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This study designs an Evolutionary Game Model (EGM) to analyze how Carbon Reduction (CR) responsibilities are shared between government entities, enterprises, and citizens during China’s Carbon Peaking (CP) and Carbon Neutrality (CN) targets. The research builds a three-player EGM to study how China manages CR obligations across its climate policy framework. The model reproduces the interactions between government agencies, businesses, and citizens while incorporating factors such as government intervention, corporate approaches, and public participation. The game system achieves its optimal outcome through the positive benefits of resident participation in CR combined with balanced costs or business advantages. Research findings show that organizations without government monitoring can adopt Low-Carbon Production (LCP) techniques while citizens become active participants in the development of Low-Carbon Societies (LCS). The research demonstrates that the government should broaden its scope from just economic regulation costs to take an active part in encouraging public involvement and responsibility in CR initiatives. The study results establish vital knowledge that helps policymakers create practical responsibility-sharing systems that unite governmental agencies with businesses and communities to achieve CR objectives for national and worldwide climate strategies.
Introduction
China’s Dual Carbon Goals (DCGs) set two critical targets for 2030 and 2060, which encompass sector-wide climate objectives for emission reduction and international commitment fulfillment. A quantitative analysis of 41 national policy documents demonstrated significant climate policy changes, which proved that institutional capacity, policy priorities, and sectoral integration determine Climate Policy Integration (CPI). The research proves that successful Climate Change (CC) management depends on sectoral integration while identifying multiple barriers to green economic development alongside clean energy transitions (Xu et al. 2024; Bao and Jin 2025). China has introduced a sequence of “dual-carbon” policies between 2021 and 2022 to promote sustainable advancement and fulfill the “Dual-Carbon” target. The advancement of the “dual-carbon” objective requires defined emission reduction rights along with corresponding duties and responsibilities. Through its normative and obligatory nature, law provides both clarity and stability for this process. The implementation of the “dual-carbon” strategy demands a clear legal definition of obligations, which must be supported by ongoing legislation. Legal accountability ensures that legal standards work efficiently, which serves as the foundation for their proper implementation. The creation of a well-defined legal accountability framework serves as a crucial foundation for legislative initiatives because its empirical basis determines the implementation of legal standards (Liu et al. 2024).
The development of an organized system for legal responsibility forms the essential basis for legislative programs. China maintains a complete environmental responsibility framework, which lacks specific CR responsibilities for Greenhouse Gas Emission (GHGE) management. Environmental regulation evolves rapidly to address gaps and establish better accountability systems, while ecological civilization continues its development (Ji et al. 2024).
The initial step in addressing the question of how to distribute the burden of Greenhouse Gases (GHGs) among the global community is to clarify the fundamental principle of GHGE allocation (Dong et al. 2023), that will subsequently be used as the basis for each country’s GHG registration. A new set of responsibility rules are the results of present research for minimizing Carbon Dioxide (CO2) responsibility. These studies mainly focus on the ways in which the Carbon Emission (CE) liability is shared among various parties responsible for the problem.
The producer accountability principle, which is an offshoot of the “polluter pays” principle, states that producers have to take the necessary steps to reduce GHGEs caused by the burning of fossil fuels that occur during the manufacturing process (Xu and Chen 2025). It highlights emissions directly from the source, making monitoring easier and showing an area’s potential for CR. This concept has been largely adopted in early stages because of its straightforwardness and clear responsibility (Pan et al. 2008). It could, however, lead to an unfair distribution of the tasks and carbon leakage because it ignores the implicit carbon transfer, particularly from the developing countries that are not well equipped with low-carbon technology (Peters 2008). The principle’s shortcomings, despite its simplicity, impede efficient CR, particularly with carbon-intensive items (Li and Qi 2024; Kong et al. 2024). The consumer responsibility principle, proposed by scholars, in addition, at the micro level, scholars have mostly studied the game between the government and producers as well as consumers based on the perspectives of cooperation and management of CR.
Research on the allocation of CR responsibilities has established several principles, concentrating on both production and consumption aspects. These models vary according to the locus of responsibility, with researchers evaluating their benefits and suggesting carbon mitigation measures accordingly. Although current research predominantly enhances the theoretical framework of the “polluter pays” and “beneficiary pays” principles, it inadequately investigates the responsibilities of various social actors (government, enterprises, and residents) at the micro level. The intricacy of CR accountability stems from the varied interests of these stakeholders, resulting in conflicts that game theory can resolve. Game theory facilitates the analysis of strategic decisions and the influence of normative constraints on the CR process. However, currently, under the background of the “dual carbon” policy, there is still a lack of systematic research on the strategic interaction and dynamic evolution relationship between government regulation, low-carbon innovation of enterprises, and public participation. In view of this, this article intends to focus on exploring the following three issues: (1) How can the government, enterprises, and the public form an interactive relationship in fulfilling their carbon reduction responsibilities? (2) How will the equilibrium strategies of various entities dynamically evolve under different policy constraints and cost conditions? (3) What insights does the above interactive mechanism provide for building a fair and effective responsibility sharing system?
To answer these questions, this article constructs an evolutionary game model (EGM) that covers the three parties of government, enterprises, and residents, in order to reveal the strategic evolution law of multi-party carbon reduction behavior, and based on this, propose policy recommendations to promote collaboration and efficient emission reduction, hoping to provide theoretical support and institutional reference for the realization of China’s “dual carbon goals”.
