Incentives for promoting climate change adaptation technologies in agriculture: an evolutionary game approach

Climate change adaptation technologies (CCATs) have become increasingly important for farmers as they face the challenges of climate change and natural disasters. Despite this, many rural areas still rely on traditional agricultural techniques. To promote the adoption of CCATs in agriculture, it is necessary to explore the incentives and conditions for the effectiveness of the policy. We develop an evolutionary game model to analyze the behavior of local governments and farmers in promoting CCATs. Our findings indicate that, under certain conditions, the promotion of CCATs can achieve equilibrium. The incentive for farmers to adopt CCATs increases within a certain range when local governments provide risk subsidies and cost sharing. When subsidies are too high, however, local governments may choose not to promote CCATs, which reduces the incentives for farmers to adopt them. Publicity is also an important factor in promoting CCATs. Our study provides insight into the development of policies aimed at promoting CCATs in agriculture.


Introduction
Since the 1950s, there have been significant changes in the global climate system, with global warming becoming a reality (Kerr 2007;Berrang-Ford et al. 2021), such as unusually high temperatures, melting glaciers, and warming and humidification of the north. To combat climate change, various countries have identified national contributions according to their circumstances to reduce the negative impacts and risks associated with climate change through adaptation and mitigation measures (Hussain et al. 2020;Ghahramani et al. 2019;Dagestani et al. 2022;He et al. 2023). However, it is difficult to rely on climate change mitigation actions alone to reduce the negative impacts of climate change in the short term. It is urgent to improve resilience and recovery from the adverse effects of climate change by developing and implementing climate change adaptation policies (van Valkengoed and Steg 2019).
Agriculture is one of the most sensitive areas affected by climate change, which has more negative than positive impacts on crop yields (Shaffril et al. 2018). Since 2000, many researchers have begun to explore adaptive management implementation strategies in the context of climate change (Gilman et al. 2008;Berrang-Ford et al. 2021). Agricultural climate change adaptation management is a hot spot in agricultural sustainable development research (Suresh et al. 2021). How to adapt agricultural systems to climate change to minimize the adverse effects of climate change and fully utilize the beneficial effects brought about by climate change is of great significance for promoting sustainable agricultural development and ensuring food security. Many studies have shown that promoting the use of climate change adaptation technologies (CCATs) in agriculture is a crucial response measure to climate change (Howden et al. 2007;Anwar et al. 2013). CCATs encompass diverse scientific, technological, and managerial measures used to mitigate and adapt to the adverse effects of climate change and enhance the resilience of social, economic, and ecological systems, including but not limited to energy-saving and Responsible Editor: Eyup Dogan * Ruihui Yu yuruihui1@outlook.com 1 low-emissions technologies, water resource management, conservation agriculture techniques, natural disaster management, and other integrated technologies and management methods (Abid et al. 2016). The promotion of climate-adaptive technologies in agriculture is heavily based on the participation of stakeholders, including local governments, enterprises, and farmers (Howden et al. 2007;Anwar et al. 2013). However, in smallscale agricultural economy, the contribution of enterprises is relatively small compared to that of local governments and farmers (Mitter et al. 2018;Laube et al. 2012). Adapting to climate change is a systemic project that requires huge financial support, especially for developing countries, which need to invest more in adaptation actions, thus requiring the participation of governments. As the main provider of public goods and services for the whole agricultural production process, an important participant in agricultural adaptation to climate change, and an influencer of farmer adaptation, governments play a key role in agricultural adaptation to climate change (Stage 2010;Ramirez-Villegas et al. 2012). Farmers are the direct subjects engaged in agriculture and are the micro-decision makers of agricultural adaptation to climate change. Farmers' decisions about whether to adopt CCATs are influenced by their costs and benefits, and their goal is to maximize benefits under cost constraints, which may conflict with local governments that seek to maximize public interest (Quan et al. 2019;Tompkins and Eakin 2012;Chen et al. 2022;Zhang et al. 2020). Adaptation to climate change in agriculture requires cooperation between local governments and farmers to achieve mutual benefits, and there is also a game of interaction between local governments and farmers in the promotion of CCATs in agriculture.
