Evolutionary Simulation of Carbon-Neutral Behavior of Urban Citizens in a “Follow–Drive” Perspective

Abstract

The implementation of low-carbon behavior by citizens is of the utmost importance in constructing China’s ecological civilization and achieving its dual-carbon objectives. As a result, exploring the formation and recurrence mechanisms of carbon-neutral citizenship behavior may have a positive impact on realizing China’s carbon reduction targets. This study explores a comprehensive analysis method of multi-subject interactive evolution of carbon-neutral citizenship behavior. It expands the connotation of behavioral intervention from individual single execution (citizens actively adhere to carbon-neutral behavior) to multi-driven implementation (citizens inspire other residents to comply with carbon-neutral behavior based on their own adherence). Furthermore, this study constructs a collaborative and interactive “follow–drive” mechanism for carbon-neutral citizenship behavior. Through Python software 3.8 simulation, this study examines the formation and stabilization process of carbon-neutral citizenship behavior under different influencing factors. The research findings are as follows: (1) If the government neglects its duties more severely, it is more inclined to adopt incentive policies, thereby increasing the likelihood that both kinds of the citizens will choose to follow carbon-neutral behavior. This suggests that the proactive introduction of relevant policies and regulations by the government has a positive influence on citizens’ carbon-neutral behavior. (2) With a higher perceived level of psychological–physical bimetric health among citizens, both kinds of the citizens are more inclined to follow and drive carbon-neutral behavior, while the chances of the government selecting incentive policies decrease, and it takes longer to attain final stability (i.e., selecting incentive policies). (3) In situations where there is a greater loss of group norms in the external environment of the citizen group, both kinds of the citizens are more likely to opt for and drive carbon-neutral behavior. This, in turn, reduces the likelihood of the government selecting incentive policies. Finally, based on the research findings, relevant policy recommendations are given.

1. Introduction

In response to the impacts of climate change, almost 200 countries have signed the Paris Agreement with the goal of achieving net zero emissions by the second half of this century [1]. As the world’s largest energy consumer and carbon emitter, China accounts for about 1/3 of the world’s total carbon dioxide emissions [2]. Therefore, China’s effectiveness in reducing emissions is widely regarded as a crucial factor in the effort to limit the global average temperature increase to 1.5 °C, which is a key requirement for effectively implementing the Paris Agreement [3]. To achieve this goal, in September 2020, China proposed a dual-carbon target of reaching carbon peak by 2030 and achieving carbon neutrality by 2060 [4].

Carbon neutrality refers to the state where the amount of carbon dioxide emissions produced directly or indirectly by a country, company, or individual over a specific period is offset by the utilization of new energy sources, energy-saving measures, and emission reduction efforts [5], resulting in a relative “zero emission” state, i.e., a net-zero state of carbon dioxide emissions. Currently, achieving carbon neutrality is not yet a mandatory requirement in society and it heavily relies on the environmental awareness and perceptions of climate change of individuals, corporations, cities and national governments. This includes efforts towards individual carbon neutrality, corporate carbon neutrality, as well as city and national level carbon neutrality.

The public plays a crucial role as both the practitioners and influencers of carbon-neutral actions. Changing public behavior is a fundamental aspect of achieving carbon neutrality goals. Increasing awareness of conservation, encouraging public participation, promoting the adoption of green lifestyles, and transforming green concepts into conscious actions among the public are all critical in the effort to achieve carbon-peaking targets. Moreover, such initiatives can also have a significant impact on the psychological and physical health of citizens. Thus, this study defines carbon-neutral citizenship behavior as additional voluntary actions taken by citizens to help achieve the goal of carbon neutrality, specifically in terms of offsetting their carbon dioxide emissions. Furthermore, it classifies such citizen behaviors into two types: consensual citizenship behaviors and adequate citizenship behaviors. Consensual citizenship behavior refers to voluntary energy-saving and emission-reduction actions performed by urban citizens to minimize their carbon emissions, while adequate citizenship behavior refers to voluntary carbon dioxide offsetting actions taken by urban citizens, such as utilizing carbon sequestration technology, increasing carbon sinks through tree planting or purchasing saplings.

This study focuses on analyzing the carbon-neutral citizenship behavior of urban citizens from the perspective of “follow–drive”. It also includes the design of a simulation model to analyze the behavior of urban citizens in relation to carbon neutrality. The research explores the leading approaches and conditions that encourage citizens to follow and drive others towards practicing carbon-neutral citizenship behavior. Moreover, it identifies the key factors and effective methods to influence urban citizens to practice carbon-neutral citizenship behavior. Compliance refers to the willingness of individuals to adhere to such policies, while motivation refers to their eagerness to promote these policies to others and encourage more people to practice them.

The innovations of this study are as follows. First, the theoretical system of carbon-neutral behavior of urban citizens is built based on the perspective of “follow–drive”, which extends the connotation of behavioral intervention from individual single implementation to multi-driven and is an expansion of the theory of individual behavioral intervention in the field of resources and environment. The establishment of this policy system is an important theoretical guidance for enriching the theory of carbon-neutral citizen behavior and how to better play the macroeconomic control role of the policy, as well as expanding the motivation perspective of individual behavior research, which is an important supplement to the theory of environmental protection and dual carbon behavior motivation. Second, through the method of the evolutionary game and systematic simulation, we explore the formation and recurrence mechanism of carbon-neutral citizens’ behavior. This enables the policy theory research to shift from qualitative to quantitative, enriching the theory of policy design and facilitating the formation of institutional design methodology related to citizens’ carbon-neutral behavior. Third, the carbon-neutral citizenship behavior is divided into two types: consensual citizenship behavior and adequate citizenship behavior, so the carbon-neutral behavior of citizen subjects is explored more deeply.

The subsequent chapters of this study are organized as follows: the second part reviews the literature on carbon neutrality at the individual level and the factors influencing the carbon-neutral behavior of urban citizens; the third part develops a tripartite game model of government, citizens, and other citizens for two types of citizen subjects; the fourth part conducts a systematic simulation and changes the initial probabilities and initial values of key factors for sensitivity analysis; the fifth part discusses the results concerning the actual situation; and the sixth part draws conclusions and proposes feasible suggestions for the carbon-neutral behavior of urban citizens from a “follow–drive” perspective.

2. Literature Review

2.1. Research on Carbon Neutrality at the Individual Level

Carbon neutrality at the individual level generally refers to individuals offsetting their carbon dioxide emissions by planting trees, purchasing seedlings, and choosing low-carbon lifestyles to reduce carbon dioxide emissions. Currently, there are relatively few studies that specifically focus on individual carbon neutrality. The existing studies mainly revolve around measuring the carbon emissions of citizens and households, exploring personal carbon trading options, and analyzing the factors that influence individuals’ willingness to pay for the concept of “carbon neutrality”.

