Firstly, the government plays an important role in the development of marine ranching. The government encourages and supports the development of MREs through the implementation of incentive policies. The policies include capital subsidies, tax incentives, technical support and other forms, and the target of the subsidy is usually the enterprise, aiming to reduce the operating costs of the enterprise and improve its market competitiveness. At the same time, the target of subsidies can also be consumers, through government subsidies to reduce the price of products or services, giving consumers purchase concessions. In addition, the government also regulates the operating behavior of MREs, protects the rights and interests of consumers, and maintains fair competition in the market by formulating relevant regulations and policies. All these efforts will enable the government to obtain different degrees of performance benefits, such as improvement of the ecological environment and increase in social credibility.

Secondly, MREs, as the main undertakers of marine ranching construction, bear important economic and social responsibilities, and are the backbone of promoting the technological progress and industrial upgrading of marine ranching. While carrying out the construction and operation of marine ranching, enterprises can make use of government subsidies and preferential policies, invest capital and technology, carry out scientific breeding management and technological innovation, improve the yield and quality of marine products, expand the functions of fisheries, and create diversified eco-products to meet the diversified needs of consumers. At the same time, technological innovation can also better ensure the rational utilization of marine resources and the protection of the ecological environment, create more ecological benefits and establish a more positive corporate image.

Finally, the profits generated by the sale of marine products and services are an important guarantee for the sustainable development of the enterprise, and the source of these profits is largely dependent on the purchasing behavior of consumers. Consumer demand and purchasing behavior for marine products and services directly affects MRE’s sales revenue and profit level. Consumers will weigh the quality, price, safety and other factors of the product and choose the product that meets their preferences, and different products bring different utility to consumers. For enterprises, consumers’ choice of strategy is the direction and extent of technological innovation. Producers will decide whether and how to innovate technologically based on market demand, technical feasibility, and other factors. In addition, when the government implements a subsidy policy for consumers, consumers may enjoy lower prices for marine products and services, thus increasing their purchasing power. Enterprises may also organize publicity and educational activities to increase consumer awareness and trust in marine products and services, further promoting the growth of market demand. In the process of evolutionary games, the strategic choices between consumers and MREs will be continuously adjusted and evolved. Changes in consumer preferences will lead producers to make technological innovations, which in turn will influence consumer preferences. This process of mutual influence and adaptation promotes the continuous innovation and development of MRE technology. The relationship between the three parties are show in Figure 1.

Based on the above analysis, in order to establish the three-party evolutionary game model of MRE, government and consumers, this paper puts forward the following hypotheses:

H1: MRE, government and consumers are all finite rationality. The strategy choice of the game parties is based on the consideration of maximizing their own interests to make the corresponding strategy choice.

H2: The strategy set of MRE is {innovate, not innovate}, in which the probability of enterprises choosing technological innovation is x, and the probability of no technological innovation is 1 − x . The prices of products and services corresponding to the two strategies are P n , P t ; and the costs are C n , C t , respectively. The investment cost paid by enterprises for technological innovation is I. The additional benefit obtained is R 1 , and the part of the enhanced ecological and environmental benefits in R 1 indirectly affects the governance effect of the government, and the feedback factor is m, 0<m<1 (Gao et al., 2022).

H3: The government’s strategy set is {support, not support}{supportive, Unsupported}, where the probability that the government supports the technological innovation is y, and the probability that it does not support it is 1 − y . When the government supports it will provide subsidies, where the subsidy to enterprises is S 1 , the subsidy to strong preference consumers is S 2 , and the subsidy to weak preference consumers is S 3 . At the same time the government will also receive an additional benefit R 2 . When the government chooses not to support it will not provide a subsidy and only enjoys the base benefit R 3 . The government tax on technologically innovative enterprises is T 1 and the tax on traditional enterprises is T 2 , with T 1 < T 2 .

