Abstract

Considering the government reward and punishment mechanism and the collusion behavior between third-party testing agencies and drug enterprises, based on the coregulation information platform, this paper constructs an evolutionary game model of coregulation supervision, which involves the participation of local government, drug enterprises, and third-party testing agencies. The stable equilibrium points of each participant’s strategic choices are solved. The stability of the strategic combination is analyzed by Lyapunov’s first method, and MATLAB 2020b is used for simulation analysis to verify the influence of each decision variable on different players’ strategic choices. The results show that, firstly, the government-increased awards and penalties will promote the integrity of drug enterprises and noncollusion of third-party testing agencies, but it is not conducive to strict performance of regulatory responsibilities by the local government. Secondly, the provision of real drug test reports by third-party testing agencies to the coregulation information platform can supervise drug enterprises and restrict local government to perform its duty. Thirdly, the central government’s punishment to the local government’s dereliction of duty is significant to enhancing the robustness of drug enterprises’ integrity operation. Furthermore, reasonably setting rewards and punishments and perfecting the coregulation information platform will help form a coregulation pattern of government supervision, self-discipline of drug enterprises, and social supervision. Finally, drug quality is highly related to whether drug enterprises operate with integrity. Standardizing coregulation supervision of drug enterprises’ integrity operation is the key to ensuring the safety of the source of drug quality. Therefore, this paper enriches and expands the theoretical basis of the coregulation supervision of drug enterprises’ integrity operation and proposes corresponding countermeasures and suggestions.

1. Introduction

In recent years, drug enterprises’ integrity operation affects drug quality and safety, which is related to people’s life and health, economic development, and social stability. The World Health Organization (WHO) recommends that government be responsible for establishing national medicine regulatory agencies (MRA), clarify their responsibilities, exert effective market control capabilities, and establish a monitoring and evaluation mechanism. The US Food and Drug Administration (FDA) focuses on cultivating talents and setting up regulatory scientific institutions to effectively fill the knowledge gaps in the research and development of drugs, reduce the uncertainty of regulatory decision-making, and ensure that drug enterprises produce high-quality drugs to meet the needs of patients and the market. The European Medicines Agency (EMA) has established a relatively complete drug risk supervision system for a long time to ensure that the public can use drugs safely and effectively. The Pharmaceuticals and Medical Devices Agency (PMDA) of Japan has gradually attached importance to the development of regulatory science, giving full play to its functions in drug testing, new drug applications, inspection and conformity assessment of drug enterprises management practices, and so on.

Over the years, India has learned from the experience of Western countries in drug supervision and has continuously adjusted its management structure. It has established a central drug management agency and a central drug standard control organization to be fully responsible for drug standards and inspections and provide drug enterprises with reference standards for various drugs. After years of practice, Australia has gradually established a relatively complete drug regulatory system. Through the joint consultation of industry members, the opinions and suggestions of member enterprises are reflected on the government in order to exert influence on government decision-making. The drug administration shall perform supervision and management functions within the scope prescribed by law and implement appropriate reward and punishment mechanisms. The Chinese government also has very strict regulatory requirements for drug enterprises. In order to promote scientific drug supervision and continue to build a healthy China, it has carried out international exchanges and technology introduction and established a scientific and reasonable drug enterprises supervision system based on national conditions (the above information comes from the official website of the World Health Organization, the European Union, and national medicine regulatory agencies of countries, such as FDA, EMA, PMDA, CIPL, TGA, and NMPA).

Therefore, this paper considers the government reward and punishment mechanism [1], based on the coregulation information platform, and constructs an evolutionary game model [2] involving the participation of local government, drug enterprises, and third-party testing agencies. Evolutionary game theory [3] is an effective method to study the dynamic changes of the strategy of the subject of bounded rationality in the process of long-term repeated games under the condition of asymmetric information [4]. Its strategic choice is continuously adjusted over time [5]. By the stability theorem of replication dynamic system and Lyapunov’s first method, the stability of the strategic combination and the influence of changes in decision variables on strategic choice are analyzed [6], which are aiming to solve the following three problems: at first, how does the reward and punishment mechanism affect the strategic choices of three participants, then how to play the role in the coregulation information platform to promote the coregulation supervision, and finally, how does the participation of local government and third-party testing agencies affect the strategic choices of drug enterprises.