The attitudes and behaviors of farmers are key to their adoption of CCATs. According to the theory of behavioral bias, when a behavior brings both benefits and risks, the actors are more likely to maintain the status quo to avoid risks (Menapace et al. 2013;Jin et al. 2015). Although CCATs can help farmers adapt to climate change and protect agricultural production, there are also uncertainties about their benefits. Furthermore, the additional input costs and asymmetric information about technology further increase the risk of inappropriate use of technology by farmers, making them consider profit maximization and risk minimization objectives in the production process and reducing the likelihood that farmers adopt CCATs. For example, Tong et al. (2019) found that risk aversion reduces the adoption rate of CCATs among rice farmers in the Jianghan Plain. Jin et al. (2015) found that farmers with higher risk aversion are less likely to adopt CCATs.
Policy support is crucial for farmers to adopt CCATs. The main government policy measures for promoting CCAT in agriculture include awareness raising, education, and financial subsidies. Research has shown that awareness raising and education can increase farmers' knowledge about climate change and agricultural technologies and enhance their ability to adapt to climate change. Technology training and technology demonstrations reduce information asymmetry by providing farmers with information on the economic benefits of technology, increasing their understanding of the technology, and promoting the adoption of CCATs by farmers. For example, Goyal and Netessine (2007) found that demonstration households can disseminate technology information to neighboring farmers, effectively reducing the time cost for other farmers to access the information and having a demonstration effect on the promotion of CCATs. Furthermore, some studies have also shown that technology subsidies reduce the costs of technology adoption by providing them with financial support, leading to the adoption of agricultural technologies (Hoffmann and Jones 2021;Ramirez-Villegas et al. 2012), which may have similar effects on the promotion of CCATs.
According to the above analysis, farmers and local governments are the two important stakeholders in the process of promoting CCATs in agriculture. Local government departments try to guide farmers to adopt CCATs through various promotion measures to achieve climate change adaptation in agriculture and improve government performance, while farmers will choose whether to adopt CCATs according to the market environment and actual conditions. Both local governments and farmers are considered bounded rational actors who learn and improve their strategies through trial and error (Sun et al. 2021;Sun et al. 2022;Tian et al. 2022;Mao et al. 2023). This approach reflects a critical characteristic of policymaking in China's policy formulation process, namely, the emphasis on gradualist reform (Lin et al. 2004). These are all in line with the conditions of the evolutionary game ( Fig. 1), which we adopt to analyze the behavior of local governments and farmers for policy insights.
Several studies have used evolutionary game models to investigate the diffusion and adoption of technology (Li et al.  Hu et al. 2020;Zhao and Liu 2019;Wu and Ma 2020). The authors conducted an evolutionary game analysis of government-enterprise and enterprise-enterprise interactions in the diffusion of technology. However, they did not address the game theory of promoting CCATs and did not thoroughly explore the impact of different government policies on farmers' behavior. In China, there are already policies in place to promote the diffusion of CCATs, but the success of these policies varies from region to region. It is crucial to recognize the complex relationship between the government and farmers when promoting policies for CCAT diffusion. By doing so, policymakers can develop more effective strategies that account for the different needs, motivations, and constraints of farmers. So understanding this game theory could help policymakers target subsidies and other incentives to enhance farmers' adoption of CCATs.
Based on evolutionary game theory, we analyze the interactive game process between local governments and farmers in the context of promoting CCATs in agriculture and propose policy recommendations to promote adaptation to climate change in agricultural systems. Our contribution lies in two aspects. First, while previous studies mainly analyze the impact of government policies on farmers' adoption of CCATs in a static way, we adopt a dynamic and comparative analysis method, which enriches management insights on promoting CCATs in agriculture based on a multi-scenario analysis. Second, we systematically sort out the stakeholder relationships in promoting CCATs in agriculture and construct an integrated analysis framework involving both the local government and farmers as the main participants. By taking into account the perspectives of both the government and farmers, more effective policies can be formulated to promote the widespread adoption of CCATs.
We organize the rest of the paper as follows. In the second section we review the relevant literature on stakeholder behavior in climate change adaptation in agriculture, promotion and adoption of CCATs, and evolutionary game theory. In the third section we introduce the model setup and discuss the assumptions. In the fourth section we conduct model analysis and derive the equilibrium conditions. In the fifth section we perform a numerical simulation to illustrate the model results. Finally, in the sixth section, we conclude the paper and suggest topics for future research.