Regarding the measurement of citizen and household carbon emissions, Guo et al. (2018) conducted a comprehensive measure of transaction-oriented household carbon emissions through the emission factor method and input-output model [6]. Xue (2020) conducted an empirical study on the characteristics and key influencing factors of household carbon emissions in mining areas based on descriptive statistics and multiple regression analysis using the consumption lifestyle approach as the research paradigm. The results showed that the characteristics of household carbon emissions are closely related to specific resource endowments, household income levels, education levels, and social development and that education levels and policy regulation can effectively reduce carbon emissions, while the household size can increase carbon emissions [7].

Individual carbon trading is a way to shift citizens from passive emission reduction to active emission reduction and to promote the achievement of a national or regional carbon reduction target through individual participation in carbon trading [8]. It is widely recognized as an effective measure to reduce carbon emissions at the household and individual levels [9]. Regarding the research related to individual carbon trading, Guo et al. (2019) analyzed the influence of heterogeneous government and individual sentiments on the equilibrium strategy of the individual carbon trading scheme implementation model based on rank-dependent expected utility theory, using game models and numerical simulations. The results showed that the government’s strategy can be influenced by individuals’ emotions, and the government would move toward the “mandatory mode” strategy when individuals were optimistic and toward the “voluntary mode” strategy when individuals were pessimistic [10]. In addition, scholar Guo (2019) defined the key institutions of individual carbon trading mechanisms in her doctoral dissertation. On this basis, she constructed a hierarchical theoretical framework of urban citizens’ tendency to react to individual carbon trading and analyzed the factors influencing urban citizens’ tendency to react to individual carbon trading and their mechanisms of action. A theoretical model of the key institutions of individual carbon trading mechanisms and the influence mechanism of urban citizens on individual carbon trading tendency avoidance was also constructed [11]. Based on data from 1190 surveys, Tan et al. (2019) investigated the factors influencing public participation in a voluntary individual carbon trading scheme in a pilot project in Guangzhou, China. The findings indicate that perceived usefulness has a considerable and positive impact on the direct willingness to participate in low-carbon initiatives. In contrast, participation risks have negative effects on willingness to participate, and the institutional and technical environment have positive effects on willingness to participate. Additionally, participation feedback and perceptions of low-carbon living have indirect but positive effects on willingness to participate through the mediating effect of perceived usefulness. It Is worth noting that, in this study, the implementation costs do not significantly affect willingness to participate in low-carbon initiatives [12].

Regarding the factors influencing the willingness of individuals to pay for carbon neutrality, scholar Liu (2019) pointed out that monthly income and interpersonal influence had a positive effect on citizens’ willingness to pay, while education and personality variables had an inverse relationship with willingness to pay. However, there was no significant relationship found between gender, age, city of residence, and geographic location of the city of residence and willingness to pay. Additionally, cognition, attitude, and incentives were also found to have no significant effect on willingness to pay for carbon neutrality [13].

2.2. City Factors Influencing Carbon-Neutral Behavior of City Citizens Study

As end-users of production, citizens’ daily carbon emissions comprise not only the direct carbon emissions produced by energy consumption but also the indirect carbon emissions formed during the production and transportation processes behind the goods and services they purchase to satisfy their needs, i.e., indirect carbon emissions from citizens’ consumption [14]. Compared to direct carbon emissions, indirect carbon emissions from consumption are implicit in the goods and services that citizens consume, and they often go unnoticed. According to the estimation of Zhu et al. (2022), each citizen generates about 1.55 tons of carbon emissions per year due to direct and indirect consumption of daily life. In terms of the composition of the carbon footprint, the carbon footprint generated by direct energy consumption such as electricity, liquefied gas, and natural gas accounts for 70.75% of the total carbon footprint; the carbon footprint generated by the consumption of food, transportation, daily necessities, and waste accounts for 13.89%, 7.01%, 6.94%, and 1.40%, respectively [15]. Lulu Peng et al. (2021) found that “food” and “housing” consumption are the main sources of indirect carbon emissions for citizens, accounting for 42% to 48% [16]. This shows that the indirect carbon emissions caused by citizens’ consumption are the main source of carbon emissions. Thus, the carbon emissions caused by citizens’ consumption may be great resistance to carbon neutrality in cities. Therefore, it is important to investigate the factors influencing citizens’ carbon-neutral behavior in cities and implement intervention mechanisms to encourage citizens’ voluntary and conscious adoption of carbon-neutral behaviors.

2.2.1. Intrinsic Psychological Factors

Social psychological theories, such as the Theory of Planned Behavior, the Norm Activation Model, and the Values–Beliefs–Norms Model, highlight how internal psychological factors such as environmental attitudes, values, and subjective norms play a critical role in shaping citizens’ pro-environmental behavior [17]. Currently, there is a limited amount of academic research on the carbon-neutral behavior of urban citizens. However, in the broader context of pro-environmental behavior among urban citizens, several studies have identified factors that influence carbon-neutral behavior. By analyzing studies on related behaviors such as energy-saving behavior, green travel, green consumption, and green lifestyle, we can identify some of the factors that affect the carbon-neutral behavior of urban citizens.

Environmental Values

Values are the fundamental principles, desired objectives, and moral guidelines that guide people’s everyday lives and decisions. They are reflected in people’s thoughts and perceptions, and they reflect their innermost preferences. Although values do not have a physical form, they are stable over time and play an important role in shaping people’s attitudes and behaviors [18].

As abstract and meaningful goals, values can influence individual behavior through attitudes, norms, beliefs, and other psychological factors. According to the Values–Beliefs–Norms (VBN) theory, when a person’s underlying values are threatened or challenged, this can lead to corresponding behaviors aimed at mitigating the threat and restoring a sense of balance [19]. Therefore, guiding citizens to develop and internalize appropriate values can be a powerful way of promoting pro-environmental behavior. The influence of values on environmental behavior can be understood in two main aspects.

One is that values have a more significant impact on environmental behavior. Tolppanen et al. (2021) pointed out that ecological values were the main determinants of carbon footprint behavior through a study of four values, carbon footprint and willingness to act environmentally, and also pointed out that altruistic values could have a positive effect on environmental behavior when they were matched with hedonistic values [20].

Chan et al. (2020) suggested that in more restrictive social contexts, it is difficult for values to promote environmental behaviors and that supporting self-expression, i.e., giving opportunities to demonstrate one’s values may help to enhance corresponding value behaviors [20].

In addition, the idea that there is a harmonious relationship between materialistic values and environmental behavior has been proposed [21]. Groups holding egoistic values tend to have less influence on environmental behavior, but Ling et al. (2020) found in their study that hedonists pursuing egoistic, materialistic values may participate in environmental activities with greater value-added significance due to the pursuit of status, trendy participation, and goal acquisition [22].

