.

4. The central government should focus on the construction of an emergency response system to ensure that there is an institutional basis for emergency material reserves, emergency production, distribution, punishment and compensation in the management of emergencies such as the COVID-19 pandemic, and ensure that local governments are sufficient resources. When emergencies occur, the central government can set up special funds to help local governments allocate special resources and adjust the unreasonable allocation of local governments, but the use of punishment means requires the support of incentive means, and they need to ultimately realize the rational use of incentive and punishment mechanisms. The central government should strengthen the implementation of accountability, recovery mechanisms, mobilize local governments to monitor the enthusiasm, and improve the environmental awareness of grassroots-responsible subjects so that local officials do not have a fluke mentality and dare not act across the line, which could be a way to reduce the cost of inspectors.

There are two limitations of this study. First, this study is applicable to countries with a high modernization level, whose enterprises have a higher degree of digital and intelligent technology application, and its reference significance is weak for less developed countries. Secondly, the research in this paper is aimed at pure strategic equilibrium under asymmetric information. In the future, the information barrier between government and enterprises will be reduced, and the strategic equilibrium situation under symmetric information also needs to be studied. Moreover, in recent years, emergencies have occurred frequently around the world, and the degree of impact on less developed countries, which are not highly digitalized and intelligent, is huge, and it is difficult for them to reduce the impact of emergencies by using new generation technologies. Thus, it is important to further study the governance of emergencies in less developed countries. The above will be our next research direction.