Literature review
The behaviors of stakeholders involved in responding to climate change are key to addressing the challenge in agriculture, and there has been increasing research on stakeholder behaviors and their impacts (Shaffril et al. 2018;Abid et al. 2019). Related studies can be divided into three main categories. First, some research focuses on farmers' perceptions of climate change, behaviors, and the impacts of their behaviors (Khanal et al. 2018;Huang et al. 2015;Chen et al. 2022). Second, some research focuses on government policy measures to address climate change in agriculture and its effects (Bryan et al. 2009;Aryal et al. 2020). Third, some research focuses on the interactions between government policies and farmers ( Chen et al. 2014;Zhang et al. 2018;Matewos 2019), which confirms the positive effect of government support. Additionally, some studies attempt to construct a framework for synergistic participation of the public and private sectors in agricultural climate adaptation to guide common action in agriculture in response to climate change (Mitter et al. 2018). When looking at climate change through the lens of stakeholder perspectives, designing measures to address the challenges is considered crucial and informative (Shaffril et al. 2018;Abid et al. 2019). From this perspective, paying attention to the application of climate change adaptation technologies (CCATs) will also be enlightening.
The application of CCATs in agriculture not only depends on their innovation in addressing climate change and natural disaster risks but also on the promotion and adoption of technology. Some studies have shown that farmers are risk averse and prefer to maintain the status quo to avoid risk (Jin et al. 2015;Menapace et al. 2013), so there is a high degree of uncertainty in farmers' behaviors toward adopting CCATs. Government measures to promote CCATs in agriculture can effectively reduce the cost for farmers, compensate farmers for the cost of risk, and increase their willingness to adopt CCATs in agriculture (Ramirez-Villegas et al. 2012). In summary, existing research on the promotion of CCATs relies mainly on static and historical analyses (Ayanlade et al. 2018;Claessens et al. 2012), lacking dynamic comparative analysis that takes into account the stakeholders of the behavioral game, as well as the potential stable equilibrium states under different policy measures. In fact, to better implement the promotion of agricultural climate adaptation technologies, it is necessary to analyze the behavioral game between government and farmers, and the potential effects of different policy measures, in order to optimize and develop more effective policies.
Evolutionary game theory replaces the traditional game theory assumption of perfect rationality with finite rationality and learning ability, which states that both parties cannot find the optimal equilibrium point in every game. It has been widely used in the study of multi-player cooperation and policy analysis (Sun et al. 2021;Sun et al. 2022;Tian et al. 2022;Kou et al. 2021). Several studies have used evolutionary game models to investigate the diffusion and adoption of technology. For example, Li et al. (2022) utilized an evolutionary game model to simulate the adoption of cleaner production technology among enterprises by modeling group behavior. Similarly, Zhao and Liu (2019) established a government-enterprise evolutionary game framework to examine issues related to the adoption of carbon capture and storage at the microlevel. Some studies based their analysis on complex network modeling to explore the evolutionary process (Li et al. 2022;Hu et al. 2020), while others relied on replicator dynamics to explore it (Zhao and Liu 2019;Wu and Ma 2020). Replicator dynamics, based on a system of differential equations, is the most widely recognized model for examining the replication process in this context (Taylor and Jonker 1978;Sasaki and Unemi 2011;Sun et al. 2021). These studies skillfully revealed the micromechanisms of technology diffusion and highlighted how evolutionary game theory can inspire new insights into the impact of dynamic changes in related parameters on technology diffusion outcomes. Evolutionary game theory provides a unified analytical framework that enables researchers to identify critical players, key parameters, and potential outcomes in multiagent games as a whole. As a result, it can prove highly beneficial for our research objectives, helping us gain a more comprehensive understanding of the underlying processes of CCAT diffusion.
Although there have been studies on stakeholder behavior in promoting climate-adaptive technologies in agriculture, there are several gaps in the existing literature. Firstly, many studies tend to focus on farmer perceptions and behaviors when it comes to climate-adaptive technologies, but often neglect the interactions between farmers and the government. Secondly, existing research tends to rely on static and historical analysis that lacks dynamic comparative analysis of different policy measures. Thirdly, evolutionary game theory has not been adequately applied to the promotion of climate-adaptive technologies in agriculture, despite its potential insights. Our study uses evolutionary game theory as a new analytical framework to analyze the impact of different policy measures on the promotion of climate-adaptive technologies in agriculture and gain a more comprehensive understanding of the underlying processes of technology diffusion. In doing so, our research sheds light on the potential benefits of using evolutionary game theory to better understand and guide the promotion of climate-adaptive technologies in agriculture, providing guidance for policymakers looking to develop more effective policies.

