Evolutionary Game and Strategy Analysis of Carbon Emission Reduction in Supply Chain Based on System Dynamic Model

: At the 75th session of the United Nations General Assembly, China proposed the ambitious goal of achieving carbon peaking by 2030 and carbon neutrality by 2060. To investigate the impact of emission reduction behaviors of upstream and downstream enterprises in the supply chain, this paper focuses on the inﬂuencing factors of the supply chain enterprises’ emission reduction decision-making. The study aims to explore the emission reduction behaviors of these enterprises in the context of China’s carbon trading market. Using the theory of system dynamics, an evolutionary game model was developed and simulated using AnyLogic software. The simulation analyzed the effects of carbon price, subsidies, and punishment strategies on the emission reduction decisions of supply chain enterprises, providing insights into their behavioral impact. The results demonstrate that punishment, subsidy intensity, and carbon price changes all inﬂuence the emission reduction decisions of upstream and downstream enterprises. Suppliers are more sensitive to carbon price, while manufacturers are more sensitive to subsidy intensity. Additionally, the closer the equilibrium carbon price, subsidy, and market are, the shorter the time for the emission reduction probability of both enterprises to stabilize. Therefore, it is recommended that supply chain companies increase their awareness of environmental responsibility and enthusiasm for green innovation, actively respond to the carbon trading system, improve their internal subsidy system, and promote green technology innovation.


Introduction
The carbon emission trading market is a market established based on the Kyoto Protocol. It is controlled by humans and aims to reduce global greenhouse gas emissions [1]. The market mechanism plays a significant role in realizing the reduction of greenhouse gas emissions and promoting China's double carbon goal (double carbon, which refers to achieving carbon dioxide peaking by 2030 and carbon neutrality by 2060, is a significant goal for China. The abbreviation is derived from the terms 'carbon peak' and 'carbon neutrality') [2,3]. As the world's largest carbon emitter, China's past rapid development has resulted in excessive carbon emissions. In the government work report on 5 March 2023, Premier Li Keqiang proposed to steadily promote energy conservation and carbon reduction while ensuring a safe and stable energy supply and promoting scientific and orderly carbon peaking and carbon neutrality in green and low-carbon development [4]. In contemporary China, promoting green technology innovation and building a green, low-carbon, and circular economic system are essential to achieve pollution and carbon reduction. Thus, reducing carbon emissions and establishing a global carbon trading market is a top priority. Green technology innovation is crucial to transform and upgrade the industrial structure and achieve high-quality development. It is the key engine to achieve the 'double carbon' goal [5].
Green technology innovation is a crucial element for upgrading industrial structure and achieving high-quality development. It serves as a key driver for the 'dual carbon' goal.
Scholars both domestically and internationally have analyzed China's green innovation from three perspectives: technology, systems, and culture [6].The industrial low-carbon transformation mechanism for achieving the goal of 'carbon neutrality and carbon peak' is a pressing issue for policy-making departments and the manufacturing industry. Can carbon pricing regulations, subsidy policies, and technological innovation incentives promote the realization of these goals in the manufacturing industry? Additionally, can the mutual incentive mechanism of upstream and downstream enterprises in the supply chain promote technological innovation to achieve low-carbon transformation? To address these questions, the academic community must conduct forward-looking research on supply chain emission reduction behavior under the carbon trading mechanism. Understanding the impact of different policies on enterprise emissions reduction efforts is a theoretical issue that requires urgent attention [7].
In recent years, there has been an increase in both domestic and foreign research on carbon trading and supply chains. However, there still remains a gap in knowledge. Domestic research on carbon trading mechanisms primarily focuses on policy design, market operation, and influencing factors. On the other hand, foreign scholars tend to concentrate on the environmental and economic benefits of carbon trading. More research is needed to explore the relationship between carbon trading and other factors.The effectiveness of carbon trading in promoting technological innovation among enterprises for the purpose of energy conservation and emission reduction is contingent upon a confluence of factors, including carbon pricing, tax rates, and subsidies. Alterations to any of these elements within the system may result in changes to the behavioral decisions of enterprises within the supply chain [8][9][10].
Consequently, drawing upon the principles of system dynamics theory, the present study shall concentrate on the technological innovation and technology subsidy conduct of supply chain firms. Specifically, a game-theoretic model shall be developed to examine the evolution of emission reduction behavior among supply chain enterprises. Furthermore, the impact of individual factors on the emission reduction behavior of firms shall be analyzed via numerical simulation.