Green Personality

Personality is a relatively stable and enduring psychological characteristic that defines and distinguishes an individual from others. It contains three dimensions: inner experience, motivation, and physiological response, which in turn present outward behavior. At present, psychologists have analyzed different personality traits and dimensions, among which the Big Five personality traits have attracted widespread academic attention, specifically including agreeableness (high agreeableness–low agreeableness), responsibility (high responsibility–low responsibility), emotional stability (high emotional stability–low emotional stability), extraversion (extroversion–introversion) and openness (high openness–low openness).

Regarding personality traits and green low-carbon behavior, a study by Busic-Sontic et al. (2017) noted that personality traits indirectly would influence one-time, high-cost energy efficiency investments through environmental attitudes and risk preferences; while low-cost pro-environmental habits were mediated only through environmental attitudes, such as saving energy and purchasing green products [23]. Wang et al. (2021) explored the role of personality traits in households’ willingness to save energy by linking the theory of planned behavior to the Big Five personality traits and households’ willingness to save energy. The results of the study showed that, except for extraversion, the other four personality traits influenced household intention to save energy through different mechanisms, with agreeableness and openness showing positive correlations with all three predictors of TPB. Conscientiousness was also positively correlated with perceived behavioral control, whereas neuroticism was only negatively correlated with attitude [24].

The concept of a “green personality” refers to a set of personality traits that are associated with a high sense of responsibility towards environmental issues, as well as a strong interest and openness to new ideas and perspectives. Individuals who exhibit these traits tend to be more supportive of pro-environmental behavior and are more likely to engage in green, low-carbon practices. We believe that incorporating the concept of green personality traits into models of carbon-neutral citizenship behavior can help to better understand the factors that drive environmentally sustainable behavior among urban citizens.

Psychological Empowerment Perception

Psychological empowerment is the integration of an individual’s subjective judgment or perception of the autonomy of work, his or her influence, the value and meaning of the role, and his or her work ability [25]. It is a measure of a comprehensive psychological perception experienced by individuals in the workplace and mainly includes the four aspects of work: meaning, competency, i.e., self-efficacy, autonomy, and influence [26,27]. Work meaning refers to an individual’s subjective appraisal or perception of the importance or value of their work goals, according to their own personal criteria [28]. Competence, also known as self-efficacy, refers to an individual’s subjective perception of their ability to perform a particular job or task [29]. Autonomy refers to an individual’s subjective perception of the degree to which they have control over their own behavior or work style [30]. Influence, in the context of psychological empowerment, refers to an individual’s subjective perception of their ability to impact organizational strategy or management [31].

Some research findings on psychological empowerment show that psychological empowerment has a positive impact on attitudes, behaviors, and performance [32]. For example, psychological resource theory suggests that when individuals have the appropriate perceptions of psychological empowerment, they positively construct their work roles, uncover hidden values, make innovation their intrinsic pursuit, and increase innovative behavior [33]. Gregory et al. (2010) clarified the existence of an individual–organizational fit, which assesses the alignment of human and organizational values. Individuals’ beliefs about job autonomy and control over workplace outcomes are indeed important factors that influence the individual–organizational fit. It has been found that employees’ perceptions of psychological empowerment positively influence organizational citizenship behaviors such as altruistic helpfulness, courtesy, and giving back [34]. Therefore, we believe that incorporating the perception of psychological empowerment into the theoretical model driving carbon-neutral citizenship behavior of urban citizens is important. Three dimensions of perceived efficacy, perceived meaning, and perceived impact should be considered in the model, as they have been found to positively influence a citizen’s willingness to engage in carbon-neutral citizenship behavior. It is important to note that since urban citizens’ carbon-neutral citizenship behavior is a voluntary carbon reduction behavior, the factor of autonomy may not necessarily be a primary consideration in the psychological empowerment perception model. Thus, for now, our model will not specifically address the factor of autonomy in relation to carbon-neutral citizenship behavior.

The aforementioned research demonstrates that internal psychological factors, including environmental values, green personality, and perceived psychological empowerment, influence citizen carbon-neutral behavior. Guiding citizens to adopt the correct environmental values can better promote environmental behavior. A green personality, which is characterized by high sensitivity and responsibility towards environmental issues, can lead to low-carbon environmental protection behavior. Furthermore, having a perception of psychological empowerment can positively influence citizen carbon-neutral behavior. These commonalities suggest that the proposed model can explain and predict citizen behavior to a certain extent.

2.2.2. Extrinsic Contextual Factors

An institutional theory emphasizes the important role of contextual factors such as regulation, norms, and cognition [35]. Individual behavior is not only directly driven by intrinsic psychological factors but also by situational factors. Hines (1987), in a meta-analysis of 128 papers, indicated that situational variables could significantly influence the occurrence of environmental behavior [36].

Policy Context

The government is an important subject to promote the implementation of environmentally friendly behavior. It regulates the behavior of individuals or organizations through strict laws and regulations, and each actor will be severely punished for their bad behavior. Such punishment is often more costly than taking low-carbon measures, so government policy regulation is an important factor to guide and promote the implementation of citizens’ carbon-neutral behavior. Yue et al. (2020) analyzed artificial neural networks and simulations based on Chinese citizens’ energy-saving behavior and pointed out that it was difficult to form energy-saving behavior in the absence of policy-guided behavioral intentions [37]. This means that policy improvement and diffusion are important contextual factors that influence urban citizens’ participation in energy conservation and emission reduction activities.

In addition to the popularization and improvement of policies, the degree of government policy implementation also has a significant impact on citizens’ behavior. For example, the model of factors influencing public low-carbon consumption patterns constructed by Wang and Wang using rooting theory confirms that the factor of policy implementation has an impact on citizens’ low-carbon consumption behavior [38].

Cost Scenarios

The costs of choosing to live a green and low-carbon life and implementing carbon-neutral behaviors include the premium price of energy-saving and emission-reducing products or services, the time consumed by the implementation of the behavior, and the convenience sacrificed. These are also important factors that influence urban citizens to implement carbon-neutral citizenship behaviors. The higher the anticipated cost of participation, the less inclined individuals are to engage in the behavior. Taking the purchase of electric vehicles as an example, research indicates that the higher cost of purchasing an electric vehicle directly reduces consumer willingness to buy [39]. In addition to the objective direct purchase cost, the behavioral cost of participating in emission reduction measures is also an important factor influencing citizens to implement green behaviors. Dong et al. (2018) also found in their study of the impact of governmental actions on public participation in environmental decision-making that the level of public perception of the smoothness and convenience of participation channels was relatively low, and the cost and benefits of participation constrained the public’s motivation to participate in governmental environmental decision-making [40]. The study by Cheng et al. (2019) found that macro trends in group decision-making among citizens practicing green lifestyles were driven by the costs of implementing such lifestyles and the benefits lost if not implemented. They also highlighted the need to reduce the costs of time and convenience paid by citizens to engage in green environmental behavior, thereby enhancing their satisfaction and sense of achievement in practicing such lifestyles [41]. Therefore, it can be argued that costs, which include both objective and behavioral costs, play a crucial role in limiting the carbon-neutral citizenship behavior of urban residents. Hence, these costs must be considered as a moderating variable in the theoretical model.