Model assumption
Both local governments and farmers are effectively rational groups whose game is a repeatable process. Players adjust their strategies in response to relevant changes in the other party, and the changed strategies form an evolutionary stable equilibrium. Taking into account the real-life scenario of farmers' adoption of CCATs, we make the following assumptions (Table 1).
Assumption 1: Farmers and local governments are two important stakeholders in the promotion of CCATs. Local governments can adopt the two strategies to promote and not to promote CCATs, where the probability of local governments choosing to promote strategy is x, and the probability of choosing not to promote strategy is 1 − x; correspondingly farmers can adopt the two strategies to adopt and not to adopt CCATs, where the probability of farmers choosing to adopt CCATs is y and the probability of choosing not to adopt CCATs is 1 − y, where x, y ∈ [ 0, 1]. Assumption 2: Local governments make promotion decisions based on certain benefits and cost considerations. C g is the cost of local governments that promote CCATS, and A g is the benefit when it chooses the promotion strategy and farmers adopt the strategy. The benefit is an incentive from the central government to local governments. Local governments take certain measures to incentivize farmers to adopt CCATs, S is the risk subsidy from local governments, and w is the proportion of technology purchase cost sharing. Local governments also incentivize farmers to adopt CCATs through publicity; C p is the cost of publicity of local governments and m is the effort of publicity of local governments. If farmers choose not to adopt CCATs, local governments will pay the costs to treat the environment, which is C e . Assumption 3: Farmers will have the benefit when they choose not to adopt or adopt CCATs, R n is the benefit when they choose not to adopt CCATs, and R a is the benefit when they choose to adopt CCATs. C a is the cost of purchasing CCATs from farmers. Farmers with environmental awareness will have an environmental preference benefit when they adopt CCATs for agricultural production, which is R e . And when the public relations efforts of local governments are greater, they are more likely to promote farmers' awareness of environmental protection, leading to an increase in their environmental preferences.

Payment matrix
Based on the above assumptions, we derive the payoff matrix of the game (Table 2).

Local governments' revenue expectation function
Letting the expected revenue for local governments that choose to promote CCATs be E 11 , the expected revenue for local governments that choose not to promote CCATs be E 12 , and the average revenue be E 1 . Then Eq.

Farmers' revenue expectation function
Letting the expected revenue for farmers choosing to adopt CCATs be E 21 , the expected return for a farmer choosing not to adopt CCATs be E 22 , and the average revenue be E 2 . Then, Eq.

Replication dynamics equation for local governments
In the evolutionary game, we assume that the strategic choices of the game participants are independent of one another and the game is played repeatedly, so we can separately discuss the replication dynamics of the strategy choice behaviors of different stakeholders. According to the Malthusian dynamic equation, the replication dynamics equation for the choice of local governments to promote CCATs is Eq. (3).
From the stability theorem for replicated dynamic differential equations and the nature of the evolutionary stability strategy, we know that x* is an evolutionary stability strategy when F(x) = 0 and F'(x) < 0. Therefore, we have the following results: (i) If A g -S − C a w ≤ 0, then x = 0 is the globally unique stable equilibrium strategy, that is, local governments choose not to promote CCATs. Based on the hypothesis that y > 0, the value of y* = (C g + m C p )/(A g -S − C a w) does not exist. We show the replication dynamics trend diagram under this scenario in Fig. 2a.
(ii) If A g − S − C a w > 0, when y = (C g + m C p )/(A − S − C a w), then F(x) = 0 and F'(x) = 0, that is, for local governments, the value of x does not affect the stability of the outcome of the evolutionary game; when y > (C g + mC p )/(A g − S − C a w), then x = 1 is the globally unique stable equilibrium strategy, that is, local governments choose to promote CCATs; when y < (C g + m C p )/(A g − S − C a w), then x = 0 is the globally unique stable equilibrium strategy, that is, local governments choose not to promote CCATs. Based on the hypothesis that y > 0, the value of y* = (C g + m C p )/(A g − S − C a w) exists and can be represented by the line G 1 . We show the replication dynamics trend diagram under this scenario in Fig. 2b.

Replication dynamics equation for farmers
Similarly, we derive the replication dynamics equation for the farmer's choice to adopt CCATs in Eq. (5).
From the stability theorem for replicated dynamic differential equations and the nature of the evolutionary stability strategy, we know that y* is an evolutionary stability strategy when F(y) = 0 and F'(y) < 0. Therefore, we have the following results.
(i) When x = (C a − R a − R e + R n )/(m R e + S + C a w), then F(y) = 0 and F'(y) = 0, that is, for the farmer, the value of y does not affect the stability of the evolutionary game outcome.
(ii) When x > (C a − R a − R e + R n )/(m R e + S + C a w), then y = 1 is the globally unique stable equilibrium strategy, that is, the farmers choose to adopt CCATs.
(iii) When x < (C a − R a − R e + R n )/(m R e + S + C a w), then y = 0 is the globally unique stable equilibrium strategy, that is, the farmers choose not to adopt CCATs (Fig. 3).