Theoretical Basis Carbon Emissions Trading
Carbon emissions trading is a market-oriented policy tool aimed at controlling greenhouse gas emissions. It addresses the issue of environmental resource constraints by clarifying property rights and transferring the costs of carbon-dioxide-emitting enterprises to society through market-oriented means. The specific transaction method involves allocating carbon emission rights to various enterprises based on a comprehensive assessment of the environmental capacity and resource status in the region, as well as the total amount of carbon dioxide control. This creates a market where enterprises can trade carbon emission rights. Participation in carbon emissions trading is voluntary and dependent on an enterprise's external income and operating costs [11]. Enterprises with lower carbon emission reduction costs can sell their excess carbon emission rights to enterprises with higher carbon emission reduction costs. This allows the former to exceed their carbon emission reduction tasks, while the latter can avoid punishment for not meeting their own carbon emission reduction targets due to insufficient carbon emission rights. Therefore, both companies that choose to reduce emissions and those that choose to acquire them can benefit from carbon emissions trading. The essence of this trading is to allocate environmental resource rights through market mechanisms, thereby achieving the optimal allocation of resources and reducing the total amount of carbon emissions [12]. The carbon emission trading market utilizes the carbon price as a signal to encourage and incentivize companies to conserve energy and decrease emissions. Its goal is to optimize the allocation of carbon emission resources to effectively reduce the overall emission reduction costs of society while adhering to the established carbon emission reduction targets [13,14].
Recent studies on corporate green innovation and carbon trading have focused on various aspects. For instance, Xie, X.M. et al. conducted a longitudinal multi-case study to analyze the internal mechanism of the green transformation evolution process of manufacturing companies. This study enriched the attention-based view on green innovation and provided useful management insights for the green transformation and upgrading of Chinese manufacturing enterprises under the 'double carbon' goal from a practical perspective [15]. In their study, Hu, Y.F. et al. utilized double differences and analyzed the pilot project of carbon trading as a policy impact. They systematically evaluated the mechanism of carbon trading and discussed the controversy surrounding environmental regulation after its implementation. The authors suggest that these reforms provide valuable inspiration for future policy decisions [16]. Liao, W.L. et al. conducted an empirical analysis on the relationship between carbon trading pilot, a market-based environmental regulation method, and green economic growth. They concluded that carbon trading can effectively stimulate innovation and promote the growth of the green economy [17]. Feng, C. [18], Li, G.M. [19], Qi, S.Z. [20], Song, D.Y. and colleagues [21] have conducted research on the impact of the carbon emission trading mechanism on the green innovation of enterprises and the green economic growth of industries. Their study provides theoretical guidance and suggestions on how market-oriented policies can better promote corporate low-carbon technology innovation by clarifying the impact mechanism of market and policy factors on corporate green innovation.
The current research on the supply chain issues combined with carbon emission right trading mainly includes the following. Xia et al. [22] have conducted research on the supply chain problem in conjunction with carbon emission trading. Their study involves the construction and comparison of a game model of enterprises under three carbon emission reduction policies based on the authorized remanufacturing model. The authors have also analyzed the impact of government carbon emission reduction policies on the authorized remanufacturing supply chain. The authors Wu et al. developed game-theoretic models to examine various modes of carbon emission reduction costs using both historical emission and benchmark methods. They also investigated the effects of different carbon quota allocation methods on relevant variables [23]. The study conducted by Feng et al. [24] examined the impact of carbon emission links and carbon policy changes on the operational decisions of fresh low-carbon supply chains. Specifically, the authors focused on the scenario where retailers outsource logistics to third-party logistics service providers and producers undertake carbon emission reduction efforts. The findings indicate that the conduct regarding carbon emissions by members of the supply chain will have an indirect impact on the efficacy of carbon emission reduction initiatives undertaken by emission reduction enterprises. This outcome furnishes a dependable theoretical foundation for advancing the growth of a low-carbon fresh food supply chain in China. Guan, Z.M. examined the issue of dynamic optimization and coordination in supply chain collaborative green innovation. The focus was on decision makers who exhibit disappointment avoidance behavior and the dynamic changes in the green level of products [25]. In a low-carbon context, carbon emission rights are considered as a resource input for enterprise production and services, which can generate profits. As a result, the restriction and trading of carbon emission rights will eventually change the industrial structure and profit model of enterprises, ultimately affecting their profitability and production behavior. The low-carbon incentive effect of carbon emission rights varies across different industries. Scholars such as Xie, X.P. [26]; Luo, R.L. [27]; Qin, Y.H. [28]; Ke, L.S. [29]; Pang, Q.H. [30]; Huang, Z.C. [31]; Lu, L. [32]; Zhang, L.R. [33]; and Memari, Y. [34] have conducted research on the optimization of the supply chain under these conditions and provided constructive advice on how to adjust and optimize the carbon trading mechanism for the green transformation of the supply chain.

