The relevant bodies involved in the regulatory system for the safety of imported aquatic products in China are government agencies, importers and consumers. Government agencies are the main regulators of the safety of imported aquatic products, including customs agencies responsible for entry safety and market supervision authorities responsible for the safety of domestic market circulation; Importers are the key entities responsible for the safety of imported aquatic products and the main duty bearers, subject to the supervision of government agencies and consumers, as well as self-monitoring to ensure the safety of the aquatic products they sell; Except for the direct demanders of imported aquatic products, consumers are the direct bearers of the safety. Also, they play a role in monitoring the safety of the products. Government agencies, importers and consumers form a constraint relationship (Figure 1) and are jointly responsible for the safety of imported aquatic products. The following basic assumptions are made based on the safety monitoring behavior of the three main actors of imported aquatic products in China.

Government agencies, importers and consumers are all rational agents. In this paper, we assume that the principle of maximizing the benefits of government agencies is to save the cost of regulation and reduce the loss of reputation. We do not directly assume that social welfare is maximized because there are many evaluation indicators of social welfare maximization, and this paper mainly discusses from the perspective of regulation. Therefore, government agencies choose two strategies: strict regulation or loose regulation. Besides, we assume that importers choose two strategies of regulated imports or unregulated imports according to the profit maximization principle, while consumers choose two strategies of reporting or not reporting according to the utility maximization principle. The utility maximization principle here specifically means that consumers decide on the optimal strategy by comparing the health loss, the cost of reporting, and the compensation from the unsafe event.

The two-by-two static game models between government agencies and importers, and between importers and consumers are available in the Supplementary Material. The following section constructs a three-way sequential dynamic game model between importers, government agencies and consumers, which are the main actors involved in the regulation of imported aquatic products. It is assumed that the level of regulation of imported aquatic products by government agencies is given, which is in line with the current level of regulation of imported aquatic products by government agencies in China. The three-way sequential dynamic game model is used to analyze the strategic choices of importers, government agencies and consumers. The sequence is as follows: firstly, importers decide to choose whether regulated imports or unregulated imports; secondly, government agencies decide whether to strictly regulate or not in response to the choice of importers; and finally, consumers choose to report or not. The game tree is used to demonstrate the specific decision process in Figure 2, where the importer corresponds to I, the government agency to G and the consumer to C.

The game tree shown in Figure 2 has eight combinatorial strategy choices, denoted by nodes ①-⑧. The vector of benefits at each node is expressed as importer, government agency, consumer, as shown in Table 1. R is the additional revenue gained by the importer for unregulated imports, C 1 is the regulatory cost saved by the government agency for loose regulation, C 2 is the import cost saved by the importer for unregulated imports, C 3 is the cost saved by the consumer for not reporting, U 1 is the loss of reputation of the government agency for unsafe imports, U 2 is the future revenue lost by the importer for unsafe imported aquatic products, U 3 is the physical and mental health loss of the consumer for unsafe imported aquatic products, F 1 is the fine imposed by the government agency for unregulated imports of importer, F 2 is the compensation gained by the consumer for reporting when the importer adopts unregulated imports.

The equilibrium strategies of the three-party game model are analyzed below using the inverse induction method. First, the analysis starts with the consumer strategy, comparing the consumer gains at each node in Table 1 according to the utility maximization principle. Choose ② among ① and ②, ④ among ③ and ④, ⑥ among ⑤ and ⑥, and compare ⑦ and ⑧. If F 2 > C 3 then choose ⑦, otherwise choose ⑧. Then, compare the government agency gains for each node in Table 1. Choose ④ from ② and ④, compare ⑥ and ⑦ or ⑥ and ⑧, and choose ⑥ if F 1 > C 1 − U 1 , otherwise choose ⑦ or ⑧. Finally, compare the gains to importers at each node in Table 1. Compare ④ and ⑥ and select ⑥ if > U 2 − C 2 + F 1 , otherwise select ④. Compare ④ and ⑦, if R > U 2 − C 2 + F 2 then choose ⑦, otherwise choose ④. Comparing ④ and ⑧, if R > U 2 − C 2 then choose ⑧, otherwise choose ④. The refined Nash equilibrium for the subgame of the three-way sequential game is thus derived as follows.

(1) When F 1 > C 1 − U 1 and R > U 2 − C 2 + F 1 ,⑥ is chosen, the three-way game strategy is for importers to choose regulated imports, government agencies to regulate strictly and consumers not to report. The results show that government agencies choose strict regulation when the benefit of fines gained from strict regulation is greater than the difference between the saved cost of regulation and the loss of reputation from loose regulation; Importers choose unregulated imports when the additional benefits and import cost savings gained from unregulated imports are greater than the future loss of revenue and fines to be paid to government agencies.