Stabilization strategies for game subjects
The combination of Eqs. (3) and (5) results in a two-dimensional dynamical system (I), which can be expressed as Eq. (7).
Letting (F(x), F(y)) = dx dt , dy dt = (0, 0) , we can obtain E 1 = (0,0), E 2 = (0,1), E 3 = (1,0), E 4 = (1,1), and E 5 = ((C a − R a − R e + R n )/(m R e + S + C a w), (C g + C p m)/(A g -S − C a w)). These equilibrium outcomes are not necessarily stable strategies for the evolutionary game system (ESS), so it is important to discuss whether these equilibrium points are stable strategies and the conditions under which they become stable strategies. We use the Jacobi matrix to determine the local stability of the above equilibrium points. Specifically, we take the first-order partial derivatives of F(x) and F(y) concerning x and y, respectively, to obtain the Jacobi matrix of the game equation as follows: where a 11 = (− 1 + 2 x) (C g + C p m + (− A g + S + C a w) y), a 12 = (− A g + S + C a w) (− 1 + x) x, a 21 = − (m R e + S + C a w) (− 1 + y) y, and a 22 = (R a + R e − R n + m R e x + S x + C a (− 1 + w x)) (1 − 2 y).
Finding that the determinant of the Jacobi matrix J is detJ = a 11 a 22 − a 12 a 21 and the trace is trJ = a 11 + a 22 , and noting that the equilibrium point is a stable state when detJ > 0 and trJ < 0, we derive the stability results in Table 3.
Based on the results of the analysis of the Jacobi matrix, we identify three evolutionary stable strategy (ESS), namely, (0,0), (0,1), and (1,1), which we discuss in six scenarios (Table 4, Fig. 4). Among them, four can achieve the stable equilibrium strategy of (0,0), and two can achieve the stable equilibrium strategy of (1,1) as follows:    Scenario 1: When A g − S − C a w > 0, 0 < C g + m C p < A g − S − C a w, and R e < C a − R a + R n < R e (1 + m) + S + C a w, (0,0) and (1,1) are the stable equilibrium points, and (0,1) and (1,0) are unstable points. Scenario 2: When A g − S − C a w > 0, C g + m C p > A g − S − C a w, and R e < C a − R a + R n < R e (1 + m) + S + C a w, or when A g − S − C a w < 0, C g + m C p > 0, and R e < C a − R a + R n < R e (1 + m) + S + C a w, (0,0) is the stable equilibrium point, (0,1) and (1,1) are saddle points, and (1,0) is an unstable point. Scenario 3: When A g − S − C a w > 0, 0 < C g + m C p < A g − S − C a w, and C a − R a + R n < R e , (1,1) is the stable equilibrium point, (0,0) and (0,1) are saddle points, and (1,0) is an unstable point. Scenario 4: When A g − S − C a w > 0, C g + m C p > A g − S − C a w, and C a − R a + R n < R e , or when A g − S − C a w < 0, C g + m C p > 0, and C a − R a + R n < R e , (0,1) is the stable equilibrium point, (0,0) and (1,1) are saddle points, and (1,0) is an unstable point. Scenario 5: When A g − S − C a w > 0, 0 < C g + m C p < A g − S − C a w, and C a − R a + R n > R e (1 + m) + S + C a w, (0,0) is the stable equilibrium point, (1,0) and (1,1) are saddle points, and (0,1) is an unstable point. Scenario 6: When A g − S − C a w > 0, C g + m C p > A g − S − C a w, and C a − R a + R n > R e (1 + m) + S + C a w, or when A g − S − C a w < 0, C g + m C p > 0, and C a − R a + R n > R e (1 + m) + S + C a w, (0,0) is the stable equilibrium point, (1,0) and (1,0) are saddle points, and (1,1) is an unstable point.
Based on the results of the asymptotic stability analysis of local equilibrium points, we derives three evolutionary stable strategies that pertain to different stages in the promotion of CCATs in agriculture. Among them, (0,0) is a relatively undesirable stable equilibrium strategy under which local governments do not promote and farmers do not adopt CCATs, which corresponds to the stage when the technology has not yet been promoted, i.e., the stage of application of traditional technology. (1,1) and (0,1) are two relatively ideal equilibrium strategies. Under the equilibrium strategy (1,1), local governments promote and farmers adopt CCATs, whereby local governments effectively promote CCATs, which corresponds to the early stage of technology promotion; under the equilibrium strategy (0,1), local governments do not promote but farmers adopt CCATs, which corresponds to the later stage of technology promotion when farmers adopt CCATs. This scenario corresponds to the later stage of technology promotion when farmers have developed the habit of using CCATs.