Research Method
The methods used in this study mainly focus on system dynamics and evolutionary games. System Dynamics (SD) is a methodology that does not rely heavily on data. It begins by analyzing the internal structure of a system and uses limited data to calculate and analyze complex problems. SD utilizes causality of various elements and computer technology to find solutions. This methodology is particularly useful in researching the carbon trading market as it involves complex high-order nonlinear dynamic equations [12,[35][36][37]. Evolutionary game theory is founded on the premise that individuals have limited rationality and explores how groups of individuals interact in a dynamic process to attain a state of equilibrium by utilizing learning, imitation, and strategic adaptation.The utilization of evolutionary game theory to analyze the dynamic processes of enterprises operating in the carbon trading market is a valuable tool for examining the strategic adjustments made by actors and identifying the key factors that influence emissions reduction. This approach provides significant analytical advantages when studying the carbon trading market.
(1) System dynamics is a modeling and analysis method used to study complex systems, including society, ecology, economy, and engineering. It has found extensive applications in various fields such as environmental management, urban planning, and medical care. Currently, scholars worldwide are conducting research on system dynamics. For instance, Sayyadi, R. et al. proposed a comprehensive method that evaluates sustainable transportation policies based on analytic network process (ANP) and system dynamics (sd). This numerical research highlights the significance of travel sharing policies [38] Cheng et al. [39] conducted a systematic analysis of the equilibrium and evolution law of the new energy vehicle market following subsidy withdrawal. This was achieved through the construction of a dynamic game model of the production SD of the new energy vehicle supply chain under the subsidy policy. Kong, Shi et al. [40] developed a system dynamics model of China's carbon emissions to predict the future trend of China's carbon emissions. The findings indicate that China's carbon emission reduction targets can be achieved primarily through technological innovation, while a deceleration in economic growth may impede the attainment of peak carbon emissions. Gao, Pan et al. conducted a dynamic study on Shanghai's carbon dioxide emissions and established a dynamic model of Shanghai's economy-energy-carbon emissions system in light of China's carbon peak and carbon neutral goals. They formulated specific and effective low-carbon measures for Shanghai, which can serve as a reference for the development and implementation path [12]. In their study, Luo, Z.D. et al. conducted a comparison of different methods for estimating carbon emissions and utilized a system dynamics model to construct a tourism carbon emission simulation system [41]. Daneshgar, S. et al. utilized a system dynamics model to construct a dynamic production profit model that simulates the operation of a reservoir system and the profit process of a hydropower producer [42]. Their study provides valuable insights for decision-making optimization in the electricity market [43].
(2) Evolutionary game theory has been applied by scholars to analyze the field of low-carbon manufacturing in enterprises. Both domestic and foreign researchers have conducted studies on evolutionary game theory, which includes: Cheng et al. [44] conducted research on the evolutionary game problem that arises between renewable energy generation enterprises and government incentives in the context of carbon trading. The study revealed that a distinct evolutionary stabilization strategy exists between the two parties under a dynamic reward and punishment mechanism. This finding has implications for the formulation of government incentive policies. In their study, Yang et al. [45] developed a decision model based on the Gounod model to analyze power generation in thermal power enterprises. The authors investigated the dynamic evolutionary trend of these enterprises' transformation under various carbon emission regulation contexts in China. The study aimed to provide effective guidance for promoting the clean transformation of thermal power enterprises in China. Cao et al. employed the principles of cleaner production and industrial symbiosis to develop a game model that examines the evolution of heaping practices in the context of a re-competitive market of manufacturer groups operating under a carbon trading mechanism. The authors investigated the production decisions and emission reduction behaviors of these groups and identified strategies for achieving evolutionary stabilization [46].Fu, Q.F. et al. focused on the positive impact of carbon emission reduction in the supply chain. They explored the behavior and strategy of suppliers and manufacturers towards carbon emission reduction input, and addressed the gap in the research on internal governance factors for carbon reduction in the supply chain. However, they also noted the need for further research on decision-making methods for emission input behavior [47].

Brief Summary
In the research on corporate emission reduction behaviors under the background of carbon emission rights trading, there has been limited exploration of technological innovation game issues. The choice of game methods is predominantly a master-slave game, however, the carbon trading market is often complex, with variable and difficult to quantify data. This paper aims to address this by combining evolutionary game theory with system dynamics. Using the evolutionary game matrix of carbon emission reduction of upstream and downstream enterprises in the supply chain, the factors that affect the carbon emission reduction behavior of enterprises in the context of my country's carbon trading market are calculated and analyzed. AnyLogic software is then used to create an SD simulation model, providing feasible strategies for enterprises in the carbon trading market from a supply-side perspective.

Evolutionary Game Model Construction
The study presents a model of the secondary supply chain, which includes suppliers and manufacturers. The model considers the carbon trading market mechanism, where upstream suppliers adopt eco-friendly technologies to reduce the carbon emissions generated per unit of product during the production process. As a result of the spillover effect, the downstream producer benefits from the technological advancements made by the upstream provider [40]. To address the issue of manufacturers taking advantage of suppliers' innovation without contributing to it, it is crucial for manufacturers to provide a certain level of innovation subsidy to suppliers to incentivize their technological advancements [48]. To comprehensively examine the impact of various factors on the carbon reduction strategies of upstream and downstream companies in the supply chain, several hypotheses have been developed while ensuring the original problem statement's coherence.

Hypothesis 1.
Whether the upstream and downstream enterprises in the supply chain are all subject to carbon emission regulations: yes.
The carbon trading market mechanism is initiated by government authorities setting carbon emission targets. Each entity is then issued carbon emission rights in the form of allowances. These entities have the option to either sell their carbon emission rights in the market or reduce their emissions independently to comply with the required emission reduction standards.This study posits that both suppliers and manufacturers, as business entities, are subject to carbon emissions regulations and can participate in the carbon trading marketplace. Supplier decision-making behavior can be broadly categorized into two types: first, purchasing carbon credits without reducing emissions, and second, utilizing innovative green technology to achieve the objective of reducing carbon emissions. This study categorizes manufacturers' decision-making behavior into two primary types: providing innovation subsidies to suppliers or refraining from providing them. Table 1 presents the strategy combination matrix used by both upstream and downstream companies during the game process.
Hypothesis 2. Whether the emission reduction decision-making behavior of upstream and downstream enterprises in the supply chain is influenced by carbon price: yes. This can be broken down into specific points: H2a: Whether the suppliers' emission reduction behavior is influenced by the carbon price: yes. H2b: Whether the manufacturers' emissions reduction behavior is influenced by the carbon price: yes.
The growth of the carbon market heavily relies on its price mechanism, which acts as a policy instrument to reduce emissions and associated costs. The price of a commodity is determined by several factors, such as the pricing mechanism, allocation of allowances, compensation mechanisms, trading model, market openness, and regulatory framework. These factors have different levels of influence on the price formation process.
In accordance with the theory of price elasticity of demand [40], it can be inferred that the demand for carbon credits would be at its peak and the price of carbon would be lower if both the manufacturer and the supplier opt to "reduce emissions". This would entail the supplier engaging in innovative practices while the manufacturer provides innovation subsidies to the supplier. It is assumed that the market price of a unit of carbon credits at present stands at p H . Conversely, if both the manufacturer and the supplier choose to pursue alternative courses of action, the demand for carbon credits may be impacted differently. In the scenario where both the manufacturer and the supplier opt to purchase carbon credits in the carbon trading market, without any innovation from the supplier or subsidization of innovation from the manufacturer, the carbon price is estimated to be p L . However, if one party chooses to adopt an emission reduction strategy while the other does not, the carbon price will be calculated as p M and p L < p M < p H .