H4: Consumers in the market have different preferences, the preference set is {strong preference, weak preference}, the probability of strong preference consumers is z, and the probability of weak preference consumers is 1 − z . Strong and weak preferences affect consumers’ price sensitivity to products and services. Strong preference consumers are more inclined to choose products and services that meet marine ecological standards and have little impact on the environment, and they are more interested in diversified products and services after technological innovation of enterprises, so they are less price sensitive and show stronger willingness to buy, with a sensitivity coefficient of γ 1 . While weak preference consumers are less interested in products and services with new and diversified products and services, and it is harder for them to accept the premium, so they are more price sensitive, and the sensitivity coefficient is γ 2 , γ 1 < γ 2 . Different products and services have different utility to consumers, the utility to consumers of new products and services produced by technologically innovative enterprises is U 1 , and the utility to consumers of traditional products and services is U 2 , U 1 > U 2 .

H5: To simplify the calculation, referring to Zheng and Yu, 2022; Guo et al., 2024; Jie and Xin, 2024; Wang et al., 2024, we define the demand for different products by consumers with different preferences as: q 1 1 = Q − γ 1 P n , q 1 2 = Q − γ 2 P n , q 2 1 = Q − γ 1 P t , q 2 2 = Q − γ 2 P t , where q 1 1 , q 1 2 represent the demand of strong preference and weak preference consumers for new products and services; q 2 1 , q 2 2 represent the demand of strong preference and weak preference consumers for traditional products and services, and Q is the maximum market size. Based on the above analysis, the parameter setting table is obtained, as shown in Table 1 .

According to Table 2 , the expected benefit for the MRE when choosing technological innovations is represented as E 11 , while the expected benefit when choosing no technological innovations is E 12 . The average benefit, calculated based on these two scenarios, is E 1 ¯ .

Substituting Equations 1 and 2 in Equation 3, we can obtain the replication dynamic equation for the MRE. Also we can get its first derivative with respect to x:

The expected benefit of supportive strategy and unsupported strategy of the government E 21 , E 22 and the average benefit E 2 ¯ are, respectively:

Substituting Equations 6 and 7 in Equation 8, we can obtain the replication dynamic equation for the government. Also we can get its first derivative with respect to y:

The expected benefit for strong preference consumers is  E 31 , while the expected benefit for weak preference consumers is E 32 . The average benefit, calculated based on these two scenarios, is E 3 ¯ .

Substituting Equations 11 and 12 in Equation 13, we can obtain the replication dynamic equation for the consumers. Also we can get its first derivative with respect to z:

According to the stability theorem of the differential equation of evolutionary game, in order to keep a certain strategy in a stable state, the probabilities x, y and z of MRE, government and consumers choosing this strategy must be satisfied respectively: F ( x ) = 0 , d ( F ( x ) ) / d x < 0 ; F ( y ) = 0 , d ( F ( y ) ) / d y < 0 ; F ( z ) = 0 , d ( F ( z ) ) / d z < 0 . Based on the above analysis, according to Equations 5, 10 and 15, when z = z * = T 1 − T 2 − R 1 + I − ( P n − C n ) ( Q − γ 2 P n ) + ( P t − C t ) ( Q − γ 2 P t ) − S 1 y P n ( P n − C n ) ( γ 2 − γ 1 ) − P t ( P t − C t ) ( γ 2 − γ 1 ) , at this point, d ( F ( x ) ) / d x ≡ 0 , and the strategy chosen by the MRE is not stable. However, when z < z * , d ( F ( x ) ) / d x | x = 0 < 0 , and x = 0 is the evolutionary stable point for the MRE. Conversely, when z > z * , d ( F ( x ) ) / d x | x = 1 < 0 , and x = 1 is the evolutionary stable point.