Numerical simulation
To further test the accuracy of the model analysis and to explore the incentives of CCAT promotion in agriculture and its sensitivity, we conducted simulations using Matlab to analyze the evolutionary game process between local governments and farmers and the stability of the equilibrium strategy.

Model testing
According to the analysis of stable equilibrium strategy, the evolutionary game of promotion of CCATs in agriculture constructed in this paper can be stable equilibrium under scenarios 1-6. To verify the correctness of the model analysis, we set the parameters (Table 5) according to the constraints under the six scenarios to test the model. Based on research in Guangdong, Hubei, and Tibet in China, many rural areas governments have taken measures to promote CCATs, but the results are relatively limited, so we roughly estimate the probability that governments choose the promotion strategy x as 0.6 and the probability of farmers choosing the adoption strategy y as 0.5. We set the simulation period t to 20. The numerical simulation results show that there are two possible evolutionary stable strategies (Fig. 5), that is, (0,0) and (1,1), under scenario 1, and one stable equilibrium strategy under the other five scenarios. The simulation results are consistent with the model analysis, which shows the accuracy of our analyses of the stability of the equilibrium strategy of the evolutionary game of CCAT promotion with the participation of local governments and farmers. The results also show that when the initial probability of the strategies changes, only scenario 1 changes the stable equilibrium strategy, while under the other scenarios, the change in the initial strategy selection ratio does not affect the final stable equilibrium.

Sensitivity analysis
We further analyzed the sensitivity of the relevant influences through Matlab simulations. The focus is on the impacts of parameter changes with policy implications on the evolutionary game system. According to our analysis, the stable equilibrium under scenario 1 is not unique and corresponds to the real situation where the uncertainty in the behaviors of the agents of the promotion and adoption game in some regions leads to difficulty in policy formulation. Therefore, without loss of generality, the simulation is based on scenario 1, again assuming that the probability x of governments choosing the promotion strategy was 0.6 and the probability y of farmers choosing the adoption strategy was 0.4. We again set the simulation period t to 20.

Impact of local government risk subsidy and cost sharing on the evolution of the system
As shown in Fig. 6a, the results indicate that when S = 1, the probability of government promotion tends to 1, and the probability of adoption by farmers also tends to 1. However, when S = 2 and 3, the probability of government promotion tends to 0, and the probability of adoption by farmers also tends to 0. This suggests that as the one-time risk subsidy (S) provided by the local government increases, farmers' willingness to adopt strategies increases. However, when such subsidies become excessive, the local government may face high policy support costs and choose to withdraw promotion efforts. At this point, the policy incentives disappear and the willingness of farmers to adopt strategies decreases significantly. Similarly, the cost-sharing policy (w) has a similar impact path (Fig. 6b). In comparison, one-off risk subsidies are less effective than cost sharing in motivating farmers to adopt CCATs.
Our survey has revealed that the application of CCATs in many rural areas of China faces numerous challenges, including high technical barriers, high risk costs, and weak awareness among farmers. These factors make it difficult for farmers to independently bear the associated costs. Therefore, local governments have had to implement corresponding policy measures to promote the application of CCATs. As described in this paper, compared to one-time risk subsidies, cost-sharing policies are more targeted toward the implementation of technological usage. Therefore, local governments can improve farmers' willingness to adopt CCATs by implementing cost-sharing policies when promoting their use. At the same time, to prevent the loss of policy incentives and fraudulent behavior, it is necessary to appropriately increase the thresholds for risk subsidies and cost sharing to ensure that only farmers who genuinely require technical assistance receive support.