Hypothesis 3.
Whether there is a cooperation or incentive mechanism between upstream and downstream enterprises in the supply chain, and that motivates them to reduce emissions: yes. This can be broken down into specific points: H3a: Whether the manufacturers' emission reduction behavior is influenced by the punishment and subsidies: yes H3b: Whether the supplier's emission reduction behavior is influenced by the punishment and subsidies: yes.
Assuming a mutual agreement between the upstream and downstream entities, failure on the part of the upstream supplier to engage in environmentally-friendly innovation without subsidy from the downstream supplier is deemed as "free-rider" conduct and is punishable by a penalty referred to as N m . Conversely, if the downstream manufacturer provides subsidy while the upstream supplier fails to innovate in a green manner, a penalty known as N s is imposed. Table 2 displays the meanings and symbols, while Table 3 presents the pertinent elements of the earnings matrix.
During the course of gameplay, the strategies employed by both parties will undergo continuous adjustments. Table 3 displays the benefits matrix. It is assumed that the probability of the supplier opting out of technological innovation is (1 − x), where x is a value between 0 and 1. The supplier selects between two strategies, namely the "technology innovation" strategy (U 1 ) and the "no technology innovation" strategy (U 2 ), withŪ representing the supplier's anticipated overall return.
Let the probability that a manufacturer chooses not to subsidize be (1−y) (0 y 1). Then, the manufacturer chooses the "subsidy" strategy (V 1 ), the "no subsidy" strategy (V 2 ), and (V) represents the overall expected return to the manufacturer.
The equations governing the replication dynamics of the supplier and manufacturer are derived from the evolutionary game replication dynamics equation:

Cause-and-Effect Loop Diagram
The extent to which suppliers engage in technological innovation is influenced by factors such as the price of carbon, the subsidy per unit of product, and the penalties incurred under different decisions. On the other hand, whether manufacturers subsidize suppliers is determined by factors such as the price of carbon, the penalties incurred under different decisions, and the subsidy per unit of product. The causal loop diagram of the system dynamics model provides a clear representation of the interaction between these elements. This paper proposes a model for reducing emissions in the supply chain, which is divided into two subsystems: a manufacturer technology innovation strategy and a supplier subsidy strategy. The paper analyzes the cause-effect relationships and establishes causal loop diagrams to better understand the intrinsic factors at play.

Supplier Technology Innovation Strategy Sub-System
The diagram depicted in Figure 1 illustrates the supplier technology innovation system. The "+" indicates that the variable at the beginning of the arrow is positively correlated with the end variable, and the "−" indicates that the variable at the beginning of the arrow is negatively correlated with the end variable. This causality diagram consists of the following main The following five feedback loops are included. Among these, Loop 1 and Loop 2 function as the carbon trading market mechanism, thereby facilitating equilibrium in the carbon trading market. Loops 3, 4, and 5 serve as a mechanism for mutual regulation within supply chain enterprises, promoting the advancement of environmentally sustainable and coordinated development among upstream and downstream enterprises in the supply chain. Furthermore, enterprises that opt for the technology innovation strategy and those that opt for the technology subsidy strategy are both categorized as entities that select the emission reduction strategy.
Loop1: Firms that choose emission reduction strategies→Expected benefits of non technological innovation →Expected return margin for suppliers→Probability of technological innovation→Firms that choose emission reduction strategies Loop2: Firms that choose emission reduction strategies→Expected benefits of technological innovation→Expected return margin for suppliers→Probability of technological innovation→Firms that choose emission reduction strategies Loop3: Firms that choose emission reduction strategies→The penalty for not innovating but subsidizing→Expected return margin for suppliers→Probability of technological innovation→Firms that choose emission reduction strategies Loop4: Firms that choose emission reduction strategies→Subsidy→Expected benefits of technological innovation→Expected return margin for suppliers→Probability of technological innovation→Firms that choose emission reduction strategies Loop5: Firms that choose emission reduction strategies→The penalty of innovation but not subsidizing→Expected benefits of technological innovation→Expected return margin for suppliers→Probability of technological innovation→Firms that choose emission reduction strategies The market mechanism is responsible for the impact of an increase in the number of firms on the supply and demand of carbon credits, regardless of whether or not they receive technology subsidies. Changes in the carbon price prompt firms to spontaneously modify their emission reduction strategies. During Loop 1, if fewer firms choose to implement an abatement strategy, there will be a surplus of carbon credits in the market. This surplus will cause an increase in the carbon price, which will in turn lead to a decrease in the expected return for firms that opt not to innovate their technology. As a result, the disparity in expectations between the two choices becomes more pronounced, prompting an increase in the number of companies that choose to develop new technologies. This adaptation ultimately results in the achievement of the equilibrium quantity.
Manufacturers have the ability to adjust the subsidy they provide to suppliers based on the level of supplier motivation to innovate. This adjustment can prompt suppliers to modify their strategy in order to increase their motivation to innovate. In the fourth iteration of the loop, it was observed that the manufacturer responded to a low number of suppliers' technological innovation firms by increasing the expected benefits of supplier technological innovation. Increasing the subsidy provided to suppliers per unit of product amplifies the expected benefits of the two decisions, resulting in a higher likelihood of supplier technological innovation and an increase in the number of firms undertaking technological innovation.