For the government, when x = x * = ( S 3 − S 2 ) z + R 2 − S 3 S 1 , at this point, d ( F ( y ) ) / d y ≡ 0 , and the government’s strategy is not a stable strategy. Nevertheless, when x < x * , d ( F ( y ) ) / d y | y = 1 < 0 , and y = 1 is the evolutionary stable point for the government. In contrast, when x > x * , d ( F ( y ) ) / d y | y = 0 < 0 , and y = 0 is the evolutionary stable point.

For the consumers, when y = y * = [ P t ( U 2 − P t ) ( γ 2 − γ 1 ) − P n ( U 1 − P n ) ( γ 2 − γ 1 ) ] x − P t ( U 2 − P t ) ( γ 2 − γ 1 ) S 2 − S 3 , at this point, d ( F ( z ) ) / d z ≡ 0 , and the consumers cannot determine a stable strategy. But when y < y * , d ( F ( z ) ) / d z | z = 0 < 0 , and z = 0 is the evolutionary stable point for the consumers. On the contrary, when y > y * , d ( F ( z ) ) / d z | z = 1 < 0 , and z = 1 is regarded as a stable strategy for consumers. The phase diagram of the replication dynamics for the MRE, government, and consumer parties is shown in Figure 2 .

According to F ( x ) = 0 , F ( y ) = 0 , F ( z ) = 0 , the equilibrium points of the three- party evolutionary game can be obtained from Equations 4, 9, and 14. The Jacobian matrix of the replicated dynamic equation system is shown below.

Since the equilibrium of the three- party evolutionary game must be a strict Nash equilibrium, eight pure strategy points can be derived, and substituting them into the Equation 16 yields the eigenvalues of the different strategies as shown in Table 3 , and the stable point represents the evolutionary stable strategy (ESS) when all the eigenvalues are negative.

Without loss of generality, assuming that P n > P t >0, C n > C t >0, U 1 > C n >0, U 2 > C t >0, S 2 > S 3 >0, it can be concluded that E₂(1,1,0), E₄(1,0,0), E₆(1,0,0) and E₈(0,0,0) are the unstable points based on the above assumptions. The remaining four cases are further analyzed below.

Case 1: S 1 + R 1 − T 1 − I + ( P n − C n ) ( Q − γ 1 P n ) < ( P t − C t ) ( Q − γ 2 P t ) − T 2 and R 2 < S 3

For consumers with different preferences, the benefits of MRE are different. According to the assumption conditions, facing the same products and services, the strong preference consumers bring more benefits to the MRE than the weak preference consumers bring to the MRE, which has nothing to do with whether the MRE carries out technological innovation or not, and such a conclusion is consistent with the reality. In other words, ( P n − C n ) ( Q − γ 1 P n ) > ( P n − C n ) ( Q − γ 2 P n ) , ( P t − C t ) ( Q − γ 1 P t ) > ( P t − C t ) ( Q − γ 2 P t ) . Regardless of consumer preferences, when the benefits to MREs from technological innovation are smaller than those from traditional operations, and the government subsidy to MRE technological innovation is not sufficient to make up the difference, then MREs will choose not to engage in technological innovation. Similarly, when R 2 < S 3 , it is easy to know that R 2 < S 1 + S 2 + S 3 , and the government will choose not to support technological innovation when the additional benefit gained from government support for MRE technological innovation is less than the cost of government subsidies to the outsiders. Purchase of products can bring additional utility to consumers, strong preference consumers purchase more than weak preference consumers, the former get more utility naturally, weak preference consumers will shift towards strong preference consumers. At this point E₇ (0,0,1) is the stabilization point. In this equilibrium, MRE chooses no technological innovation strategy, the government chooses no unsupported strategy, and the consumers are strong preference consumers.