Literature review
The definition and allocation of carbon emission reduction responsibilities have always been a core issue in environmental governance research, which is related to the reasonable division of costs, benefits, and obligations among different social entities within the framework of global climate goals. The academic community has proposed various theoretical paths around the division of responsibilities, gradually developing from the early producer responsibility and consumer responsibility models to a comprehensive framework emphasizing multi-party participation and shared responsibility. The following literature review will systematically sort out this evolutionary trajectory from three aspects: (1) theoretical foundations of carbon reduction responsibility, (2) empirical studies and modeling advances, (3) evolutionary dynamics and policy implications.
Theoretical foundations of carbon reduction responsibility
Munksgaard and Pedersen (Munksgaard and Pedersen 2001) believe that consumers should share responsibility for carbon emissions (CEs) during the production and consumption process based on the principle of “beneficiary pays”. This viewpoint addresses issues such as indirect emissions and implicit carbon transfer that cannot be covered by the principle of producer responsibility (Ferng 2003). Kondo (Kondo et al. 1998) first proposed the “consumer responsibility principle”, believing that it is unfair for a single party to bear carbon emission reduction obligations in international trade. He advocated for proportional distribution of responsibility between exporters and importers, and extended this principle to the level of the industrial chain, emphasizing the shared responsibility of producers, consumers, and suppliers for direct and indirect emissions (Wang et al. 2023a, b). Marques et al. (Marques et al. 2012) pointed out that both producer responsibility and consumer responsibility models have their own shortcomings, and suggested combining them with the principle of “beneficiary responsibility” to redefine carbon responsibility allocation from the perspective of “beneficiary source”.
Empirical studies and modeling advances
Now, implicit carbon transfer has become a research hotspot. Yang et al. (Yang et al. 2025) analyzed inter provincial carbon transfer in China and found that the scale of carbon transfer is positively correlated with geographical distance, with fossil energy consumption being the main contributing factor. Pancorbo and Ola (Pancorbo and Ola 2018) believe that the consumer responsibility model can help redistribute emission reduction tasks and reduce inter regional carbon leakage, but due to the fact that only consumers are responsible, producers lack innovation motivation (Zhang et al. 2018).
Cong et al. (Cong et al. 2018) studied the carbon responsibility calculation methods in Beijing, Tianjin, Hebei and other places, and pointed out significant differences in the results. It is recommended to adopt a comprehensive framework. Jin and Ju (Jin and Yi 2018) analyzed the allocation of greenhouse gas responsibilities in countries such as China and Japan based on the concept of consumer responsibility, and found that the implicit emissions in China’s bilateral trade are huge and growing rapidly.
Chen and Li (Chen and Li 2022) used value chain theory and multi regional input-output model to analyze carbon transfer in urban agglomerations, and proposed a responsibility sharing framework based on the “benefit principle”. Jun et al. (Jun et al. 2022) constructed a Full MRIO model to quantify carbon transfer and trade benefits, and improved the sharing coefficient of provincial responsibility allocation.
At the industry level, Wang et al. (Wang et al. 2023a, b) studied the impact of carbon peaking policies on economic structure based on a general equilibrium model; Lyu et al. (Lyu et al. 2022) modeled the carbon peak path of industrial parks and proposed reallocating carbon emission quotas based on land and carbon productivity; Du (Du 2023) explored the path to achieving “carbon peak carbon neutrality”, emphasizing industrial restructuring, sustainable energy, and low-carbon transportation; Chu et al. (Chu et al. 2024a, b) studied the sludge treatment industry and predicted that carbon peak would be achieved by 2030, but pointed out that achieving carbon neutrality still requires auxiliary measures such as carbon sinks.
Evolutionary dynamics and policy implications
In recent years, an increasing number of studies have adopted evolutionary game models (EGM) to analyze the dynamic interactions between government, businesses, and the public.
Meng et al. (Meng et al. 2024) found that corporate social responsibility (CSR) significantly improves corporate carbon performance, with government subsidies playing a partial mediating role. Zhang et al. (Zhang et al. 2024) pointed out that the strengthening of the Central Environmental Protection Inspection (CEPI) can help the government and enterprises improve their carbon reduction strategies and enhance stability under low-cost and high-yield scenarios. Zou et al. (Zou et al. 2025) found through EGM that government incentives, penalties, and carbon trading mechanisms can jointly promote emissions reduction in the process of urban renewal.
Jun et al. (Jun et al. 2023) analyzed the low-carbon transformation in the field of canal transportation and believed that government subsidies and cooperation with shippers are key driving forces. Su and Zhang (Su and Zhang 2025) studied the field of green building and found that government incentives have a significant promoting effect in the early stages of the market, but gradually weaken as the market matures. Zhang and Chen (Zhang and Chen 2024) pointed out that the credibility of incentive policies and tiered carbon taxes can effectively enhance corporate participation. Barazanchi and Rasheed (Al Barazanchi and Rasheed 2024) emphasized that green technology can reduce energy consumption by 25%, improve carbon capture efficiency by 85%, and reduce greenhouse gas emissions by 50% within ten years, demonstrating its significant potential for global sustainable development.