The remaining parts of this paper are arranged as follows: Section 2 combs and reviews the relevant literature; Section 3 makes hypotheses and constructs an evolutionary game model which involves local government, drug enterprises, and third-party testing agencies; Section 4 analyzes the stability of the strategic choice of the three participants; Section 5 analyzes the stability of strategic combination according to Lyapunov’s first method; Section 6 is the simulation analysis with MATLAB 2020b; Section 7 discusses and outlines related suggestions; and Section 8 provides the conclusions.

2. Relevant Literature

Nonintegrity operation of drug enterprises refers to the fact that the procurement, production, inspection, storage, and sales of drugs do not meet GSP management standards, resulting in low-quality drugs. After drugs are marketed, strong data-driven methods are needed to support and enhance regulatory decision-making [7]; once a drug quality accident occurs, the scope of risk exposure is difficult to control [8]. The outbreak of COVID-19 in 2019 has aroused widespread attention from various drug enterprises on the development of new effective drugs [9] and has strengthened the key performance of the rapid development and survival of drug enterprises [10]. Therefore, the issue of drug quality and safety has attracted widespread attention from all walks of life. In recent years, many scholars have done a lot of research work in drug enterprises operation, government supervision, and third-party participation, which have provided a preliminary basis for the research of this paper.

The motivation for nonintegrity operation and lower production standards of drug enterprises is to seek greater benefits [11]; the participation of third-party testing agencies in collusion makes it more difficult to contain, which seriously affects drug quality and safety. The problems and potential hidden dangers in the field of drug quality and safety cannot be underestimated [12]. Regulatory channels are becoming more and more extensive [13], but the cost of surprise inspections is high, which is not conducive to the self-discipline of enterprises [14]. Compared with other national drug safety monitoring systems, China currently lacks postmarketing supervision of drugs [15], and drug enterprises have failed to fulfill their social responsibilities [16]. The establishment of a digital information platform is the future trend of drug enterprises supervision [17], and the government should play a more active role in further optimizing the decision-making process [18]. Economic incentives can promote the integrity behavior of drug enterprises [19], and the government reward and punishment mechanism can effectively promote the active operation of enterprises [20], give full play to market vitality, and maintain good market order.

The recorded feedback of test results from participants outside the government can play a key role in strengthening and maintaining a country’s regulatory system [21]. Third-party participation has a positive role in promoting efficient government supervision [22] and is conducive to standardizing the behavior of drug enterprises, achieving regulatory goals [23], and advancing the quality supervision mechanism technically and objectively. However, there will be a risk of collusion, and collusive behavior will produce negative effects [24]. Establishing a collusion fine mechanism can play a deterrent effect [25], and strengthening information disclosure and perfecting reputation mechanisms can curb collusive behavior [26] and improve the efficiency of supervision.

In summary, the existing literature mainly discusses the role of local government, drug enterprises, and third-party testing agencies in drug quality supervision from the perspective of a single player. There is still a lack of consideration of three participants from the perspective of coregulation supervision. In addition, the influence of third-party testing agencies’ collusion behavior and government reward and punishment mechanism on the different strategic choices of each participant in the coregulation supervision is not taken into account.

Therefore, the research contributions of this paper have the following three points. Firstly, considering the government reward and punishment mechanism, based on the coregulation information platform, this paper builds a game model of tripartite participation involving local government, drug enterprises, and third-party testing agencies; secondly, considering the influence of the collusion and noncollusion of third-party testing agencies on the strategic choices of other participants, the evolutionary stable strategic combination under different conditions is solved; finally, the influence of each decision variable on the strategic choices of the three participants is solved and analyzed. And through MATLAB 2020b simulation analysis, the validity of the model is verified, and countermeasures and suggestions are put forward for coregulation supervision.