Case 2: S 1 + R 1 − T 1 − I + ( P n − C n ) ( Q − γ 1 P n ) < ( P t − C t ) ( Q − γ 2 P t ) − T 2 and R 2 > S 1 + S 2

This case is similar to Case 1, for either type of consumer, when the benefits to the MRE from technological innovation are less than the benefits from traditional operations, and the government’s subsidy to the MRE’s technological innovation is not sufficient to make up the difference, the MRE will choose not to engage in technological innovation at this point. It is worth noting that when R 2 > S 1 + S 2 , the government will choose to support technological innovation when the additional benefits gained from government support for MRE technological innovation are greater than the cost of government subsidies to MREs and consumers. At this time, E₅ (0,1,1) is the stabilization point. In this equilibrium, MRE chooses the no technological innovation strategy, the government chooses the support strategy, and consumers are the strong preference consumers.

Case 3: S 1 + R 1 − T 1 − I + ( P n − C n ) ( Q − γ 2 P n ) > ( P t − C t ) ( Q − γ 1 P t ) − T 2 and R 2 > S 1 + S 2

This case builds on Case2 by changing the MRE’s strategy. Regardless of the type of consumer, when the benefits of technological innovation by the MRE are greater than the benefits of traditional operations, the MRE will choose to engage in technological innovation. When R 2 > S 1 + S 2 , the government will choose to support technological innovation when the additional benefits gained from government support for MRE technological innovation are greater than the cost of government subsidies to MREs and consumers. At this time E₁ (1,1,1) is the stabilization point. In this equilibrium, MRE chooses the technological innovation strategy, the government chooses the support strategy, and the consumers are the strong preference consumers.

Case 4: R 1 − T 1 − I + ( P n − C n ) ( Q − γ 2 P n ) > ( P t − C t ) ( Q − γ 1 P t ) − T 2 and R 2 < S 3

This case is based on Case3 and changes the government’s strategy. Similarly, for either preference consumer, when the benefits of MRE to carry out technological innovation are greater than the benefits of traditional business, MRE will choose technological innovation strategy. However, when R 2 < S 3 , it is known easily that R 2 < S 1 + S 2 + S 3 , the government will choose not to support technological innovation when the additional benefits gained from government support for MRE technological innovation are less than the cost of government subsidies to the outsiders. At this point E₃ (1,0,1) is the stabilization point. It is important to note that in this equilibrium condition, the government chooses the unsupported strategy, and in the absence of government subsidies, MRE still chooses the technological innovation strategy, the consumers are strong preference consumers, and the interests between the enterprises and the consumers achieve a good market-oriented cycle, which is a kind of ideal state of market maturity.

To confirm the above constructed evolutionary game model and derive the results, the model and its parameters were simulated and analyzed using MATLAB software. Referring to the research of Wan et al., 2021; Sun et al., 2024; Wang et al., 2024 and combining with the actual situation, while considering the overall equilibrium of the system and the basic assumptions based on the evolutionary game, the initial assignments of specific parameters are shown in Table 4 .

As a new industry, Marine ranching industry also follows the basic laws of life cycle theory, including introduction period, growth period, maturity period and decline period. At different stages of development, the Marine ranching industry is facing different market environments and challenges. Introduction period: immature technology, low market awareness, need a lot of research and development and government support; Growth period: gradually mature technology, market awareness, rapid development of the industry; Maturity stage: Market saturation, fierce competition, need product differentiation and service innovation to maintain advantages; Recession period: The industry is declining, and it needs to transform and upgrade, find new growth points or consider quitting. The application of life cycle theory to Marine ranching industry is helpful to promote the sustainable development of Marine ranching industry.

Based on the life cycle theory, technological innovation in MRE can be simplified into three stages (Yang et al., 2021; Piila et al., 2022; Pan et al., 2023), the initial stage - governmental guidance and assistance, the development stage - the enterprise independent R&D and innovation practice, and mature stage - market maturity and self-driven. These three stages can correspond to each of the four cases analyzed above. In order to simplify the analysis, we will change certain values on the basis of one case to show the evolution process between the cases.