Research gaps and novelties
Overall, existing research has laid a solid theoretical and methodological foundation for understanding the multidimensional characteristics of carbon emission reduction responsibility. However, most of the results mainly focus on the relationship between a single subject or two types of subjects, presenting the characteristics of subject fragmentation and domain dispersion. There is a lack of a unified analytical framework that can systematically depict the dynamic game relationship between the government, enterprises, and residents. The responsibility and interests involved in carbon emission reduction are diverse. The diversification of subject interests determines the complexity of conflicts of interest among relevant responsible parties. In the context of establishing carbon emission reduction responsibilities, the behavior of each type of responsible party will have a significant and significant impact on other responsible parties, directly affecting the changes in costs and benefits of different carbon emission reduction responsible parties, leading to different game strategies among multiple parties. Therefore, it is necessary to consider how the corresponding benefits of each type of subject’s action strategy can be achieved, in order to effectively play the incentive role of institutional norms on carbon emission reduction responsible parties and solve the conflict between climate and environmental protection and economic development efficiency. Based on this, this study analyzes the game behavior between different responsible parties under carbon emission reduction responsibility from the perspective of cost and benefit, providing a preliminary reference for the design and analysis of the carbon emission reduction responsibility system in the future.
Specifically, this article addresses such weaknesses and thus it puts forward the experimental tripartite EGM, which simultaneously joins the government, enterprises, and the people. The model embodies the forces of CR commitments while delving into the strategic games and the effect of different parties in the diffusion of environmentally friendly behavior. The novelty lies in the use of various solutions for each party government intervention, businesses’ low-carbon and high-carbon development, and the different levels of resident participation, thus covering a wider range of CE reductions. This model is very helpful to policymakers as it provides them with more inclusive and effective CR programs that match the objectives of the national and global climate.
Paper organization
In the following sections, it will therefore be: The authors of this paper in Sect. 2 have elaborated their method and description of the modeling of the EGM which they have adopted for the study of the interactions among the government, the enterprises and the residents, the list of the main assumptions, the parametrization, and the game strategy matrix. Section 3 includes a few examples of numerical simulations for checking the correctness of the model and different option assessments, followed by the analysis of the findings and their implication for the policy. Section 4 ultimately finishes the work by encapsulating the findings, providing recommendations for policymakers, and proposing avenues for future research.
Methodology
Model building
To promote the implementation of CR and effectively respond to the CC crisis, it is necessary to bring into play the respective roles of the government, enterprise, and residents in the CR cause, and to standardize the CR responsibilities of these different categories of responsible subjects. Based on the overall perspective of the construction of responsibility for the CR system, this study combines the types and contents of the responsibilities of different responsibilities for CR, and creates the three-part game “government,” “enterprise,” and “resident.”
Model assumptions and parameterization
To analyze the influence relationship between different game participants, this study makes the following assumptions about the above game model:
Hypothesis 1
The game’s primary body
The government is the game participant 1, the enterprise is the game participant 2, and the resident is the game participant 3. At the same time, the three types of game participants have limited rationality, and there is information asymmetry. That is to say, the government, enterprise and resident of the individual three types of participants themselves have a certain game analysis ability, but based on the existence of information asymmetry and other issues, the lack of CR work of the overall prediction ability, resulting in the three types of subjects in the game process, are in the state of complete rationality and incomplete rationality between the state of the premise of the corresponding decision-making.
Hypothesis 2
Game strategy space
The government’s game strategy space exists in “intervention” and “non-intervention”, two kinds. Among them, “intervention” refers to the government’s CR work, investing certain administrative resources in CE regulation of enterprise, such as through taxation, financial subsidies and other regulatory tools and means for the positive implementation of CR work of enterprise to give the appropriate incentives or incentives, for the negative implementation of CR work of the enterprise with the corresponding penalties, to This will promote the advancement of enterprise toward energy saving and low-CE. “Non-intervention” means that the government does not take any administrative measures to intervene in the implementation of GHG by enterprises.
There are two types of gaming strategies for enterprise: “low-carbon development” and “high-carbon development”. Among them, “low-carbon development” refers to the enterprise in the daily production and operation development, adopting the concept and attitude of low-carbon development, through the product design, production, recycling, and other phases of green low-carbon technology innovation or transformation, and actively implementing the responsibility of CR. “High-carbon development” means that enterprises still adopt the development mode of high-carbon production and operation that ignores the problem of CC in CR, and do not take any green and low-carbon measures to implement CR.
There are two types of gaming strategies for residents: “participation” and “non-participation”. Among them, “participation” refers to the active participation of residents in the development of energy-saving and low-carbon causes, playing their role as members of the public, and monitoring the CE behavior of enterprises, to promote the smooth realization of CR work. The term “non-participation” means that residents do not participate in any work related to CR.
In summary, the three categories of game subjects’ behavioral strategies, namely “government”, “enterprise”, and “resident”, include positive and negative strategies, respectively. Among them, “intervention”, “low-carbon development” and “participation” are positive strategies, “non-intervention”, “high-carbon development” and “participation” are negative strategies.
Hypothesis 3
Probability of adopting the game strategy
It is expected that “government” uses “intervention” and “non-participation” as negative strategies in the early stages of the game of “government,” “enterprise,” and “resident.” The likelihood that a “government” will choose the “intervention” strategy is x, and the likelihood that it will choose the “non-intervention” strategy is 1-x, where x∈[0,1];” The likelihood that a “firm” will choose the “low-carbon development” strategy is y, and the likelihood that it will choose the “high-carbon development” strategy is 1།y, where y∈[0,1]; With z∈[0,1], the likelihood that a “resident” will choose the “participation” strategy is z, and the likelihood that he or she will choose the “non-participation” strategy is 1།z.