Manufacturer Subsidy Strategy Sub-System
As shown in Figure 2, the manufacturer subsidy strategy system has five main balancing loops, of which Loop 1 and Loop 2 play the role of carbon trading market mechanisms and are regulating loops. Loop 3 and loops 4 and 5 are augmentation loops.
Loop1: Firms that choose emission reduction strategies→Expected benefit of non subsidy→Expected return margin for manufacturers→Probability of subsidy→Firms that choose emission reduction strategies Loop2: Firms that choose emission reduction strategies→Expected benefit of sub-sidy→Expected return margin for manufacturers→Probability of subsidy→Firms that choose emission reduction strategies Loop3: Firms that choose emission reduction strategies→The penalty for not subsidizing but innovation→Expected benefit of non subsidy→Expected return margin for manufacturers→Probability of subsidy→Firms that choose emission reduction strategies Loop4: Firms that choose emission reduction strategies→Subsidy→Expected benefit of subsidy→Expected return margin for manufacturers→Probability of subsidy→Firms that choose emission reduction strategies Loop5: Firms that choose emission reduction strategies→The penalty for not innovation but subsidizing→Expected benefit of subsidy→Expected return margin for manufac-turers→Probability of subsidy→Firms that choose emission reduction strategies

Stock Flow Diagram
This study presents a simulation model based on system dynamics (SD) to analyze the effectiveness of emission reduction strategies adopted by upstream and downstream enterprises in the supply chain. The model was developed using a causal feedback diagram and benefits matrix. The state variables considered in the model are the probability of manufacturer subsidy and the probability of supplier technological innovation. The rate variables are defined as the rate of change of technological innovation and the rate of change of subsidy. The study presented a system flow diagram, as shown in Figure 3, that outlines the emission reduction decisions made by the enterprises being examined. To analyze the impact of changes in four parameters on the emission reduction strategies of upstream and downstream enterprises in the supply chain, the researchers utilized AnyLogic's SD simulation model. This study investigates the impact of different parameters on the effectiveness of a policy aimed at promoting innovation in the supply chain. The parameters examined include the carbon price, the subsidy per unit of product provided by the manufacturer to the supplier, the penalty imposed when the manufacturer provides subsidies but the supplier fails to innovate technology, and the penalty imposed when the supplier innovates technology but the manufacturer does not provide subsidies [50].

Data Simulation and Analysis
Given the authenticity and availability of data, based on the introduction of dynamic equations and the above constraints, this paper refers to the China Carbon Emissions Trading Network, the China Carbon Market Review and Outlook (2022), and the 2021 Study on Domestic Carbon Price Formation Mechanism and assigns values to the relevant parameters in the light of the actual situation, as shown in Table 4. The average daily transaction price of the national carbon market in 2022 fluctuates within the range of RMB 40-60 per ton. So set the carbon price p M = 50 and the relevant values for the remaining parameters are set as follows: β = 0.2, q = 50, r s = 0.5, r m = 0.4, C = 2500, π s = 100, π m = 100. Since the initial probability of upstream and downstream supply chain firms is not the focus of this paper, a probability of 0.5 for supplier technological innovation and a probability of 0.5 for manufacturer subsidy are assumed, that is x = y = 0.5. (The China Carbon Emissions Trading Network, available at http://www.tanpaifang.com/ (25 April 2023), calculates the average carbon price based on online transaction data from seven carbon trading pilot cities in 2020). In this paper, we propose a three-level model approach to analyze the influence of punishment strategy, subsidy intensity, and carbon price on the emission reduction strategies of manufacturers and suppliers. Their horizontal pattern variables are shown in Table 5.