In conclusion, consumers choose to report when the cost savings from non-reporting decreases; consumers choose to report when the compensation they receive for reporting increases; government agencies choose to regulate strictly when the regulatory cost savings from loose regulation decreases and the loss of reputation increases; government agencies choose to regulate strictly when the profits from fines received from strict regulation increase; and importers choose regulated imports when the additional revenue gained and import cost savings from unregulated imports decrease, and when future revenue losses, fines paid to government agencies and compensation paid to consumers increase.

It can be seen that among the respondents who participated in this questionnaire (Table 2), 63.6% were female, which was slightly higher than that of male; 365 respondents were aged 36-50, accounting for 70.3%; the percentage of respondents with education in high school or junior college or below was smaller, 20.7%, while the percentage of respondents with education in bachelor or college was the largest, 46.8%, and the second largest, 32.6%, was postgraduate; respondents mainly came from East China, including Shandong, Jiangsu, Anhui, Zhejiang, Fujian and Shanghai, with a total of 396 people, accounting for 76.3%; the majority of respondents had a per capita monthly household income of RMB 5,000-10,000, with 204 people, accounting for 39.3%. Most of East China is near the sea, consumers in this region prefer to buy seafood, and the highly educated group focuses on the nutrition and quality of food, which is one of the main consumers of imported aquatic products. At present, Chinese families are still mainly related to women cooking, and the proportion of female consumers buying imported aquatic products is usually higher than men. Therefore, the group structure of the respondents is in line with the actual situation of imported aquatic products consumers in China, and the survey sample is representative.

Based on the above two-two game analysis between government agencies and importers, two-two game analysis between importers and consumers, and three-way game analysis between government agencies, importers and consumers, the following hypotheses to test are proposed between government agency regulation, importer self-regulation, consumer monitoring and imported fish safety in the structural equation model.

Hypothesis 1:

Government agency regulation has a positive effect on self-regulation of importers.

Hypothesis 2:

Consumer monitoring has a positive impact on importer self-regulation.

Hypothesis 3:

Importer self-regulation has a positive impact on the safety of imported aquatic products.

Hypothesis 4:

Government agencies have a positive impact on the safety of imported aquatic products.

Linear SEM estimates two kinds of models: a measurement model and a structural model. A measurement model specifies some number of latent, unmeasured variables or factors, each with a specified number of measured indicators or variables. A structural model includes a set of paths (regression coefficients) or correlations between the various measured and unmeasured variables in the overall model. Y = θ X + e (1) Y = λ Y i Y i + e Y i (2) X = λ X i X i + e X i (3)

A structural model can be expressed as Eq. 1, where Y (latent variable) represents importer self-regulation or imported aquatic products, X represents government regulation or consumer monitoring. θ is the coefficient of action between latent variables, i.e., the direction and degree of action of latent variables on other latent variables, e is the residual term, reflecting the part that cannot be explained between latent variables. Eqs 2, 3 are the measurement equation, where Y i denotes the observable indicators that reflect the importer self-regulation and the safety characteristics of imported fishery products respectively, X i denotes the observable variables that reflect the characteristics of government agency regulation and consumer monitoring respectively, λ Y i denotes the extent to which the observable indicators Y i can explain the latent variables Y ; λ X i denotes the extent to which the observable indicators X i can explain the latent variable X, e Y i and e X i denote the error terms respectively, reflecting the part of the latent variables that cannot be explained by the observable indicators, i denotes the number of observable indicators.

In this paper, the measurement model and the structural model is displayed in Figure 3. The circles represent unobserved, latent variables, and the squares represent the observed variables. All analyses were conducted by using the SPSS 26.0 for Windows computer package and Amos 26.0. The model estimation was performed using the great likelihood method, and the estimation results are shown in the Table 3. The standardized coefficients in the table can be used directly to compare the degree of influence between different variables. For example, the standardized coefficient of government agency regulation on importer self-regulation is 0.650, while the standardized coefficient of consumer monitoring on importer self-regulation is 0.121, which indicates that the degree of influence of government agency regulation on importer self-regulation is greater than the degree of influence of consumer monitoring on importer self-regulation. All paths reach the statistical significance level, while observing the standardized path coefficients among the latent variables is not difficult to find: the standardized coefficient of government agency regulation on importer self-regulation is positive, indicating that government agency regulation on importer self-regulation is a positive influence, Hypothesis 1 holds; The standardized coefficient of consumer monitoring on importer self-regulation is positive, indicating that consumer monitoring has a positive effect on importer self-regulation, assuming that Hypothesis 2 holds; The standardized coefficient of self-regulation of importers on the safety of imported fish products is positive, indicating that self-regulation of importers on the safety of imported fish products is positive, and the Hypothesis 3 is valid; The standardized coefficient of government agency regulation on the safety of imported fish products is positive, indicating that government agency regulation on the safety of imported fish products has a positive impact, and the Hypothesis 4 is valid.