Hypothesis 4
Assumptions on the relevant parameters of the game strategy
Table 1 illustrates the pertinent parameter assumptions established in this work regarding the Evolutionary Game (EG) strategy’s cost, benefit, incentive, and regulation elements.
In terms of the behavioral costs of the game strategy, when the enterprise adopts the strategy of “low-carbon development”, the cost of low-carbon equipment and low-carbon technological innovation, etc., is C1, and when the enterprise adopts the strategy of “high-carbon development”, the cost of high-CE production and operation development is C2. When the government adopts the “intervention” strategy, the cost of administrative resources is C3, and the cost of addressing CC brought on by GHGEs behavior is C4 when it uses the “non-intervention” approach. When residents adopt the “participation” strategy, the cost of monitoring the CE behavior of the enterprise is C5.
In the behavioral benefits of the game strategy, the enterprise adopts the “low-carbon development” strategy, the gain is U1, and adopts the “high-carbon development” strategy, the gain is U2. The potential benefit to the government when the business adopts the strategy of “low-carbon development” is U3.
In terms of behavioral incentives and regulations in game strategy: when the government adopts an “intervention” strategy, the rewards and incentive subsidies given to enterprise that adopt a “low-carbon development” strategy are W1; When resident adopt the “participation” strategy, obtaining government funding is W2; When the government adopts an “intervention” strategy, the punishment imposed on enterprise that adopt a “high-carbon development” strategy is T1; When resident adopt the “participation” strategy, the loss suffered by enterprise that adopt the “high-carbon development” strategy is T2.
Table 1. Certain EGM parameter selections and their interpretations
Typology | Parameter | Meaning |
|---|---|---|
Cost | C1 | Costs paid by companies for LCP |
C2 | Costs paid by firms for high-carbon production | |
C3 | Costs of government intervention in business | |
C4 | Costs of government regulation of CEs when firms produce at high-carbon levels | |
C5 | Costs of participation by residents in building an LCS | |
Benefit | U1 | Benefits to the enterprise of adopting LCP |
U2 | Benefits to the enterprise of adopting high-carbon production | |
U3 | Potential economic benefits to the government from LCP by the enterprise | |
Incentive and regulation | W1 | Government intervention in subsidizing LCP enterprises |
W2 | Government Subsidies for Individual Participation in an LCS | |
T1 | Penalties for government intervention on high-carbon producers | |
T2 | Losses suffered by high-carbon producers as a result of public scrutiny |
Game payment matrix construction
Based on the game behavior strategies of the three kind of participating subjects, namely the government, enterprise and resident, the number of game strategy combinations among the three categories of themes can be calculated to be 8, (intervention, low-carbon development, participation), (intervention, low-carbon development, non-participation), (intervention, high-carbon development, participation), (intervention, high-carbon development, non-participation), (non-intervention, low-carbon development, participation), (non-intervention, low-carbon development, non-participation), (no intervention, high-carbon development, participation), (no intervention, high-carbon development, non-participation).
According to the parameter assumptions in Table 1, it can be seen that when the combination of game strategies is (intervention, low-carbon development, participation), the government needs to pay the intervention cost C3 and pay the subsidy W1 for low-carbon enterprise and the subsidy W2 for the implementation of low-carbon participation behaviors of resident, but at the same time can obtain the potential benefits U3 brought by the enterprise’s LCP; the enterprise needs to pay the cost C1 generated by the low-carbon development, but at the same time can obtain the corresponding, but at the same time can obtain the corresponding revenue U1 and government subsidy W1; resident need to pay the cost of participation C5, but at the same time will obtain the corresponding government subsidy W2. Similarly, the relevant benefits, costs, incentives, and regulations of the government, enterprise, and resident under other combinations of game strategies. The game payment matrix of this three-way EGM is illustrated in Table 2.