The Impact of Carbon Prices on Corporate Decisions to Reduce Emissions
This study examines the impact of carbon pricing on upstream and downstream enterprises in a supply chain when the agreed punishment strategy is medium-level (N s = 1300, N m = 1500) and high-level (N s = 1500, N m = 1800), and the manufacturer's subsidy decision is a low-level subsidy strategy (d = 5). The study investigates whether the decision to reduce emissions has an impact. Figure 4 shows the evolutionary impact of changes in carbon price (p) on the decision-making behavior of supply chain enterprises while keeping other parameters unchanged. The horizontal axis represents the simulation time, and the vertical axis represents the probability of the enterprise choosing to reduce emissions. The line segments in the figure represent the change trend of the enterprise's emission reduction probability at different price levels.
Based on the simulation results, it can be observed that as the carbon price (p) increases, the evolution path of supply chain emission reduction also changes. Specifically, when p is low (p = 40), the evolution path tends towards (0,1). At a medium level (p = 50), the evolution path shifts towards (1,1). Finally, when p is high (60), the evolution path tends towards (1,1). The study found that: (1) when the carbon trading price (p) is set at 40, the supplier is more likely to break the contract, fail to innovate technologically, and provide subsidies. (2) However, when p is set at 50, the path evolves into (1,1), indicating a qualitative change in the emission reduction decisions made by manufacturers and suppliers. This suggests that there exists a value ε ∈ (20,40), where only when the carbon trading price exceeds this value will the supplier consider improving carbon emission efficiency through technological innovation and trade in the carbon market to obtain surplus. (3) Furthermore, when p is set at 60, the time for the supplier's technological innovation probability to stabilize is 0.34 years and 0.04 years, indicating that the path evolution probability is increasing at a faster rate. In addition, as shown in Figure 5, when both parties agree on a high-level punishment and a low-level subsidy, and the carbon price is set at 40, 50, and 60, respectively, the time it takes for the supplier's technological innovation probability to stabilize decreases as the carbon price gets closer to the market equilibrium price. This suggests that carbon prices must fluctuate within a reasonable range to have a positive impact on companies' emission reduction efforts. Additionally, the closer the carbon price is to the market equilibrium price, the shorter the time it takes for the probability of corporate emission reduction to stabilize.  The study found that: (1) When a low carbon price is combined with a medium-level model penalty and a low-level subsidy strategy, suppliers may be more likely to break the contract. Additionally, small fluctuations in the carbon price and subsidy levels will not encourage suppliers to make emission reduction decisions. In this scenario, incentives do not motivate suppliers to invest in technological innovation. Manufacturers may be more willing to provide subsidies as a means of encouraging suppliers to reduce emissions and gain a competitive advantage in the market. (2) When the carbon price is at a medium or high level, the system tends to evolve towards (1,1), with the supplier's decision-making on emission reduction evolving at an increasingly rapid pace. It is evident that as the carbon price approaches the market equilibrium price, the likelihood of technological innovation by the supplier also increases, leading to a shorter time for stabilization. (3) Excessive carbon prices incentivize suppliers to engage in technological innovation. In response, suppliers tend to purchase new equipment and improve their technological capabilities. Furthermore, manufacturers face economic pressure to reduce emissions, which leads them to provide subsidies to suppliers as a means of encouraging further innovation.

Impact of Penalty Strategies on Firms' Emission Reduction Decisions
The use of punishment strategies serves as a fundamental method to incentivize both parties in the supply chain to comply with the terms of the contract. This approach can effectively motivate supply chain enterprises to reduce their emissions. In instances where a supplier implements technological advancements, a low-level subsidy strategy (d = 5) is typically employed by the manufacturer to incentivize the supplier's efforts. The impact of penalty strategies on upstream and downstream enterprises in the supply chain is explored when the carbon price is in the middle-level mode (p = 50), while the initial value of other parameters remains unchanged. The figure below ( Figure 6) illustrates the probability of enterprise emission reduction when different values are taken, displaying the trend of the evolution of the value change of the penalty strategy on the enterprise's decision-making behavior.
Based on the simulation results, it can be observed that the evolution path of the supply chain emission reduction system tends to (0,1) when the penalty strategy is at a low level (N s = 200, N m = 500). Similarly, when the penalty strategy is at a medium level (N s = 1300, N m = 1500), the path tends to (1,1). Moreover, when the penalty strategy is at the middle level (N s = 1500, N m = 1800), the evolution path of the supply chain emission reduction system tends to (1,1).The specific analysis is provided as follows: (1) When the punishment for non-compliance is low and the subsidy offered by the manufacturer to the supplier is also low, the supplier is more likely to breach the contract and avoid investing in technological innovation. In such cases, the supplier may choose to prioritize external returns over a small subsidy. (2) When the penalty strategy is set at the middle or high level, it is likely that the supplier will increase their investment in technological innovation, and the probability of the manufacturer providing subsidies for technological innovation to the supplier will also increase significantly. (3) When the penalty strategy is set to middle or high level, the time it takes for the supplier's technological innovation probability to stabilize is 0.33 years and 0.03 years, respectively. This suggests that as the penalty parameter increases, the supplier's technological innovation probability stabilizes more quickly, with higher penalties resulting in shorter stabilization times.
To further examine the impact of high-level punishment strategies on the emission reduction decisions of supply chain enterprises, we conducted a study with a high-level punishment model (N s = 1500, N m = 1800) and a low-level subsidy strategy (d = 5) at different levels of research carbon price. Figure 5 illustrates the performance of the supply chain evolution system in this model. Regardless of whether the carbon price is low, medium, or high, the evolution path of the supply chain tends towards (1,1). This indicates that when the punishment is strong enough, manufacturers and suppliers will choose to cooperate, irrespective of the carbon price level.
The study found that: (1) When the manufacturer's subsidy to the supplier is low, meaning that the subsidy has the least impact on the supplier's decision to reduce emissions, both medium and high-level punishment strategies can encourage the supplier to innovate technologically and the manufacturer to provide subsidies. This is due to the fact that the higher cost of breaching the contract will deter both parties in the supply chain from engaging in breach behavior. (2) Even when the penalty strategy is set at a high level, the system evolution path still tends towards (1,1), suggesting that the relationship between the penalty strategy and the probability of corporate emission reduction is not a simple positive correlation. (3) As the punishment agreed upon in the supply chain becomes stronger, the supplier's decision regarding technological innovation evolves at a faster pace. It can be observed that as the penalty parameter increases, the time taken for the probability of the supplier's technological innovation to stabilize decreases.