The assessment of the model fit is also revealed by the goodness of fit index (GFI) and other statistics such as the NFI and CFI. It is generally recognized that the GFI, NFI and GFI close or to above 0.90 indicate a good model fit. Parsimonious goodness-of-fit index (PGFI) above 0.5 indicates a good model. The smaller the Consistent Akaike information criterion (CAIC), the better (Table 4).

The direct, indirect and total effects among variables are generally used to analyze the results of structural equation model estimation. The standardized coefficients and coefficient products among latent variables are used to represent the direct and indirect effects respectively. The sum of the direct and indirect effects is the total effect.

As can be seen from Table 5; Figure 4: the direct effect of government agency regulation and consumer supervision on importer self-regulation is 0.650 and 0.121 respectively, which means that for every 1 unit increase in the level of government agency regulation and consumer supervision, the level of importer self-regulation will increase by 0.650 and 0.121 units respectively. Therefore, strict government regulation will lead to increased self-regulation by importers. The direct effect of importer self-regulation and government agency supervision on the safety of imported fish products is 0.224 and 0.468, that is, the level of importer self-regulation and government agency supervision for each unit increases, the level of safety of imported fish products will be increased by 0.224 and 0.468 units respectively. The indirect effect of consumer supervision on the safety of imported fishery products is 0.027, that is, for every 1 unit increase in the level of consumer supervision, the level of safety of imported fishery products will be indirectly increased by 0.027 units through the effect of self-regulation of importers. The above illustrates the important role of government agencies and self-regulation of importers in the regulation of imported aquatic product safety. On the one hand, the importer is directly responsible for the safety of imported aquatic products. On the other hand, the importer plays an intermediate role as a bridge between government agencies and consumers to promote the safety of imported aquatic products. In terms of the strength of the effect, the role of government agencies to regulate importers themselves is more effective. At the same time government agencies in addition to promoting the safety of imported fish through the regulation of importers, its regulatory measures can also play a direct role in the safety of imported aquatic products.

Although the issue of imported food safety is receiving more and more attention, scholar have conducted many relevant studies. However, fewer are based on behavioral analysis of relevant subjects in the food safety supply chain, while even fewer use standardized role coefficients to quantitatively evaluate the responsible subjects for food safety problems. In this paper, we analyze the behavioral strategies of imported aquatic product safety regulatory bodies from the perspective of government agencies, importers and consumers using a game model, and then establish a structural equation model for empirical analysis to quantitatively study the relationship between imported aquatic product safety regulatory bodies and the factors influencing the implementation of effective regulatory behavior, and accordingly propose a series of policy recommendations to ensure the safety of imported aquatic products. On the one hand, it can enrich the application of game model and structural equation model in the field of imported aquatic products safety, and on the other hand, it can provide theoretical basis for the improvement of China’s imported aquatic products safety regulatory policy system.

Imported aquatic products as a consumer product increasingly purchased by residents, to ensure the quality and safety of imported aquatic products is of great importance to the improvement of public diet quality. In order to solve the quality and safety problems of imported aquatic products in China and minimize the safety risks of imported aquatic products, it is necessary to study the regulatory effectiveness of different stakeholders on the quality and safety of imported aquatic products in terms of the relevant subjects involved. In this paper, we analyze the behavioral strategies of stakeholders such as government agencies, importers and consumers using game theory and empirical research to propose policy recommendations to promote the safety of imported aquatic products in China, with respect to the current situation of imported aquatic products safety in China. This study has important practical significance for government agencies to strictly regulate, importers to strengthen the awareness of the first responsible body, and consumers to improve food safety and rights awareness. It also has certain reference value for the implementation of multi-governance to promote the healthy development of China’s imported aquatic products industry.

It is difficult to achieve “zero risk” of imported aquatic products safety, but it is possible to reduce the occurrence of unsafe imported aquatic products by optimizing the regulatory system to prevent safety hazards and reduce safety risks, and a perfect supervision and management system of imported aquatic products safety should be able to make the relevant actors tend to make good choices. Given the existing problems of China’s existing regulatory mechanism for imported aquatic products safety, combined with the game behavior between government agencies, importers and consumers, the specific policy recommendations of the major regulatory bodies to optimize the game equilibrium solution.