Table 2. The game payment matrix of the three-party EGM of government, enterprise, and residents
Strategy combination | Government | Enterprise | Resident |
|---|---|---|---|
(intervention, low-carbon development, participation) | U3-C3།-W1།-W2 | U1-C1+W1 | -C5+W2 |
(intervention, low-carbon development, non-participation) | U3-C3།-W1 | U1-C1+W1 | 0 |
(intervention, high-carbon development, participation) | -C3།C4+T1།W2 | U2-C2།-T1།-T2 | -C5+W2 |
(intervention, high-carbon development, non-participation) | -C3།-C4+T1 | U2-C2།-T1 | 0 |
(non-intervention, low-carbon development, participation) | U3-W2 | U1-C1 | -C5+W2 |
(non-intervention, low-carbon development, non-participation) | U3 | U1-C1 | 0 |
(no intervention, high-carbon development, participation) | -C4།-W2 | U2-C2།-T2 | -C5+W2 |
(non-intervention, high-carbon development, non-participation) | -C4 | U2-C2 | 0 |
Modeling of EGs
Construction and solution of replicated dynamic equations
Let the government select the “intervention” strategy of the Expected Return (ER) of Ub1, select the “non-intervention” strategy of the ER of Ub2, and the average ER of Ub. The government is one of the game participants. Its “intervention” strategy, “non-intervention” strategy, and average ER are as follows:
1
2
3
Similarly, the ER of the enterprise selecting the “low-carbon development” strategy is Uc1, the ER of the enterprise selecting the “high-carbon development” strategy is Uc2, and the average ER is Uc. The ER and average ER of the business implementing “low-carbon development” and “high-carbon development” strategies as the second party of the game are as follows, based on the game payment matrix of the three-party EGM mentioned above. On this basis, according to the game payment matrix of the three-party EGM above, it can be concluded that as the second party of the game, the ER and average ER of the enterprise adopting the strategy of “low-carbon development” and the strategy of “high-carbon development” are as follows, respectively:
4
5
6
Similarly, assuming that the ER of a resident selecting the “participation” strategy is Ur1, the ER of selecting the “non-participation” strategy is Ur2, and the average ER is Ur. On this basis, according to the game payment matrix of the three-party EGM above, it can be concluded that as the third participant of the game, the average ER, as well as the ER for residents who select the “participation” and “non-participation” strategies, are as follows:
7
8
9
The three parties are developing in an imbalanced manner throughout the first round of strategy selection. However, as the development goes on, the subjects involved in the three types of games change their strategic behavior to ensure that the strategy that best meets their interests is selected. Replicating the dynamic equations is a process of dynamic adjustment. According to Eq. (1) to Eq. (9), the dynamic replication equations of the three-party game model of the government, enterprise, and resident are obtained, respectively:
10
11
12
The system of dynamic equations of the three-party EG assignment is generated by associating Eqs. (10), (11), and (12) to determine the Equilibrium Point (EP) of this three-party EG, and making F(x) = F(y) = F(z) = 0 as shown in Eq. (13), which results in the 8 Pure Strategy Equilibrium Points (PSEPs): E1[0,0,0], E2[1,0,0], E3[0,1,0], E4[0,0,1], E5[1,1,0], E6[1,0,1], E7[0,1,1], E8([1,1,1] (Xu et al. 2024; Xu et al. 2024; Xu et al. 2024), and two mixed-strategy equilibria: E9[(C1-C2།U1་U2)/(T1་W1),།(C3།T1)/(T1་W1),0], E10[།(C2།C1་T2་U1།U2)/(T1་W1),།(C3།T1)/(T1་W1),1]. Among them, the domain of this EGM is bounded by the 8 PSEPs: {(x,y,z) │x = 0,1; y = 0,1; z = 0,1}. The model’s equilibrium solution domain is the area enclosed by these EPs.
13
Asymptotic stability analysis
Since pure strategy is the evolutionarily stable approach in asymmetric EGs when the information asymmetry criteria are satisfied, this research is designed to examine solely the asymptotic stability of the eight pure strategy equilibria that have been identified earlier (Ritzberger and Weibull 1995). Building the Jacobi matrix for the analysis of the asymptotic eigenvalues yields the Evolutionary Stable Strategies (ESS) of the game system at the EPs, by Lyapunov’s indirect method (Lyapunov 1992) and (Friedman 1998) study. The three-dimensional dynamical system made up of Eq. (13) can be used to generate the Jacobi matrix of the game system outlined below:
14
Among them:
15
16
17
18
19
20
21
22
23
Shows the eigenvalues of the Jacobian matrix calculated based on Eq. (14) for the PSEPs mentioned above Table 3
Table 3. Jacobi matrix eigenvalues
Pure strategy equilibrium | λ1 | λ2 | λ3 |
|---|---|---|---|
E1 | T1-C3 | C2-C1+U1།-U2 | W2-C5 |
E2 | C3-T1 | C2-C1+T1+U1།-U2+W1 | W2-C5 |
E3 | -C3།-W1 | C1-C2།-U1+U2 | W2-C5 |
E4 | T1-C3 | C2-C1+T2+U1།-U2 | C5-W2 |
E5 | C3+W1 | C1-C2།-T1།-U1+U2།-W1 | W2-C5 |
E6 | C3-T1 | C2-C1+T1+T2+U1།-U2+W1 | C5-W2 |
E7 | -C3།-W1 | C1-C2།-T2།-U1+U2 | C5-W2 |
E8 | C3+W1 | C1-C2།-T1།-T2།-U1+U2།-W1 | C5-W2 |
In this study, the asymptotic stability analysis will be developed from the following four different scenarios:
Scenario 1: Stability analysis when the conditions T1-C3 < 0, W2།-C5 > 0, and C2།-C1+T2+U1།-U2 < 0 is satisfied.
When the conditions of T1-C3 < 0, W2།-C5 > 0, and C2།-C1+T2+U1།-U2 < 0 are satisfied, Table 4 displays the Stability of the 8 Pure Strategy Equilibrium Points (S-8PSEPs) mentioned before. Corollary 1 follows from this: Under Scenario 1, EP E4[0,0,1] is the only Evolutionary Stable Position (ESP).
Corollary 1
shows that when “the government’s penalty setting for high-carbon enterprise is less than the government’s intervention cost for enterprise (T1-C3 < 0), the total benefit obtained by residents actively participating in actions to mitigate GHGEs is negative (W2།-C5 > 0), and the difference between the production gains of high-carbon development and low-carbon development is less than the sum of the loss of high-carbon production by firms as a result of public scrutiny and the disparity between the production costs of high-carbon development and low-carbon development (C2།-C1 + T2 + U1།-U2 < 0)”, the Tripartite Evolutionary Game System (TEGS) consisting of the government, enterprise and resident stabilizes at the EP E4[0,0,1], which represents the strategy combinations of (non-intervention, high-carbon development, participation).