3. Model Hypotheses and Construction

This paper chooses the evolutionary game as the research method because it abandons the assumption of complete rationality. A research object is a certain group that changes over time. It can explain the dynamic process of the evolution of each stakeholder’s strategic choice and explain why this state has been reached and how to reach it. Economists often use evolutionary game theory to analyze the influencing factors and the formation process of social habits, norms, or institutions. Of course, when building a game model, the assumptions made for various relationships often deviate slightly from reality and need to be considered repeatedly, not only to meet the actual situation but also to ensure the feasibility of the model. Therefore, after repeated discussion, the evolutionary game structure relationship involving local government, drug enterprises, and third-party testing agencies is shown in Figure 1.

Figure 1 

Three-party evolutionary game structure relationship.

Figure 1 is the structural relationship diagram that shows the relationship among the local government, drug enterprises, and third-party testing agencies based on the coregulation information platform under the government reward and punishment mechanism.

3.1. Model Hypotheses

This paper considers the benefits of different strategies of the local government, drug enterprises, and third-party testing agencies under coregulation supervision. In order to solve the evolutionary stable strategic combination in different situations and analyze the influence of each decision variable on the strategic choices of the three participants, the following hypotheses are made: H1: the local government is participant 1, the drug enterprise is participant 2, and the third-party testing agency is participant 3. The three players are bounded rational participants. The strategic choice space of the local government is (strictly supervise, loosely supervise), chooses with the probability of , and chooses with the probability of , . The strategic choice space of drug enterprises is (integrity operate, nonintegrity operate), chooses with the probability of , and chooses with the probability of , . The strategic choice space of the third-party testing agencies is (noncollusion, collusion), chooses with the probability of , and chooses with the probability of , . H2: the income from the operation of drug enterprises is , the cost of integrity operation of drug enterprises is , and the cost of nonintegrity operation of drug enterprises is (). When drug enterprises do not operate with integrity, they will seek collusion with the third-party testing agencies to pass the test; the cost of seeking collusion is . H3: the cost of strict supervision by the local government is , and the cost of loose supervision is , . When the local government strictly supervises, the drug enterprises that operate without integrity will be fined, and the fine is . The third-party testing agencies that participate in collusion will also be fined, and the fine is . Third-party testing agencies that do not participate in collusion will be rewarded, and the reward is . H4: the integrity operation of drug enterprises is conducive to the life and health of the public and the stable development of the social economy, which brings social benefits to the local government; let the social benefits be . When drug enterprises operate with nonintegrity but third-party testing agencies do not participate in the collusion, the local government with loose supervision will be punished by the central government (such as administrative removal and administrative accountability); let the penalty be . H5: the income of the third-party testing agencies is , and their detection cost is . When drug enterprises operate without integrity, if the third-party testing agencies do not participate in collusion, they will issue real test reports; if third-party testing agencies choose collusion, they need to forge test records and issue false test reports. Let the speculative cost of collusion be ().

The parameters and descriptions of this paper are shown in Table 1.

3.2. Model Construction

Based on the above hypotheses, this paper constructs a three-party mixed strategy game matrix for local government, drug enterprises, and third-party testing agencies, as shown in Table 2.

4. Analysis of the Strategic Choice Stability

4.1. The Local Government’s Strategic Choice Stability

The expected benefit of local government choosing the “strict supervision” strategy is

The expected benefit of local government choosing the “loose supervision” strategy is

The replicated dynamic equation and the first derivative of the local government’s strategic choice are

According to the stability theorem of differential equations, if the probability of the local government choosing the “strict supervision” strategy is to be in a stable state, the following conditions must be met: and .

Proposition 1. When , the local government’s stabilization strategy is “strict supervision.” When , its stabilization strategy is “loose supervision.” When , we are unable to determine its stabilization strategy. The threshold is .