Influence of local governments' publicity on the evolution of the system
As shown in Fig. 7a, the results indicate that when C p = 1, the probability of government promotion tends toward 1, and the probability of adoption by farmers also tends toward 1. However, when C p = 2 and 3, the probability of government promotion tends toward 0, and the probability of adoption by farmers also tends toward 0. Similarly, as shown in Fig. 7b, the effect of promotion effort (m) and promotion cost (C p ) on the behavior of both parties is similar. This suggests that although publicity can promote the adoption of CCATs by farmers, it can also constrain the government's information dissemination efforts. When the publicity cost becomes too high, the government may choose to withdraw from promoting agricultural climate adaptation technologies. This, in turn, can significantly reduce the willingness of farmers to adopt such technologies.
In fact, many measures have been implemented in China's rural areas to promote CCATs, resulting in enormous administrative costs and even causing dissatisfaction among grassroots governments. However, the effectiveness of these measures is not apparent, with limited impact on farmers' technology adoption behavior due to the fundamental transfer costs associated with CCAT use. These findings are consistent with our research results. To maximize the effectiveness of propaganda, it is crucial to employ materials and channels that are suitable for farmers and complement them with other conditions for farmers to adopt CCATs. Efforts must also be made to reduce the transfer costs associated with adopting new technologies, such as improving financing access and reducing adoption risks. By doing so, the adoption rate of CCATs can be increased, which ultimately fosters sustainable agricultural development.

Impact of farmer revenue change and environmental preference on the evolution of the system
As shown in Fig. 8a, the results indicate that when R a − R n = − 1, the probability of government promotion tends toward  Impact of farmer revenue change and environmental preference on the evolution of the system 0, and the probability of adoption by farmers also tends toward 0. However, when R a − R n = 0 and 1, the probability of government promotion tends toward 1, and the probability of adoption by farmers also tends toward 1. This implies that farmers' adoption of agricultural climate adaptation technologies depends on the relative profitability of these technologies compared to traditional methods. Figure 8b shows that farmers' environmental preference benefits (R e ) positively affect their adoption of CCATs and the local governments' participation in the promotion. Therefore, it is important to enhance farmers' awareness of the environmental benefits of CCATs.
Based on our interviews with farmers, the primary considerations for adopting climate adaptation technologies are affordability and substantial benefits. Propaganda measures can influence their perspective on adopting such technologies and encourage a collective mindset toward universal adoption. However, if the benefits of these technologies are insignificant, government propaganda will have little effect. Substantial government subsidies can increase farmers' motivation to adopt climate adaptation technologies, as they reduce the costs associated with implementation. Therefore, policymakers must develop targeted policies that address farmers' concerns about cost and benefit to ensure successful adoption of climate adaptation technologies. This requires a multifaceted approach that includes education, training, risk reduction measures, and cost reduction strategies.

Discussion
Agricultural adaptation to climate change in China mainly focuses on adaptation in the cultivation sector, taking into account adaptation in an agricultural environment, water resources, rural construction, and ecosystems; under the leadership of local governments, farmers, enterprises, and scientific research institutions are working together to promote this (Chen et al. 2014;Huang et al. 2015;Jin et al. 2015;Tong et al. 2019;Tian et al. 2019). Since the Eleventh Five-Year Plan, China has issued the National 12th Five-Year Plan for Agricultural and Rural Economic Development, the National Modern Agricultural Development Plan (2016-2020), the National 13th Five-Year Plan for Rural Economic Development Plan, the National Work Programme for Farmland Water Conservation Demonstration Activities, and other policy documents, providing policy guidance to promote the implementation of adaptation actions in rural communities. Relying on the National Programme to Address Climate Change issued by the State in 2008, China has carried out several climate-resilient technology promotions in rural areas, especially for agricultural cultivation, adjusting and optimizing existing technologies and projects in response to climate change impacts in terms of selection and breeding of resistant varieties, strain tillage and cultivation management, monitoring and early warning and emergency effects, and promoting the demonstration and promotion of CCATs. These policies have achieved some good results.
The multistakeholder synergy between upper and lower levels of local governments, farmers, and social organizations is key to promoting the implementation of these measures. Based on the evolutionary game model, we discuss the impact of the main strategies for promoting climate adaptation technology, including publicity and education, subsidies, and cost sharing, on the evolutionary game system, as a result of the national context for promoting agricultural climate adaptation technology in the rural areas of China. Government involvement is necessary due to the presence of transfer costs in the application of agricultural production technologies and the risk aversion of farmers. Our findings also provide insights into the design of effective mechanisms for the promotion of CCATs in agriculture.
There is also a need to continuously optimize the design of mechanisms for CCAT promotion: (1) A well-designed institutional framework is crucial for the successful promotion of CCATs, and the lack of a top-level design is a major drawback facing us today.
In the future, it is essential to establish a joint governance system for the promotion and adoption of CCATs that involves multiple levels and entities. This would require strengthening the implementation of the primary responsibility for agricultural climate adaptation, as well as the local responsibility.
(2) Local governments are the leaders in the promotion of CCATs and the main providers of public goods for climate change adaptation in agriculture. In the future, there is a need to optimize risk subsidies and cost-sharing mechanisms for the promotion of CCATs in agriculture. Care should be taken not to multiply subsidies, which would lead to inefficient subsidies. Furthermore, it is necessary to continuously evaluate and monitor of policy measures to ensure their effectiveness and sustainability in promoting CCATs in agriculture. (3) Technology training can alleviate the inhibiting effect of risk aversion on farmer CCAT adoption behavior. The government should provide more opportunities for farmers to receive training on CCATs, improve the awareness of farmers' technology, and provide farmers with continuous technical guidance through technology training to promote the promotion of CCATs in agriculture. In addition, more effective promotion and CCATs in agriculture require supporting mechanisms for scientific and technological innovation and technical service systems, sound reeducation of farmers in the use of technology, and mechanisms for linking agricultural insurance and loans. This is the basis for the promotion of CCATs in agriculture.