Group Norms

Group norms refer to the pressure from others, organizations, or society that individuals perceive in the decision-making process [42]. Studies by Shaw (2008) [43] and Valle et al. (2004) [44] found that pressure from groups related to individuals such as family, neighbors, peers, and community can have a significant impact on their willingness to recycle behavior. In this paper, we will review the relationship between group norms and pro-environmental behavior at three levels: social norms, family norms, and organizational norms involved in group norms.

Social norms encompass the codes of conduct, rules, customs, moral principles, and value standards that prevail within society and guide the behavior of its members [45]. Social norms reflect social relations, a guide, and a norm for social behavior in the absence of legal validity. Regarding social norms and environmental behavior, Cialdini et al. (2021), through an analysis of 58 papers, pointed out that social norms influenced various behaviors related to the environment, such as energy conservation, recycling, etc. [46]. Broek et al. (2019) showed that social norms were one of the factors that drive energy-saving behavior and could influence behavioral intentions either through personal norms or directly, thus having an impact on energy-saving behavior [47]. All the above studies conclude that there is a significant influence of social norms on citizens’ environmental behaviors. However, some studies had different findings. For example, Pearce et al. (2022) found no significant effect of social norms on pro-environmental behavior, meaning that social norms were not a significant predictor of pro-environmental behavior. However, they also noted that social norms were significantly related to other factors in the model, such as personal norms and connection to nature, which may have included the effect of social norms on pro-environmental behavior as stronger predictors in the model [48].

Regarding the relationship between family norms and environmental behavior, studies have shown that families, as places where individual values, social norms, and institutional requirements collide to shape consumption practices, can have a large impact on the implementation of environmental behavior [49]. Kleinschafer et al. (2021) explored the impact of family norms on household efficiency behavior through feedback from 775 households in regional Australia. The results show that family norms are one of the most important variables influencing household efficiency behavior. They have a strong and significant effect on cutting and investment behavior and mediate between established efficiency drivers and efficiency behavior, influencing efficiency drivers [50].

In addition to social and familial norms, the organizational norms in which individuals live can also have a significant impact on the implementation and participation of their environmental behaviors. Studies by Xu et al. (2021) [51] and Amrutha and Geetha (2021) [52] indicate that a strict normative system and green training within an organization can positively promote energy-saving behaviors and green practices of the company and its members. Moreover, corporate culture theory also states that as the embodiment of the core values of an organization or group, an intangible spiritual force, awareness, and normative mechanism, culture can guide and shape organizational members’ attitudes, nurture behaviors and reap results, and have a significant impact on behavior [53].

The above studies show that external contextual factors influencing citizens’ carbon-neutral behavior include policy context, cost context, and social norms. Government policy and regulations act as important factors in guiding and promoting citizens’ carbon-neutral behavior, acting as a mechanism of punishment. Furthermore, objective costs and behavioral costs become important factors limiting carbon-neutral behavior in urban citizens. At the same time, social norms, family norms, and organizational norms at three levels have a significant impact on pro-environmental behavior.

3. Evolutionary Game Analysis of Multi-Subjects under the Perspective of “Follow–Drive”

3.1. Problem Description

Combined with the factors influencing the carbon-neutral behavior of urban citizens in Section 2.2, the carbon-neutral behavior of citizens is closely related to the perception of the psychological–physical dual measure of health perception level and external situational factors. The psychological–physical dual measure of health perception level includes both psychologically empowered perceptions (perception of efficacy, perception of meaning, perception of impact, closely related to civic values under intrinsic psychological factors, green personality, etc.) and physiological perceptions; the outer situational factors include cost scenarios, policy scenarios, and group norms. The theoretical model indicating the driving mechanism of urban citizens’ carbon-neutral citizenship behavior is displayed in Figure 1.

Government policy is an important factor in guiding and promoting the implementation of carbon-neutral behavior of citizens. Since the carbon-neutral behavior of citizen subjects follows the non-compulsory principle, the government should provide incentive measures to lead the market (Zhu Min, Vice President of China Center for International Economic Exchanges, 2022). Therefore, based on active publicity and education to build a low-carbon atmosphere in society, the government can further adopt incentive policies to subsidize citizens who follow and promote carbon-neutral behavior (with different amounts of subsidies for different types of citizen agents). At the same time, citizens who actively follow carbon-neutral behavior will bring comprehensive environmental benefits to the government; while if citizens do not voluntarily follow carbon-neutral behavior, the government will bear considerable environmental management costs.

Citizens are the followers and drivers of carbon-neutral behavior, but different types of citizens will bear different behavioral and objective costs. Consensual citizens need to pay time and other costs when they follow energy-saving and carbon-reducing behaviors, while adequate citizens pay higher costs than consensual citizens when they follow carbon-increasing behaviors, including economic costs and time costs. Adequate citizens are essentially the further practitioners of consensual-citizens’ carbon-neutral behavior. When citizens themselves and other citizens follow carbon-neutral behaviors (drive role), they need to bear additional interpersonal costs (time costs, information costs, etc.). Citizens will enjoy some individual environmental benefits when they only perform compliance and will have additional individual environmental benefits when they follow and drive the situation. Group norms (social, family, and organizational norms) also influence citizens’ ‘follow–drive’ behavior. Those who do not follow the carbon-neutral behavior will bear the external situational losses, while those who follow but do not drive will face additional external situational losses. In addition, citizens will enjoy the improvement of the psychological–physical dual measure of health perception level (psychologically empowered perception, physiological perception, etc.), the satisfaction of intergroup learning ability, and the perceived benefit of trust when they follow and drive. The terminologies defined in the article are listed in

Table 1. Glossary of Definitions.

Terminology	Definition
Carbon-neutral citizenship behavior	Additional voluntary actions by residents that contribute to carbon neutrality goals, i.e., voluntary actions by urban residents to offset their own CO2 emissions
Consensual citizenship behavior	Voluntary energy-saving and emission-reduction actions performed by urban citizens to minimize their carbon emissions
Adequate citizenship behavior	Voluntary carbon dioxide offsetting actions taken by urban citizens, such as utilizing carbon sequestration technology, increasing carbon sinks through tree planting or purchasing saplings
Psychological–physical dual health perception levels	The quantitative index of both psychological perception and physical perception, which is the level of perception in a series of psychological and physical processes of awareness, sensation, attention, and perception of internal and external information
Interpersonal costs	Interpersonal costs such as time and communication costs for citizen groups to drive behavior of other citizen groups
Psychological empowerment perception	The integration of an individual’s subjective judgment or perception of the autonomy of work, his or her own influence, the value and significance of the role and his or her own work ability, i.e., a measure of an integrated psychological perception experienced by the individual in the workplace
Physiological perception	The series of processes of awareness, sensation, attention, and perception of internal and external information at the body level
Citizenship values	The guiding principles, desired goals and ethical guidelines for the treatment of daily life and things, which are reflected in people’s thoughts and perceptions and reflect their true inner preferences. Although values do not have a physical form, they remain stable over time.
Green Personality	A personality with a high level of responsibility for environmental issues and a high level of interest and tolerance for new ideas
Group Norms	The perceived pressure from others, the organization, or society in the individual’s decision-making process

.