According to the set parameter values, the simulation of each of the above four cases is carried out, and the results are shown in Figure 3 . Case1 is analyzed as the initial stage, when the parameter values of the cases satisfy the conditions S 1 + R 1 − T 1 − I + ( P n − C n ) ( Q − γ 1 P n ) < ( P t − C t ) ( Q − γ 2 P t ) − T 2 and R 2 < S 3 , E₇ (0,0,1) is the ESS, which is in consistent with the above analysis, and further verifies the stability of the analysis is correct. In the early stage of the market, consumers are solid advocates of traditional products and services.

Keeping other values unchanged, set S₁ =S_{2 =} 2, S_{3 =} 1, R_{2 =} 6 on the basis of Case1. That is, the government’s external subsidy cost is reduced, and the additional income obtained by the government in supporting technological innovation is increased. At this time, the government’s choice of support for technological innovation is profitable, and the ESS transfers from E₇ (0,0,1) to E₅ (0,1,1). Despite government support for enterprise technological innovation, in the early stages of the market, consumers’ embrace of traditional products and services makes the revenue generated by new products and services insufficient for enterprises to engage in technological innovation.

On the basis of Case2, set P_n =11.5, S_{1 =} 3.5, T_{1 =} 2, T_{2 =} 8. In order to support MREs to make technological innovations, the government reduces the innovation cost of enterprises by increasing the subsidies to MREs and reducing the tax. At the same time, it induces technological innovation in traditional MREs by imposing a higher tax burden on them. Higher prices for new types of products and services can bring more revenue to enterprises, further pushing them to choose technological innovation strategies. The case transforms from Case2 to Case3, and the ESS transforms from E₅ (0,1,1) to E₁ (1,1,1). This phase is the development stage, when the government’s support for technological innovation of enterprises is increasing, and consumers’ acceptance of new products and services is increasing, MREs will carry out technological innovation to gain more benefits.

On the basis of Case3, set P_n =12.5, R_{2 =} 0.5. In this case, the government’s choice of technological innovation strategy is a loss, if the condition R 2 < S 3 is met, the government’s stability strategy is not to support technological innovation. With the withdrawal of the government from the partnership, the maturity of the market allows MRE to offset the loss of government subsidies by increasing the price of new products and services to increase profits. The case changes from Case3 to Case4, and the ESS transforms from E₁ (1,1,1) to E₃ (1,0,1). This stage is the mature stage, and MRE and consumers have formed a good marketization relationship, which is the most ideal state of evolutionary game.

Finding 1: The government plays an important role in the growth period of MREs. The government encourages enterprises to carry out technological innovation activities through positive and negative incentives. The government’s incentive policies play a key role in the growth period of MREs, while the government can gradually eliminate the policies in the mature period of MREs.

Finding 2: In the mature period of MREs, the government can gradually eliminate the incentive policies since MRE can offset the impact of reduced government subsidies by increasing the prices of products and services.

This paper constructs a tripartite evolutionary game model including MREs, government and consumers and systematically analyzes the stability of the model. Using numerical simulation the evolution of the four scenarios of Case 1-Case 4 using MATLAB software and considers the validity of the conclusions after the hypothesis is relaxed. Finally, it further analyzes the scenario of the mature market under the withdrawal of government from the market and the cancellation of subsidies. The study found that:

Based on the above conclusions, we make the following suggestions:

The research in this paper still has some limitations. Although the conclusions drawn can provide scientific basis and theoretical support to a certain extent, the core lies in the construction of the model and the setting of parameters, which are often based on a series of assumptions and simplifications. In the subsequent in-depth research, we will continue to improve the research hypothesis and increase parameters to make the evolutionary logic more realistic. For example, under different strategies, the feedback factor m is introduced into the model as a variable rather than a quantitative one, and real cases are introduced as analysis objects. Through the combination of qualitative research methods (such as interviews and observation) and quantitative research methods (such as questionnaire survey and statistical analysis), richer and more specific data information can be provided, which helps to verify and modify the simulation model, improve the practicability and credibility of research, and contribute more valuable insights and results to the development of related fields.