Conclusions
CCATs have become an important means for farmers to cope with climate change and address the risks of natural disasters. However, little attention has been paid to the dynamic game mechanism of CCAT promotion between local governments and farmers, and the effectiveness and conditions of different policy measures. To address these issues, we analyze the interactive game process between farmers and local governments regarding CCAT promotion based on evolutionary game theory and propose relevant policy recommendations to promote CCATs in agricultural systems. The main findings are as follows: (1) Under suitable conditions, the evolutionary game of CCAT promotion can achieve three evolutionary stable strategy, namely, (0,0), (0,1), and (1,1). Four scenarios can achieve the stable equilibrium strategy of (0,0) and two scenarios can achieve the stable equilibrium strategy of (1,1). Based on the reality of the diffusion of CCATs in agriculture in China, government promotion with farmer adoption (1,1) is the ideal stable equilibrium strategy.
(2) The local governments' risk subsidy policies and costsharing policies have a certain incentive effect, but the effect is limited. One-off risk subsidies may initially incentivize farmers to adopt strategies, but when such subsidies become too high, policy incentives are lost, leading to decreased adoption rates. Cost-sharing policies prove to be more effective in encouraging farmers to adopt CCATs. (3) Publicity is an important measure to achieve the promotion of CCAT promotion in agriculture, and its motivational effects are evident. Furthermore, changes in farmer revenue changes before and after adopting CCATs and their environmental preferences are key factors that influence their technology adoption behavior. Farmers are reluctant to adopt CCATs when the benefits they receive from adoption are greater than those they would have received if they used traditional technologies; when their environmental preferences increase, their incentive to adopt CCATs increases, as does the government's incentive to participate in the promotion of CCATs.
This paper contributes to the literature on climate change adaptation technologies in agriculture by using evolutionary game theory to model the interactive game process between the local government and farmers. We also provide policy recommendations based on different scenarios to enhance the adaptation of agricultural systems to climate change. Our paper is among of the first to adopt a dynamic and comparative analysis of the effects of government policies on farmers' adoption of CCATs, which can enrich management insights on how to effectively promote CCATs in agriculture. However, there are also some shortcomings in this paper. To address the research problem, we focus on the evolutionary game analysis of both local governments and farmers. However, social organizations and enterprises have very important roles to play. They act as a bridge between the government, experts, and farmers and play an important role in the dissemination of knowledge, education, and technology. Future research should further consider the role of social organizations, enterprises, and other actors to analyze the synergistic mechanisms of CCAT promotion.
Author contribution Sun Yong: conceptualization, methodology, and writing-original draft. Ruihui Yu: formal analysis, validation, writing-review and editing, and supervision. Tai Chiu Edwin Cheng: writing-review and editing.
Funding This work was supported by the National Social Science Funds of China (Project No. 22&ZD192).

Data availability
The data underlying this article will be shared on reasonable request to the corresponding author.

Declarations
Ethical approval The research included in the current submission does not involve human or animal subjects, or involves pathological reports, etc.
Consent to participate All authors agree to participate in this study.

Consent for publication
All authors agree to the publication of this research in the journal. Manuscript is approved by all authors for publication.

Competing interests
The authors declare no competing interests.