3.2. Research Hypotheses and Parameter Setting

Based on the above analysis, the present evolutionary game is hypothesized as follows.

(1)

The government’s carbon-neutral policy for citizens is formulated as an advocacy policy proposal, and therefore only chooses whether to adopt an incentive policy of a subsidized nature.

(2)

Different citizen subjects are rational in the process of realizing their interests.

(3)

The choice of individual citizens and groups of citizens to follow a carbon-neutral behavior is effective, i.e., the net benefit value of implementing the behavior is positive.

(4)

Individuals choose to follow carbon-neutral behavior when they affect each other’s externalities to the same extent.

(5)

The “free-rider benefit” is the same for the individual himself and other individuals.

As advocates and promoters of carbon-neutral behavior, governmental entities can choose the set of actions to actively build a carbon-neutral society. A1 = {Implementation of incentive policies, No incentive policy implemented}. The set of actions that citizens can choose as the followers and drivers of carbon-neutral behavior is A2 = {Follow, Not following}. As a potential target of carbon-neutral behavior, the set of actions that can be chosen by other citizens is A3 = {Follow, Not following}. It is worth noting that when A2 ∩ A3 = {Follow}, it means that the carbon-neutral “driving” behavior of citizens is established. In the subsequent analysis, this study will build a three-way evolutionary game model from the perspective of “follow–drive”; the parameters are set out in

Table 2. Parameter setting table.

Variables	Meaning
$\mathrm{x}$	Probability of the government adopting incentive subsidies
${\mathrm{y}}_1$	Probability of consensual citizens following energy-saving and carbon-reducing behaviors
${\mathrm{y}}_2$	Adequate citizens follow the probability of increasing carbon sink behavior, where ${\mathrm{y}}_2>{\mathrm{y}}_1$
$\mathrm{z}$	The probability that the remaining citizens follow the carbon-neutral behavior (following means being driven, so the type is consistent with the citizen type)
${\mathrm{C}}_1$	Costs incurred by the government in adopting incentives
$\mathrm{h}$	The cost of government neglect in not adopting various policies
$\mathrm{a}$	Government subsidies for consensual citizens
$\Delta \mathrm{a}$	Additional government subsidies for adequate citizens
$\mathrm{b}$	Additional government incentives to actively follow and drive carbon-neutral behavior
${\mathrm{C}}_2$	The cost of publicity and education paid by the government for the construction of a carbon-neutral social climate (for citizens)
d	The combined environmental benefits of government in a citizen follow-only scenario
$\Delta \mathrm{d}$	Additional benefits of the government’s environmental portfolio in a citizen-follow and citizen-driven scenario
g	Loss of environmental governance costs to government in the case of citizens’ non-follow with carbon-neutrality
${\mathrm{C}}_3$	Costs (time costs, etc.) for consensual citizens to follow energy-saving and carbon-reducing behaviors
$\Delta {\mathrm{C}}_3$	Additional costs (economic costs, time costs, etc.) for adequate citizens to follow the behavior of increasing carbon sinks
${\mathrm{C}}_4$	Interpersonal costs (time costs, information costs, etc.) required by citizens themselves and other citizens to achieve follow and drive
$\mathrm{e}$	Individual environmental benefits of citizen-follow (follow by one citizen only, free-riding behavior on the other side)
$\Delta \mathrm{e}$	Individual additional environmental benefits for citizens in following and driven situations
${\mathrm{C}}_5$	Loss of external scenarios not followed under group norms of citizens (social, family, organizational norms)
$\Delta {\mathrm{C}}_5$	Additional external situational losses followed but not driven under group norms of citizens (social, family, organizational norms)
$\mathrm{w}$	Levels of psychological–physical bimetric health perceptions of citizens in follow-only situations (psychologically empowered perceptions, physiological perceptions, etc.)
$\Delta \mathrm{w}$	Additional psychological–physical bimetric health perceptions of citizens in following and driven situations (psychologically empowered perceptions, physiological perceptions, etc.)
$\mathrm{f}$	Perceived benefits of citizen satisfaction and trust in the ability to learn in following and driven situations

.

3.3. Game Analysis

3.3.1. Game Analysis of Consensus-Based Citizen Subjects

For consensus-based citizens, the government adopts an active incentive policy to reward citizens with subsidies for carbon-neutral follow behavior and additional rewards for citizens who drive the behavior to help achieve the carbon neutrality goal. The government, citizens, and other citizens all take the maximization of their interests as the decision criterion. The decision benefit matrix of the three parties is shown in

Table 3. Tripartite decision benefit matrix for consensual citizen subjects.

Earnings Matrix	Government	Implementation of Incentive Policies (x)		No Incentive Policy Implemented (1 − x)
	Citizens	Follow (y1)	Does Not Follow (1 − y1)	Follow (y1)	Does Not Follow (1 − y1)
Other Citizens Choose	Follow (z)	G:$\mathrm{d}+\Delta \mathrm{d}-{\mathrm{C}}_1-2\mathrm{a}-2\mathrm{b}-{\mathrm{C}}_2$	G:$\mathrm{d}-{ \mathrm{C}}_1-\mathrm{a}-\mathrm{g}-{ \mathrm{C}}_2$	G: $\mathrm{d}+\Delta \mathrm{d}-{\mathrm{C}}_2-\mathrm{h}$	G: $\mathrm{d}-{ \mathrm{C}}_2-\mathrm{g}-\mathrm{h}$
		P1:$\mathrm{e}+\Delta \mathrm{e}+\mathrm{w}+\Delta \mathrm{w}+\mathrm{f}+\mathrm{a}+\mathrm{b}-{\mathrm{C}}_3-{\mathrm{C}}_4$	P1: $\mathrm{e}-{\mathrm{C}}_5$	P1:$\mathrm{e}+\Delta \mathrm{e}+\mathrm{w}+\Delta \mathrm{w}+\mathrm{f}-{\mathrm{C}}_3-{\mathrm{C}}_4$	P1: $\mathrm{e}-{\mathrm{C}}_5$
		P2:$\mathrm{e}+\Delta \mathrm{e}+\mathrm{w}+\Delta \mathrm{w}+\mathrm{f}+\mathrm{a}+\mathrm{b}-{\mathrm{C}}_3-{\mathrm{C}}_4$	P2:$\mathrm{e}+\mathrm{w}+\mathrm{a}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_5$	P2: $\mathrm{e}+\Delta \mathrm{e}+\mathrm{w}+\Delta \mathrm{w}+\mathrm{f}-{\mathrm{C}}_3-{\mathrm{C}}_4$	P2:$\mathrm{e}+\mathrm{w}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_5$
	Not Following (1 − z)	G:$\mathrm{d}-{ \mathrm{C}}_1-\mathrm{a}-\mathrm{g}-{ \mathrm{C}}_2$	G: $-{\mathrm{C}}_1-2\mathrm{g}-{\mathrm{C}}_2$	G:$\mathrm{d}-{ \mathrm{C}}_2-\mathrm{g}-\mathrm{h}$	G: $-{\mathrm{C}}_2-2\mathrm{g}-\mathrm{h}$
		P1:$\mathrm{e}+\mathrm{w}+\mathrm{a}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_5$	P1:$-{\mathrm{C}}_5$	P1: $\mathrm{e}+\mathrm{w}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_5$	P1:$-{\mathrm{C}}_5$
		P2:$\mathrm{e}-{\mathrm{C}}_5$	P2: $-{\mathrm{C}}_5$	P2: $\mathrm{e}-{\mathrm{C}}_5$	P2: $-{\mathrm{C}}_5$