Proof. Make , when , can be calculated. Because , is a decreasing function of . When , , , and can be calculated, so is stable. When , , , and can be calculated, so is stable. When , , and can be calculated, we are unable to determine a stable strategy.
Proposition 1 shows that if decreases, the local government’s stabilization strategy will change from loose supervision to strict supervision. Therefore, when the local government realizes that the probability of drug enterprises’ nonintegrity operation is high, in order to ensure the public health and the stability of market order, it will strictly supervise the drug enterprises.
In summary, the response function of isAccording to Proposition 1, the phase diagram of local government strategic choice is shown in Figure 2.
Figure 2 shows the phase diagram that shows the evolutionary trend of the local government’s strategy obtained by calculating the response function of the probability of the local government choosing the “strict supervision” strategy.
It can be seen from Figure 2 that the volume of is the probability that the local government chooses the “strict supervision” strategy, and the volume of is the probability that the local government chooses the “loose supervision” strategy. And,

Figure 2 

Phase diagram of the local government strategic choice.

Corollary 1. When the local government pays less additional costs for strict supervision and imposes more fines on drug enterprises, it tends more to choose the “strict supervision” strategy.

Proof. According to the probability , the first-order partial derivatives of and can be calculated:Corollary 1 shows that reducing the cost of strict supervision can increase the probability of choosing a “strict supervision” strategy; increasing the fines for nonintegrity drug enterprises can increase the possibility of strict supervision by the local government.

Corollary 2. The higher the penalties for loose supervision by local government and the more fines imposed on third-party testing agencies, the lower the probability that local government will choose the “loose supervision” strategy.

Proof. According to the probability , the first-order partial derivatives of and can be calculated:Corollary 2 shows that the greater the punishment or accountability of local government loose supervision by the central government is, the more it can restrain the behavior of local government, and the probability of local government choosing “loose supervision” strategy will be reduced. As the fines colluded by third-party testing agencies are higher, the local government is unwilling to choose the “loose supervision” strategy.

Corollary 3. When , the local government will choose the “strict supervision” strategy. When , it will choose the “loose supervision” strategy. The threshold is .

Proof. According to Proposition 1, when , can be calculated. Because , is an increasing function of . When , , , and can be calculated. When , , , and can be calculated.
Corollary 3 shows that when local government loosely supervises, it will be punished by the central government. If , it is possible to ensure that the local government chooses the “strict supervision” strategy. Therefore, the central government should increase accountability and penalties to urge the local government to actively fulfill its regulatory obligations and maintain good market order.

4.2. Drug Enterprises’ Strategic Choice Stability

The expected benefit of drug enterprises choosing the “integrity operation” strategy is

The expected benefit of drug enterprises choosing the “nonintegrity operation” strategy is

The replicated dynamic equation and the first derivative of the drug enterprises’ strategic choice are

According to the stability theorem of differential equations, if the probability of drug enterprises choosing the “integrity operation” strategy is to be in a stable state, the following conditions must be met: and .

Proposition 2. When , the drug enterprises’ stabilization strategy is “integrity operation.” When , their stabilization strategy is “nonintegrity operation.” When , unable to determine their stabilization strategy. The threshold is .

Proof. Make ; when , can be calculated. Because , is an increasing function of . When , , , and can be calculated, so is stable. When , , , and can be calculated, so is stable. When , , and can be calculated, we are unable to determine a stable strategy.
Proposition 2 shows, when increases, the stability strategy of drug enterprises changes from nonintegrity operation to integrity operation. Therefore, when the local government strictly supervises, the drug enterprises will take the initiative to conduct integrity operation to avoid being punished.
In summary, the response function of isAccording to Proposition 2, the phase diagram of drug enterprises’ strategic choice is shown in Figure 3.
Figure 3 is the phase diagram that shows the evolutionary trend of drug enterprises’ strategy obtained by calculating the response function of the probability of the drug enterprises choosing the “integrity operation” strategy.
It can be seen from Figure 3 that the volume of is the probability that the drug enterprises choose the “integrity operation” strategy, and the volume of is the probability that the drug enterprises choose the “nonintegrity operation” strategy. And,

Figure 3 

Phase diagram of drug enterprises strategic choice.