Table 4. Stability of EPs for pure strategies in scenario 1
Pure strategy equilibrium | λ1 | λ2 | λ3 | Stability |
|---|---|---|---|---|
E1 | - | - | + | Saddle point |
E2 | + | Unknown | + | Unknown |
E3 | - | + | + | Saddle point |
E4 | - | - | - | ESS |
E5 | + | Unknown | + | Unknown |
E6 | + | Unknown | - | Saddle point |
E7 | - | + | - | Saddle point |
E8 | + | Unknown | - | Saddle point |
Scenario 2: Stability analysis when the conditions T1-C3 < 0, W2།-C5 > 0, and C2།-C1+T2+U1།-U2 > 0 is satisfied.
When the conditions of T1-C3 < 0, W2།-C5 > 0, and C2།-C1+T2+U1།-U2 > 0 are satisfied, Table 5 displays S-8PSEPs mentioned before. Corollary 2 follows from this: Under Scenario 2, EP E7[0,1,1] is the only ESP.
Corollary 2
shows that when “the government’s penalty setting for high-carbon enterprise is less than the government’s intervention cost for enterprise (T1-C3 < 0), the total benefits obtained by residents actively participating in actions to mitigate GHGEs are positive (W2།-C5 > 0), and the sum of the loss of firms’ high-carbon production due to public scrutiny plus the disparity between the production costs of high-carbon development compared to low-carbon development surpasses the disparity between the production gains of firms’ high-carbon development compared to low-carbon development (C2།-C1+T2+U1།-U2 > 0)”, the TEGS consisting of the government, the enterprise, and the resident stabilizes at the EP E7[0,1,1], which represents the strategy combinations of (non-intervention, low-carbon development, participation).
Table 5. Stability of EPs for pure strategies in scenario 2
Pure strategy equilibrium | λ1 | λ2 | λ3 | Stability |
|---|---|---|---|---|
E1 | - | Unknown | + | Saddle point |
E2 | + | Unknown | + | Unknown |
E3 | - | Unknown | + | Saddle point |
E4 | - | ་ | - | Saddle point |
E5 | + | Unknown | + | Unknown |
E6 | + | + | - | Saddle point |
E7 | - | - | - | ESS |
E8 | +་ | - | - | Saddle point |
Scenario 3: Stability analysis when the conditions T1-C3 > 0, W2།-C5 > 0, and C2།-C1+T2+U1།-U2 > 0 is satisfied.
When the conditions of T1-C3 > 0, W2།-C5 > 0, and C2།-C1+T2+U1།-U2 > 0 are satisfied, Table 6 displays S-8PSEPs mentioned before. Corollary 3 follows from this: Under Scenario 3, EP E7[0,1,1] is the only ESP.
Corollary 3
shows that when “the government’s penalty setting for high-carbon enterprise is greater than the government’s intervention cost for enterprise (T1-C3 > 0), the total benefits obtained by residents actively participating in actions to mitigate GHGEs are positive (W2།-C5 > 0), and the sum of the loss of firms’ high-carbon production due to public scrutiny plus the difference between the production costs of high-carbon development compared to low-carbon development surpasses the disparity between the production gains of firms’ high-carbon development compared to low-carbon development (C2།-C1+T2+U1།-U2 > 0)”, the TEGS consisting of the government, enterprise and resident stabilizes at the EP E7[0,1,1], which represents the strategy combination of (non-intervention, low-carbon development, participation).
Table 6. Stability of EPs for pure strategies in scenario 3
Pure strategy equilibrium | λ1 | λ2 | λ3 | Stability |
|---|---|---|---|---|
E1 | + | Unknown | + | Unknown |
E2 | - | Unknown | + | Saddle point |
E3 | - | Unknown | + | Saddle point |
E4 | + | + | - | Saddle point |
E5 | + | Unknown | + | Unknown |
E6 | - | + | - | Saddle point |
E7 | - | - | - | ESS |
E8 | + | - | - | Saddle point |
Scenario 4: Stability analysis when the conditions T1-C3 < 0, W2།-C5 < 0, and C2།-C1+T2+U1།-U2 < 0 is satisfied.
When the conditions of T1-C3 < 0, W2།-C5 < 0, and C2།-C1+T2+U1།-U2 < 0 are satisfied, Table 7 displays S-8PSEPs mentioned before. Corollary 4 follows from this: Under Scenario 4, EP E1[0,0,0] is the only ESP.
Corollary 4
shows that when “the government’s penalty setting for high-carbon enterprise is less than the government’s intervention cost for enterprise (T1-C3 < 0), the total benefit obtained by residents actively participating in actions to mitigate GHGEs is negative (W2།-C5 < 0), and the difference between the production gains of high-carbon development and low-carbon development is less than the sum of the loss of high-carbon production by firms as a result of public scrutiny and the difference between the production costs of high-carbon development and low-carbon development (C2།-C1 + T2 + U1།-U2 < 0)”, the EP E1[0,0,0], which reflects the combination of the strategies of non-intervention, high-carbon development, and non-participation, is where the TEGS made up of the government, enterprise, and residents stabilizes.