Note: where G stands for government, P1 stands for citizens, and P2 stands for other citizens.

.

The subjects of carbon-neutral behavior are all finite rational and will imitate and adjust their decisions to the dominant strategy to maximize their benefits, so a dynamic replication equation (the replication dynamics equation is a mechanism describing the dynamic strategy adjustment of a finite rational game party with only the ability to simply imitate the dominant strategy, which centers on the fact that the individuals adopting the more successful strategy in the population gradually increase) is established to seek a long-term evolutionary stable strategy ESS (Evolutionarily Stable Strategy, ESS). The replication dynamic equation is constructed as follows.

Expected benefits of government-imposed incentive subsidies.

$$\begin{array}{c}{\mathrm{E}}_{\mathrm{j}=1}^{\mathrm{G}}={\mathrm{y}}_1\mathrm{z}\left(\mathrm{d}+\Delta \mathrm{d}-{\mathrm{C}}_1-2\mathrm{a}-2\mathrm{b}-{\mathrm{C}}_2\right)+{\mathrm{y}}_1\left(1-\mathrm{z}\right)\left(\mathrm{d}-{\mathrm{C}}_1-\mathrm{a}-\mathrm{g}-{\mathrm{C}}_2\right)+\\ \left(1-{\mathrm{y}}_1\right)\mathrm{z}\left(\mathrm{d}-{\mathrm{C}}_1-\mathrm{a}-\mathrm{g}-{\mathrm{C}}_2\right)+\left(1-{\mathrm{y}}_1\right)\left(1-\mathrm{z}\right)\left(-{\mathrm{C}}_1-2\mathrm{g}-{\mathrm{C}}_2\right)\end{array}$$

(1)

where ${\mathrm{y}}_1$ denotes probability of consensual citizens following energy-saving and carbon-reducing behaviors, $\mathrm{z}$ denotes the probability that the remaining citizens follow the carbon-neutral behavior, $\mathrm{d}$ denotes the combined environmental benefits of government in a citizen follow-only scenario, $\Delta \mathrm{d}$ denotes additional benefits of the government’s environmental portfolio in a citizen-follow and citizen-driven scenario, ${\mathrm{C}}_1$ denotes costs incurred by the government in adopting incentives, $\mathrm{a}$ denotes government subsidies for consensual citizens, $\mathrm{b}$ denotes additional government incentives to actively follow and drive carbon-neutral behavior, ${\mathrm{C}}_2$ denotes the cost of publicity and education paid by the government for the construction of a carbon-neutral social climate, $\mathrm{g}$ denotes loss of environmental governance costs to government in the case of citizens’ non-follow with carbon-neutrality.

Expected benefits of not implementing incentive subsidies by the government.

$$\begin{gathered} {\mathrm{E}}_{\mathrm{j}=0}^{\mathrm{G}}={\mathrm{y}}_1\mathrm{z}\left(\mathrm{d}+\Delta \mathrm{d}-{\mathrm{C}}_2-\mathrm{h}\right)+{\mathrm{y}}_1\left(1-\mathrm{z}\right)\left(\mathrm{d}-{\mathrm{C}}_2-\mathrm{g}-\mathrm{h}\right) \\ +\left(1-{\mathrm{y}}_1\right)\mathrm{z}\left(\mathrm{d}-{\mathrm{C}}_2-\mathrm{g}-\mathrm{h}\right) \\ +\left(1-{\mathrm{y}}_1\right)\left(1-\mathrm{z}\right)\left(-{\mathrm{C}}_2-2\mathrm{g}-\mathrm{h}\right) \end{gathered}$$

(2)

where $\mathrm{h}$ denotes the cost of government neglect in not adopting various policies. The government implements the incentive with a non-implementation rate of x and 1 − x. Therefore, the expected return to the government.

$${\mathrm{E}}_{\mathrm{G}}={\mathrm{xE}}_{\mathrm{j}=1}^{\mathrm{G}}+\left(1-\mathrm{x}\right){\mathrm{E}}_{\mathrm{j}=0}^{\mathrm{G}}$$

(3)

where $\mathrm{x}$ denotes probability of the government adopting incentive subsidies. The replication dynamics equation for the government is

$$\begin{gathered} \mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{dx}}{\mathrm{dt}}=\mathrm{x}({\mathrm{E}}_{\mathrm{j}=1}^{\mathrm{G}}-{\mathrm{E}}_{\mathrm{G}})=\mathrm{x}\left(1-\mathrm{x}\right)\left({\mathrm{E}}_{\mathrm{j}=1}^{\mathrm{G}}-{\mathrm{E}}_{\mathrm{j}=0}^{\mathrm{G}}\right) \\ =\mathrm{x}\left(1-\mathrm{x}\right)\left(\mathrm{h}-{\mathrm{C}}_1-\mathrm{ay}-\mathrm{az}-2\mathrm{byz}\right) \end{gathered}$$

(4)

Consistent with the government’s model, the expected benefits of citizens following carbon-neutral behavior are

$$\begin{gathered} {\mathrm{E}}_{\mathrm{j}=1}^{\mathrm{P}1}=\mathrm{xz}\left(\mathrm{e}+\Delta \mathrm{e}+\mathrm{w}+\Delta \mathrm{w}+\mathrm{f}+\mathrm{a}+\mathrm{b}-{\mathrm{C}}_3-{\mathrm{C}}_4\right) \\ +\mathrm{x}\left(1-\mathrm{z}\right)\left(\mathrm{e}+\mathrm{w}+\mathrm{a}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_5\right)+ \\ \left(1-\mathrm{x}\right)\mathrm{z}\left(\mathrm{e}+\Delta \mathrm{e}+\mathrm{w}+\Delta \mathrm{w}+\mathrm{f}-{\mathrm{C}}_3-{\mathrm{C}}_4\right)+\left(1-\mathrm{x}\right)\left(1-\mathrm{z}\right)\left(\mathrm{e}+\mathrm{w}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_5\right) \end{gathered}$$