Corollary 4. The higher the penalties for nonintegrity operation of drug enterprises, the greater the probability that they operate with integrity. The higher the additional costs that drug enterprises need to pay for integrity operation, the smaller the probability that they will choose to operate with integrity.

Proof. According to the probability , the first-order partial derivatives of and can be calculated:Corollary 4 shows that punishments imposed by the local government on drug enterprises will restrict the behavior of drug enterprises. With the increase in fines for the nonintegrity operation, drug enterprises will choose the “integrity operation” strategy. When the additional cost of integrity operation of drug enterprises is greater, they will tend to choose the nonintegrity operation for economic benefits.

Corollary 5. The higher the cost for drug enterprises to seek collusion with third-party testing agencies, the lower the probability of the nonintegrity operation of the drug enterprise.

Proof. According to the probability , the first-order partial derivatives of can be calculated:Corollary 5 shows that when the cost of collusion with third-party testing agencies is greater for drug enterprises, they realize that nonintegrity operation will increase their operating costs. In order to ensure economic benefits, the probability of choosing a “nonintegrity operation” is smaller.

Corollary 6. When , drug enterprises will choose “integrity operation” strategy; when , they will choose “nonintegrity operation” strategy. The threshold is .

Proof. According to Proposition 2, when , can be calculated. Because , is an increasing function of . When , , , and can be calculated. When , , , and can be calculated.
Corollary 6 shows that when drug enterprises do not operate with integrity, they will be punished by the local government. If , it is possible to ensure that the drug enterprises choose an “integrity operation” strategy. Therefore, local government should increase the level of penalties for drug enterprises when they do not operate with integrity, to urge drug enterprises to actively conduct an operation with integrity and protect the health of people.

Corollary 7. When , drug enterprises will choose the “integrity operation” strategy; when , they will choose the “nonintegrity operation” strategy. The threshold is .

Proof. According to Proposition 2, when , can be calculated. Because , is an increasing function of . When , , , and can be calculated. When , , , and can be calculated.
Corollary 7 shows that when , in order to protect economic interests, drug enterprises will choose the “integrity operation”; when , which means that the cost of collusion by drug enterprises is small, to reduce operating costs and obtain more profits, they will choose the “nonintegrity operation.”

4.3. Third-Party Testing Agencies’ Strategic Choice Stability

The expected benefit of third-party testing agencies choosing the “noncollusion” strategy is

The expected benefit of third-party testing agencies choosing the “collusion” strategy is

The replicated dynamic equation and the first derivative of the third-party testing agencies’ strategic choice are

According to the stability theorem of differential equations, if the probability of third-party testing agencies choosing the “noncollusion” strategy is to be in a stable state, the following conditions must be met: and .

Proposition 3. When , the third-party testing agencies’ stabilization strategy is “noncollusion.” When , their stabilization strategy is “collusion.” When , we are unable to determine their stabilization strategy. The threshold is .

Proof. Make ; when , can be calculated. Because , is an increasing function of . When , , , and can be calculated, so is stable. When , , , and can be calculated, so is stable. When , , and can be calculated, we are unable to determine a stable strategy.
Proposition 3 shows that when increases, the stability strategy of third-party testing agencies changes from collusion to noncollusion. Therefore, in order to avoid being punished by the local government and get rewards for participating in the coregulation, third-party testing agencies will choose not to collude with the drug enterprises. Strict supervision by local government will promote third-party testing agencies to fulfill their social responsibilities and consciously provide true testing reports to the coregulation information platform.
In summary, the response function of isAccording to Proposition 3, the phase diagram of the third-party testing agencies’ strategic choice is shown in Figure 4.
Figure 4 is the phase diagram that shows the evolutionary trend of the third-party testing agencies’ strategy obtained by calculating the response function of the probability of the third-party testing agencies choosing the “noncollusion” strategy.
It can be seen from Figure 4 that the volume of is the probability that the third-party testing agencies choose the “noncollusion” strategy, and the volume of is the probability that the third-party testing agencies choose the “collusion” strategy. And,