Table 7. Stability of EPs for pure strategies in scenario 4
Pure strategy equilibrium | λ1 | λ2 | λ3 | Stability |
|---|---|---|---|---|
E1 | - | - | - | ESS |
E2 | + | Unknown | - | Saddle point |
E3 | - | + | - | Saddle point |
E4 | - | - | + | Saddle point |
E5 | + | Unknown | - | Saddle point |
E6 | + | Unknown | + | Unknown |
E7 | - | + | +་ | Saddle point |
E8 | + | Unknown | + | Unknown |
Numerical simulation
In the three-way EGM, each participant is characterized by referentiality and consistency. This study uses a MATLAB tool to numerically simulate how each participant’s game behavior evolves.
Assignment of model parameters
The game strategies of the government, business, and individual resident to take the probability of x, y, and z are restricted to values between 0.1 and 0.9, and the primary parameters of the game model mentioned above are assigned, and the simulation is gradually adjusted by the interval amplitude of 0.2, to cover their various initial strategies to a greater extent. Specific simulation parameter settings are detailed in Table 8. The numerical parameters adopted in Table 8 were not derived from specific empirical cases but were assigned following the common practice in evolutionary game literatureof (Chu et al. 2024a, b). The present simulation aims to explore the dynamic stability and behavioral evolution of the tripartite game system rather than to replicate any particular real-world scenario. Therefore, parameters are designed in relative magnitudes to reflect the logical relationships among costs, benefits, and penalties. This approach ensures that the simulation outcomes are determined by the ratios between parameters, which define the qualitative stability of the evolutionary system. Empirical calibration would not alter these qualitative conclusions but might reduce the comparability and internal consistency among the four simulation scenarios. Consequently, we retain the theoretical parameter settings while clarifying this rationale in the revised version.
Table 8. Simulation assignment of the main parameters of the EGM
Parameter | C1 | C2 | C3 | C5 | U1 | U2 | W1 | W2 | T1 | T2 |
|---|---|---|---|---|---|---|---|---|---|---|
Simulation 1 | 10 | 2 | 9 | 10 | 3 | 8 | 17 | 14 | 1 | 2 |
Simulation 2 | 10 | 8 | 9 | 4 | 3 | 4 | 17 | 14 | 1 | 4 |
Simulation 3 | 10 | 8 | 7 | 4 | 3 | 4 | 17 | 14 | 10 | 4 |
Simulation 4 | 10 | 8 | 9 | 10 | 3 | 4 | 17 | 9 | 1 | 2 |
Simulation results
Verification of the accuracy of the model for Scenario 1: From Table 8, it can be seen that the parameter assignments of Simulation 1 satisfy the conditions of T1-C3 < 0, W2།-C5 > 0, and C2།-C1+T2+U1།-U2 < 0 of Scenario 1. The parameter assignments of Simulation 1 are simulated, and the corresponding evolutionary route of the game system is demonstrated in Fig. 1. It is evident that the evolutionary route of the game system of Simulation 1 coincides with the analysis of Scenario 1 and corresponds to the combination of strategies (non-intervention, high-carbon development, participation). The accuracy of the model derivation of Scenario 1 is verified.
[See PDF for image]
Fig. 1
Evolutionary route of the gaming system under simulation 1
Verification of the accuracy of the model for Scenario 2: From Table 8, it can be seen that the parameter assignments of Simulation 2 satisfy the conditions of T1-C3 < 0, W2།-C5 > 0, and C2།-C1+T2+U1།-U2 > 0 of Scenario 2. The parameter assignments of Simulation 2 are simulated, and the corresponding evolutionary route of the game system is illustrated in Fig. 2. The game system evolution route of Simulation 2 matches the analysis of Scenario 2, which corresponds to the strategy combination of (non-intervention, low-carbon development, participation). The accuracy of the model derivation of Scenario 2 is verified.
[See PDF for image]
Fig. 2
Evolutionary route of the gaming system under simulation 2
Verification of the accuracy of the model for Scenario 3: From Table 8, it can be seen that the parameter assignments of Simulation 3 satisfy the conditions of T1-C3 > 0, W2།-C5 > 0, and C2།-C1+T2+U1།-U2 > 0 of Scenario 3. The parameter assignments of Simulation 3 are simulated, and the corresponding evolutionary route of the game system is demonstrated in Fig. 3. The game system evolution route of Simulation 3 coincides with the analysis of Scenario 3 and corresponds to the strategy combination of (non-intervention, low-carbon development, participation). The accuracy of the model derivation of Scenario 3 is verified.
[See PDF for image]
Fig. 3
Evolutionary route of the gaming system under simulation 3
Verification of the accuracy of the model for Scenario 4: From Table 8, it can be seen that the parameter assignments of Simulation 4 satisfy the conditions of T1-C3 < 0, W2།-C5 < 0, and C2།-C1+T2+U1།-U2 < 0 of Scenario 4. The parameter assignments of Simulation 4 are simulated, and the corresponding evolutionary route of the gaming system is displayed in Fig. 4. The game system evolution route of Simulation 4 coincides with the analysis of Scenario 4 and corresponds to the strategy combination of (non-intervention, high-carbon development, non-participation). The accuracy of the model derivation of Scenario 4 is verified.
[See PDF for image]
Fig. 4
Evolutionary route of the gaming system under simulation 4
Discussion
This research employs a tripartite EGM to examine the roles of the government, enterprises, and people in CR initiatives within the framework of China’s dual-carbon objectives. The escalating imperative to tackle CC has resulted in the formulation of diverse solutions to allocate the duty of mitigating CEs. The interplay among government policies, corporate actions, and societal engagement is crucial for attaining these objectives. Nevertheless, the research is deficient in a comprehensive model that encapsulates the dynamics of these interactions among all three stakeholders, particularly in light of characteristics such as information asymmetry and bounded rationality.