(5)

where $\mathrm{e}$ denotes individual environmental benefits of citizen-follow, $\Delta \mathrm{e}$ denotes individual additional environmental benefits for citizens in following and driven situations, $\mathrm{w}$ denotes levels of psychological–physical bimetric health perceptions of citizens in follow-only situations, $\Delta \mathrm{w}$ denotes additional psychological–physical bimetric health perceptions of citizens in following and driven situations, $\mathrm{f}$ denotes perceived benefits of citizen satisfaction and trust in the ability to learn in following and driven situations, ${\mathrm{C}}_3$ denotes costs for consensual citizens to follow energy-saving and carbon-reducing behaviors, ${\mathrm{C}}_4$ denotes interpersonal costs required by citizens themselves and other citizens to achieve follow and drive, $\Delta {\mathrm{C}}_5$ denotes loss of external scenarios not followed under group norms of citizens. The expected benefits of citizens not following carbon-neutral behavior are

$${\mathrm{E}}_{\mathrm{j}=0}^{\mathrm{P}1}=\mathrm{xz}\left(\mathrm{e}-{\mathrm{C}}_5\right)+\left(1-\mathrm{x}\right)\mathrm{z}\left(\mathrm{e}-{\mathrm{C}}_5\right)-\left(1-\mathrm{x}\right)\left(1-\mathrm{z}\right){\mathrm{C}}_5-\left(1-\mathrm{z}\right){\mathrm{xC}}_5$$

(6)

where ${\mathrm{C}}_5$ denotes loss of external scenarios not followed under group norms of citizens. The probability of citizens following carbon-neutral behavior is ${\mathrm{y}}_1$ and 1 $-{ \mathrm{y}}_1$, so the expected benefit to citizens is

$${\mathrm{E}}_{\mathrm{P}1}={\mathrm{y}}_1{\mathrm{E}}_{\mathrm{j}=1}^{\mathrm{P}1}+\left(1-{\mathrm{y}}_1\right){\mathrm{E}}_{\mathrm{j}=0}^{\mathrm{P}1}$$

(7)

The replication dynamics equation for citizens is

$$\begin{gathered} \mathrm{F}\left({\mathrm{y}}_1\right)=\frac{{\mathrm{dy}}_1}{\mathrm{dt}}={\mathrm{y}}_1\left({\mathrm{E}}_{\mathrm{j}=1}^{\mathrm{P}1}-{\mathrm{E}}_{\mathrm{P}1}\right)={\mathrm{y}}_1\left(1-{\mathrm{y}}_1\right)\left({\mathrm{E}}_{\mathrm{j}=1}^{\mathrm{P}1}-{\mathrm{E}}_{\mathrm{j}=0}^{\mathrm{P}1}\right)={\mathrm{y}}_1\left(1-{ \mathrm{y}}_1\right) \\ (\mathrm{w}+{\mathrm{C}}_5-\Delta {\mathrm{C}}_5-{\mathrm{C}}_3+\left(\mathrm{a}+\mathrm{e}\right)\mathrm{x}+\left(\Delta {\mathrm{C}}_5+\mathrm{e}+\Delta \mathrm{e}+\Delta \mathrm{w}+\mathrm{f}-{\mathrm{C}}_4\right)\mathrm{z}+\left(\mathrm{b}-2\mathrm{e}\right)\mathrm{xz}) \end{gathered}$$

(8)

Similarly, the replication dynamic equation for other citizens is

$$\begin{gathered} \mathrm{F}\left(\mathrm{z}\right)=\frac{\mathrm{dx}}{\mathrm{dt}}=\mathrm{z}\left({\mathrm{E}}_{\mathrm{j}=1}^{\mathrm{P}2}-{\mathrm{E}}_{\mathrm{H}}\right)=\mathrm{z}\left(1-\mathrm{z}\right)\left({\mathrm{E}}_{\mathrm{j}=1}^{\mathrm{P}2}-{\mathrm{E}}_{\mathrm{j}=0}^{\mathrm{P}2}\right)= \mathrm{z}\left(1-\mathrm{z}\right) \\ (\mathrm{w}+{\mathrm{C}}_5-\Delta {\mathrm{C}}_5-{\mathrm{C}}_3+\left(\mathrm{a}+\mathrm{e}\right)\mathrm{x}+\left(\Delta {\mathrm{C}}_5+\mathrm{e}+\Delta \mathrm{e}+\Delta \mathrm{w}+\mathrm{f}-{\mathrm{C}}_4\right){\mathrm{y}}_1+\left(\mathrm{b}-2\mathrm{e}\right){\mathrm{xy}}_1) \end{gathered}$$

(9)

The Jacobian matrix is used to solve for the local stability and determine whether there is an ESS, which requires that the eigenvalues of the equilibrium points are all negative. The eigenvalues of eight of the 16 groups of equilibria obtained by Matlab calculation are opposite to each other and therefore cannot reach the stable state. Therefore, the eigenvalues of the remaining eight groups are analyzed and the

Table 4. Table of equilibrium characteristic values of consensual-type citizen subjects.