The Impact of Subsidy Strategy on Enterprises' Emission Reduction Decisions
This study examines the impact of subsidy strategy on emission reduction decisions of upstream and downstream enterprises in the supply chain when the punishment agreed by both parties in the supply chain is the medium-level strategy (N s = 1300, N m = 1500) and the carbon price is in the medium-level mode (p = 50). Figure 7 illustrates the evolution of penalty strategy on enterprise's decision-making behavior while keeping the other parameters constant. The line segment in the figure shows the change trend of the enterprise's emission reduction probability for different values of d.
Based on the simulation results, it is evident that the evolution path of supply chain emission reduction tends towards (1,1) when the technological innovation subsidy offered by the manufacturer to the supplier is at a low-level model (d = 5). Moreover, even when the subsidy model is at a medium or high level (d = 22 or d = 35), the evolution path of supply chain emission reduction still tends to (1,1). The specific analysis is provided as follows: (1) When the agreed punishment for breaking a contract is relatively severe, regardless of the level of subsidy strategy, the cost of breaking the contract becomes a significant burden for both parties involved. As a result, manufacturers and suppliers are more likely to choose to cooperate. (2) In cases where d takes the values 5, 22, and 35, the stabilization time for the supplier's technological innovation probability is 0.34, 0.1, and 0.07 years, respectively. It is evident that the supplier's technological innovation probability increases as the subsidy approaches the equilibrium subsidy, resulting in a shorter stabilization time. In order to investigate the sensitivity of the manufacturer's emission reduction decision to the level of subsidies, this study examines the emission reduction behavior of supply chain enterprises under different subsidy levels (high level: d = 50), penalty modes (medium level: N s = 1300, N m = 1500, high level:N s = 1500, N m = 1800), and carbon prices (low level: p = 40, medium level: p = 50).The study found that in scenarios where there is a medium-level penalty mode and a low-level carbon price, the supply chain emission reduction evolution path tends towards (0,0). In situations where there is a medium-level penalty mode and a medium-level carbon price, the path tends towards (1,0) as suppliers are likely to carry out technological innovation, while manufacturers tend to break contracts. When there is a high-level penalty mode and a low-level or medium-level carbon price, the path tends towards (1,1). The study also suggests that suppliers are more sensitive to carbon price fluctuations, while manufacturers are more responsive to subsidies, as demonstrated in Figures 7 and 8.
To reduce carbon emissions and improve supply chain efficiency, upstream and downstream enterprises can employ effective strategies such as carbon pricing, subsidies, and punishments. When carbon pricing falls within a certain threshold range, it can positively incentivize suppliers' technological innovation strategies. However, if it falls outside of this range, it will not significantly impact suppliers' technological innovation probability. Punishment strategies are not always positively correlated with suppliers' technological innovation probability and manufacturers' subsidy probability. Instead, there is a specific threshold interval where a positive correlation can be observed.

Incentive Policies for Technological Innovation in the Context of Carbon Trading
Since the Kyoto Protocol was established in 1997, the idea of reducing emissions through Dales' emission trading has gained widespread acceptance in the climate field. This has led to the development of national and regional carbon emission trading markets. However, unlike the international emissions trading mechanism, carbon emission rights trading within a country or region is mostly limited to micro-enterprises within the jurisdiction. These enterprises must determine their current carbon emission cap, and then choose whether to reduce emissions independently or purchase allowances to reduce unit emission reduction costs based on initial quotas, their own industry attributes, and emission reduction capabilities. The UK has been taking various measures to support low-carbon development. In 2002, the UK established the UK Emissions Trading System (UK ETS) to pave the way for green finance. In 2009, the 'Loan Guarantee Plan' was introduced to provide subsidies and guarantees for SME financing, encouraging SMEs to invest in green industries and promoting the capital needs of SMEs for green production. The 'Green Finance Strategy' was released in 2019, with a focus on green finance, financing, and a solid foundation. To further support green finance, the British government invested GBP 100 million to establish the Green Finance and Investment Center, which provides world-class data and analysis services to companies, banks, schools, and other organizations around the world to help them achieve green and low-carbon transformation and make better business decisions in the face of environmental and climate change [51]. Studies in the UK have indicated that fostering small and medium-sized enterprises (SMEs) in the clean technology sector can have a positive impact on green technology innovation, address developmental concerns such as cleanliness, energy supply, and climate-resilient agriculture, and also generate employment opportunities while transforming traditional manufacturing industries. By shifting the unemployed labor force towards the clean technology sector, it is possible to achieve multiple benefits in terms of employment, environmental sustainability, and economic development. Japan, at the enterprise level, shares similarities with the United States and the European Union. It employs policies to guide industry development, sets carbon emission limits, and provides financial subsidies and other measures to encourage enterprises to voluntarily adopt carbon emission reduction measures. This approach gradually changes the concept of enterprise development, leading to low-carbon development of enterprises. Japan also leverages market-oriented mechanisms to promote green technology innovation and application, maintain core technological advantages, and continuously advance the development of green industries. Additionally, Japan has established carbon emissions trading schemes such as the Resource Emissions Trading Scheme (JVETS), the Verified Emissions Reduction Scheme (JVER), and the carbon emissions trading organized by local governments, such as the Tokyo Emissions Trading System. These market mechanisms encourage enterprises to participate in emission reduction activities voluntarily.
China has placed significant emphasis on establishing a carbon trading market to meet carbon reduction commitments and control carbon emissions. In October 2011, the National Development and Reform Commission approved the pilot work of carbon dioxide emission trading in seven provinces and cities, including Beijing, Tianjin, and Shanghai. The pilot program focused on high-pollution and high-emission industries, such as iron and steel, electric power, the chemical industry, and papermaking, with the aim of encouraging enterprises to reduce emissions through total quota control and trading emission quotas. In 2014, Shenzhen issued the 'Shenzhen Business Development Incentive Measures' to encourage more companies to enter the carbon market. While the carbon market initially declined, it later rose and eventually stabilized. However, the implementation of policies in China has not fully utilized taxation, subsidies, and other means to guide and encourage companies. The coexistence of subsidy gaps and excessive subsidies in some new energy industry price subsidies has led to some companies over-relying on subsidy policies, which has affected the impact of the market price mechanism on enterprises [52].