This research applies a three-party EGM that has the government, businesses, and people as its actors. The options available to each player include the government deciding to intervene or not, the firm choosing between low-carbon or high-carbon, and the resident deciding whether to participate or not. The base of the model consists of the costs, benefits, and penalties involved with each option. Dynamic equations are used to find solutions (EPs) and to explore the strategic behavior of each player in the game. Computer simulations have been run to both check the validity of the model and to see what would happen in different situations, thus shedding light on how each player’s strategy changes over time.
The quantitative evidence shows that maximum benefits come when enterprises and local populations both implement carbon-reduction development schemes and carry out CR projects, even without direct governmental intervention. Namely, conditions where residents energetically participate in CR activities have positive impacts leading to a more sustainable and efficient CR system. The data are further consistent with the claim that the involvement of the government, although preferable, is not always essential to the achievement of low-carbon goals, since businesses and individuals can in an autonomous manner set up and carry out operations What is more, the unchanged EPs under different conditions signify the model’s flexibility and applicability to actual policy scenarios which means that even when governments have no strong regulations, collaborative participation of the business sector and citizens can still be significant in the reduction of CEs.
Nevertheless, the research is still not free from some limitations. The method mainly focuses on the economic aspects of the climate change issue, and it might have marginalized non-economic factors like political changes, public awareness, and technological limitations. In addition, the model is aimed at the three main stakeholders, but it does not take into account the external factors such as international carbon trading or the impacts of global markets, which are potential sources of further influencing the decision-making process. The practical implications of the work serve as a reminder of the importance of a well-balanced policy framework that is able to provide both corporate accountability and public involvement. Governments have to think about cutting down on intervention costs and increasing the incentives for low-carbon technologies. At the same time, they have to give subsidies for the active participation of citizens. That would mean a more comprehensive and efficient path being taken to achieve the dual-carbon goals.
Conclusions and implications
This research aimed to understand the roles and responsibilities of the government, businesses, and people in CR actions, which were driven by China’s “dual-carbon” goals. A three-sided EGM was developed for the purpose of exploring the dynamic interactions among three principal players, stressing government involvement, corporate low-carbon plans, and household participation. The study aimed to explore the evolution of these interactions over a time period and their impact on the best output of carbon emission reductions.
The methodology involved the design of an EGM, where each player (government, enterprise, and resident) could choose from strategies that were influenced by costs, benefits, and regulatory incentives. The authors of the article simulated a model with various strategic combinations to locate the EPs and check the stability of the sequences of different strategies. The research results improve understanding of the combined effect of governmental policies, corporate moves, and public participation on the clean CR pathways. The main conclusions of the study are summarized below:
Conclusions
The research uncovered that the best CR outcomes were attained when enterprises applied low-carbon development principles, and citizens participated actively in the CR process, no matter whether the government was involved or not. It also showed that government involvement, although helpful in some cases, is not always necessary for the accomplishment of low-carbon targets. The survey suggested that businesses and residents can co-operate independently to reach successful CR outcomes. The results pointed out that, in extreme cases, the self-organization of the businesses and the residents can be the drivers for the continuous sustainable reduction of the CEs at the place without heavy reliance on the government. The research indicated that shareholders’ responsibility and the public’s participation were the main issues, and all-inclusive strategies with the incorporation of all stakeholders were necessary to accomplish CN.
This study has limitations. The model primarily emphasizes economic costs and benefits, potentially neglecting essential non-economic aspects, such as political considerations, public awareness, and technological limitations. Furthermore, the model excludes exogenous factors, such as international trade and the effects of the global carbon market, which may influence the dynamics of CR. The findings indicate that governments should strive to minimize the expenses linked to regulatory measures while encouraging enterprises and communities to participate in CR initiatives. This would foster a more inclusive and efficient strategy for attaining dual-carbon objectives and improving long-term sustainability.
Implications
To sum up, for the government, the way to increase its enthusiasm in assuming the responsibility of carbon reduction mainly includes reducing the cost of administrative interventions such as system supply, supervision and management in the work of carbon reduction. For enterprise, the main ways to increase their motivation to take on the responsibility of carbon reduction include the provision of a favorable environment for low-carbon technological innovation by the government and the social supervision of their production behavior by resident. For resident, the main way to increase their motivation to take responsibility for carbon reduction is for the government to provide various economic subsidies for active participation in the construction of a low-carbon society. In addition, these elements are only based on the perspective of economic costs and benefits, and the setting of responsibility for carbon reduction should also establish the value of safeguarding the public interest of society as a whole. Therefore, to ensure the seamless execution containing carbon reduction, the binding force of carbon responsibility can be increased by means of legal and other tools, so as to raise the degree of importance attached to climate environmental protection by different responsible parties, such as the government, enterprise and resident.
Author contributions
Ziwei Li: Supervision, Conceptualization, Writing-Original draft preparation, Project administration.
Funding
Not applicable.
Data availability
Available upon request.
Declarations
Ethical approval
Each author has been directly and significantly involved in the key work that resulted in this paper and will publicly stand behind its contents.
Author statement
All authors have reviewed and endorsed the manuscript, confirming adherence to the stipulated criteria for authorship outlined previously. Each author attests that the manuscript reflects genuine effort and integrity.
Competing interests
The authors declare no competing interests.
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