Firstly, Government must improve strict regulatory effectiveness. As a comprehensive public utility, the regulation of imported aquatic products safety involves many government departments, such as fisheries, catering and trade. The different division of labor is likely to result in overlapping functions and blind spots between different departments, which greatly reduces the efficiency of governance. Only by strengthening inter-departmental coordination and cooperation, avoiding the fragmentation of departments and stopgap measures, can the effectiveness of government regulation be improved. The implementation of the “single window” and “customs and inspection” policies fully reflects the orderly coordination of inter-departmental work by the country. Besides, it is necessary to strengthen the constraints on the power of government agencies that enjoy the right to regulate food, such as customs, by making relevant laws and regulations to clearly define the responsibility of government departments for the regulation of imported aquatic products, and at the same time establish a system of accountability to deal with illegal regulatory practices, so as to avoid the abuse of power induced by interests and the opening of the “entry” channel for illegal enterprises.

Secondly, it is of great necessity to accelerate the implementation of the main responsibility of enterprises. A key reason for the frequent occurrence of quality and safety problems of imported aquatic products is that importers disregard laws and regulations and market demand due to corporate profits. Government departments should make full use of the macro-regulatory role of the law to monitor the entry and operation of importers to the large extent. Through the development of laws and regulations and the establishment of a corresponding reward and punishment system to help enterprises to achieve legal business purposes, to promote the healthy development of China’s aquatic products trade industry. Fish importers should also raise awareness of their social responsibility under the basic norms of honesty, trustworthiness and compliance, and actively provide product information related to the quality and safety of imported aquatic products in China, in order to increase buyers’ awareness of information on the process of sourcing and selling aquatic products. By actively disclosing information on the quality of imported aquatic products, importers can generate a good public image among market groups and gain wider consumer trust for greater economic benefits.

Thirdly, the public monitoring and incentive system is supposed to be improved. By enhancing the public’s knowledge of imported aquatic products such as Chinese labels, traceability information and legal customs clearance conditions, and raising awareness of safety and rights, it is beneficial for consumers to purchase quality imported aquatic products and avoid going into consumer misconceptions. However, in reality, due to the high cost of rights, the first thing that comes to the public’s mind when faced with an unsafe imported aquatic product is to withdraw from the aquatic product market. Improving the public monitoring incentive system can prompt consumers to take the initiative to take up legal weapons and actively defend their legitimate rights and interests. In addition to the need for the government to give the public some help in defending their rights and improve the ease of reporting rights, it is also necessary to implement rewards for consumers who defend their rights under the law, which could be funded by fines for imported aquatic products merchants who sell fake food. In addition, government departments can set up special media to facilitate consumers to report cases of unsafe imported aquatic products timely, and disclose information about the importers and the outcome of the disposal afterwards, so as to effectively meet consumers’ expectations for the protection of their rights.

Finally, nothing is more important than promoting the development of co-governance. The public issue is so complex that no single organization or even the authority can effectively deal with them, and it is necessary to rely on the combined efforts of multiple actors to solve them (Chen, Wang and Yin, 2019). As the safety of imported aquatic products is a broad and mobile issue, it is urgent to have a sound multi-dimensional cooperation mechanism for governance. In addition to fully mobilizing the government, enterprises and consumers to achieve safety regulation of imported aquatic products, we must actively encourage other subjects such as fisheries associations, social groups and the media to participate in the safety regulation of imported aquatic products, creating a new situation of shared governance and solving the unsafe problems of imported aquatic products in China in many ways. The joint governance body with the participation of multiple parties makes full use of the governance advantages of different subjects, realizes the sharing of information and resources through synergistic effects, and makes joint efforts to control the safety risks of imported aquatic products. This will bring “visible” and “tangible” safety protection to the consumers of imported aquatic products and effectively enhance people’s sense of security and wellbeing.

This paper also has shortcomings. The questionnaire developed in this paper needs to be further revised due to the lack of a relatively mature questionnaire that can be drawn on for the participation of subjects related to imported aquatic products safety regulation. In addition, due to the COVID-19, it is difficult to conduct offline research, and the use of online surveys may lead to the fact that the demographic characteristics of respondents in this paper’s questionnaire are not exactly the same as those of Chinese demographics, and the research findings need to be further validated. In the future, the evolutionary game model can be used to study the equilibrium strategy among the subjects of imported aquatic products safety regulation and simulated by numerical analysis. In terms of research content, it is possible to analyze the regulation of imported aquatic products in a specific region such as the Yangtze River Delta, or to study the differences between different regions.