Coordinate the Innovation of Supply Chain Enterprises
Theoretical research has focused on low-carbon supply chain operation management in recent years. Practically, there is an urgent need to solve the problem of low-carbon transformation of the supply chain through carbon trading mechanisms. This paper proposes a two-tier supply chain structure consisting of upstream suppliers and downstream manufacturers to play an emission reduction game. Suppliers and manufacturers have bounded rationality and can adjust and improve their strategies until they reach evolutionary stability. Scholars have conducted research on supply chain carbon emissions in recent years, achieving important research results with the development of game theory and the continuous improvement of the carbon trading mechanism [11,19,24,[27][28][29][30][31][32][33][34][35]47,48]. However, there are still gaps in the existing research as none of them have taken into account the spillover effect of carbon emission reduction investment in the supply chain. This effect provides a 'free ride' motivation for each node enterprise in the supply chain, which in turn impacts the decision-making of each node enterprise and leads to new characteristics in their behavior evolution. This paper proposes two hypotheses: first, the decision-making behavior of upstream and downstream enterprises in the supply chain regarding emission reduction is influenced by the carbon price, and second, the cooperation mechanism between enterprises in the supply chain motivates their emission reduction behavior or green transformation. The study found that under the condition of extremely low subsidies and moderate penalties, the carbon price within a certain threshold affects the emission reduction behavior of enterprises. Additionally, the research results show that the strategic choice of suppliers and manufacturers is related to their carbon emission reduction investment-benefit ratio. For example, when the penalty is high, both parties tend to choose emission reduction, but when the carbon price is low and the subsidy is low, the supplier's carbon emission reduction investment will be higher than its other counterparts. Therefore, they will be more inclined not to carry out technological innovation.
The growing awareness of corporate environmental protection and the increasing demand for low-carbon products by consumers has made low-carbon production the only way for corporate development. As a result, many corporate cooperation mechanisms have been established within the supply chain to encourage green innovation and low-carbon transformation. For instance, Zhang Kaipeng, senior vice president of Schneider Electric, has emphasized the need for companies to integrate carbon reduction goals into product design, parts procurement, manufacturing, transportation, delivery, and post-recycling key links to promote carbon reduction throughout the life cycle. In line with this, Schneider has committed to providing carbon emission reduction services for 1000 key suppliers by 2023, thereby creating an end-to-end green supply chain that encompasses green design, green procurement, green production, and green delivery. This underscores the role of the supply chain as a mechanism for transmitting carbon reduction efforts across the upstream and downstream of the supply chain.
To achieve carbon reduction, enterprises should implement carbon reduction measures throughout the entire supply chain and promote overall carbon reduction efforts. This requires a 'full life cycle perspective' approach, considering all stages of the supply chain from production to disposal. By adopting a comprehensive approach, enterprises can make a significant contribution to mitigating the impact of climate change.

Concluding Remarks
This study analyzes the impact of subsidies, penalties, and fluctuations in carbon prices on technological advancements in the context of China's aim to attain carbon neutrality by 2060. This study examines the impact of innovation subsidies and explores how changes in relevant parameters affect the probability of technological innovation and enterprise subsidies. The results provide a theoretical foundation for establishing appropriate carbon prices, subsidies, and penalties. In summary, this study's findings demonstrate the importance of innovation subsidies and suggest that policymakers should consider relevant parameters when designing policies to promote technological innovation and reduce carbon emissions.The study's findings can be summarized as follows: (1) The implementation of subsidy and penalty tactics, along with the fluctuation of carbon pricing, can impact the decisions of upstream and downstream firms in the supply chain to reduce their emissions. If the penalty for breaching the contract is significant, it is probable that both parties will comply with the agreement terms. If the penalty is not severe enough, suppliers may be more likely to break the terms of the contract. On the other hand, manufacturers may still provide financial incentives to reap the benefits of technological advancements.
(2) The implementation of a subsidy strategy will impact the decision-making process of both upstream and downstream enterprises in the supply chain, especially in relation to reducing emissions. The proximity of the subsidy to the equilibrium subsidy will determine how quickly the supplier's technological innovation probability stabilizes. The subsidy strategy has a defined threshold range within which it can positively influence the supplier's technological innovation decision-making and the manufacturer's subsidy decision-making. However, its impact is not significant outside of this range.
(3) As the carbon price approaches the market equilibrium, suppliers' technological innovation probability stabilizes more quickly. The impact of the carbon price on suppliers' behavior is greater than that of subsidies, which have a greater impact on manufacturers' behavior.
This paper presents an analysis of how corporations make decisions about reducing emissions by considering the policies of both upstream and downstream enterprises in their supply chain. Future research could investigate how emissions reduction strategies are negotiated among three or more parties in a supply chain. The constant increase in market demand following technological advancements has been well-established. However, future studies should take into account the impact of environmentally conscious consumer preferences and their willingness to adopt low-carbon products on the variability of this proportion.