Balancing Point	Eigenvalue 1	Eigenvalue 2	Eigenvalue 3
	Expressions	Expressions	Expressions
(0,0,0)	$\mathrm{h}-{\mathrm{C}}_1$	${\mathrm{C}}_5-\Delta {\mathrm{C}}_5-{\mathrm{C}}_3+\mathrm{w}$	${\mathrm{C}}_5-\Delta {\mathrm{C}}_5-{\mathrm{C}}_3+\mathrm{w}$
(1,0,0)	${ \mathrm{C}}_1-\mathrm{h}$	$\mathrm{a}+{\mathrm{C}}_5-\Delta {\mathrm{C}}_5-{\mathrm{C}}_3+\mathrm{w}+\mathrm{e}$	$\mathrm{a}+{\mathrm{C}}_5-\Delta {\mathrm{C}}_5-{\mathrm{C}}_3+\mathrm{w}+\mathrm{e}$
(0,1,0)	$\mathrm{h}-{ \mathrm{C}}_1-\mathrm{a}$	$-{\mathrm{C}}_5+\Delta {\mathrm{C}}_5+{\mathrm{C}}_3-\mathrm{w}$	${\mathrm{C}}_5-{\mathrm{C}}_3-{\mathrm{C}}_4+\mathrm{w}+\mathrm{e}+\mathrm{f}+\Delta \mathrm{e}+\Delta \mathrm{w}$
(0,0,1)	$\mathrm{h}-{ \mathrm{C}}_1-\mathrm{a}$	$-{\mathrm{C}}_5+\Delta {\mathrm{C}}_5+{\mathrm{C}}_3-\mathrm{w}$	${\mathrm{C}}_5-{\mathrm{C}}_3-{\mathrm{C}}_4+\mathrm{w}+\mathrm{e}+\mathrm{f}+\Delta \mathrm{e}+\Delta \mathrm{w}$
(1,1,0)	$-\mathrm{h}+{\mathrm{C}}_1+\mathrm{a}$	$-{\mathrm{C}}_5+{\mathrm{C}}_3-\mathrm{a}+\Delta {\mathrm{C}}_5-\mathrm{w}-\mathrm{e}$	$\mathrm{a} + \mathrm{b} -{\mathrm{C}}_3-{\mathrm{C}}_4+{\mathrm{C}}_5+\Delta \mathrm{e}+\Delta \mathrm{w} + \mathrm{f} + \mathrm{w}$
(1,0,1)	$-\mathrm{h}+{\mathrm{C}}_1+\mathrm{a}$	$-{\mathrm{C}}_5+{\mathrm{C}}_3-\mathrm{a}+\Delta {\mathrm{C}}_5-\mathrm{w}-\mathrm{e}$	$\mathrm{a} + \mathrm{b} -{\mathrm{C}}_3-{\mathrm{C}}_4+{\mathrm{C}}_5+\Delta \mathrm{e}+\Delta \mathrm{w} + \mathrm{f} + \mathrm{w}$
(0,1,1)	$\mathrm{h}-{\mathrm{C}}_1-2\mathrm{a}-2\mathrm{b}$	${\mathrm{C}}_3+{\mathrm{C}}_4-{\mathrm{C}}_5-\Delta \mathrm{e} -\Delta \mathrm{w} - \mathrm{e} - \mathrm{f} - \mathrm{w}$	${\mathrm{C}}_3+{\mathrm{C}}_4-{\mathrm{C}}_5-\Delta \mathrm{e} -\Delta \mathrm{w} - \mathrm{e} - \mathrm{f} - \mathrm{w}$
(1,1,1)	$-\mathrm{h}+{\mathrm{C}}_1+2\mathrm{a}+2\mathrm{b}$	${\mathrm{C}}_3- \mathrm{b} - \mathrm{a} +{ \mathrm{C}}_4-{\mathrm{C}}_5-\Delta \mathrm{e} -\Delta \mathrm{w} - \mathrm{f} - \mathrm{w}$	${\mathrm{C}}_3- \mathrm{b} - \mathrm{a} +{ \mathrm{C}}_4-{\mathrm{C}}_5-\Delta \mathrm{e} -\Delta \mathrm{w} - \mathrm{f} - \mathrm{w}$

of eigenvalues is as follows.

From the above table, it can be seen that there is no stable point in the strategy combination, let alone an ESS point. Therefore, for (1,1,1) to be an ESS point, the following equation needs to be satisfied.

$$\left\{\begin{array}{c}-h+{\mathrm{C}}_1+2a+2b<0\\ {\mathrm{C}}_3-b-a+c4-c5-\Delta e-\Delta w-f-w<0\end{array}\right.$$

(10)

The equation shows that the government chooses active incentive policies when the loss from government neglect is greater than the government’s implementation of incentive policies and various types of subsidies. When the combined government subsidies, the psychological–physical dual measure of health perception level, the satisfaction of learning ability, perceived benefits of trust, individual environmental benefits, and perceived loss of group norms are greater than the cost of following carbon-neutral behavior and interpersonal interactions, the ESS point is reached when citizens both choose to follow (drive) carbon-neutral behavior. If the government chooses not to provide incentive subsidies, the costs are more restrictive when all groups of citizens follow carbon-neutral behavior.

From the government’s point of view, the government should actively adopt incentive policies to avoid the loss from negligence; consensual citizens are more likely to implement the following behavior under the government’s incentive. The Nash equilibrium solution of the final evolutionary game is (government: implementation of incentive policies; citizens: follow; other citizens: follow).

3.3.2. Game Analysis of Adequate Citizen Subjects

Consistent with the above, the adequate citizens have higher costs and benefits in all categories than the consensual citizens choose to follow. The decision benefit matrix of the three parties is shown in

Table 5. Tripartite Decision Benefit Matrix for Adequate Citizen Subjects.

Earnings Matrix	Government	Implementation of Incentive Policies (x)		No Incentive Policy Implemented (1 − x)
	Citizens	Follow (y1)	Does Not Follow	Follow (y1)	Does Not Follow
Other Citizens Choose	Follow (z)	G:$\mathrm{d}+\Delta \mathrm{d}-{\mathrm{C}}_1-2\mathrm{a}-2\Delta \mathrm{a}-2\mathrm{b}-{\mathrm{C}}_2$	G:$\mathrm{d}-{ \mathrm{C}}_1-\Delta \mathrm{a}-\mathrm{a}-\mathrm{g}-{ \mathrm{C}}_2$	G: $\mathrm{d}+\Delta \mathrm{d}-{\mathrm{C}}_2-\mathrm{h}$	G: $\mathrm{d}-{ \mathrm{C}}_2-\mathrm{g}-\mathrm{h}$
		P1:$\mathrm{e}+\Delta \mathrm{e}+\mathrm{w}+\Delta \mathrm{w}+\mathrm{f}+\mathrm{a}+\Delta \mathrm{a}+\mathrm{b}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_3-{\mathrm{C}}_4$	P1: $\mathrm{e}-{\mathrm{C}}_5$	P1:$\mathrm{e}+\Delta \mathrm{e}+\mathrm{w}+\Delta \mathrm{w}+\mathrm{f}-{\mathrm{C}}_3-{\mathrm{C}}_4-\Delta {\mathrm{C}}_3$	P1: $\mathrm{e}-{\mathrm{C}}_5$
		P2: $\mathrm{e}+\Delta \mathrm{e}+\mathrm{w}+\Delta \mathrm{w}+\mathrm{f}+\mathrm{a}+\Delta \mathrm{a}+\mathrm{b}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_3-{\mathrm{C}}_4$	P2:$\mathrm{e}+\mathrm{w}+\mathrm{a}+\Delta \mathrm{a}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_3-\Delta {\mathrm{C}}_5$	P2: $\mathrm{e}+\Delta \mathrm{e}+\mathrm{w}+\Delta \mathrm{w}+\mathrm{f}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_3-{\mathrm{C}}_4$	P2: $\mathrm{e}+\mathrm{w}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_3-\Delta {\mathrm{C}}_5$
	Not following (1 − z)	G:$\mathrm{d}-{ \mathrm{C}}_1-\mathrm{a}-\Delta \mathrm{a}-\mathrm{g}-{ \mathrm{C}}_2$	G: $-{\mathrm{C}}_1-2\mathrm{g}-{\mathrm{C}}_2$	G:$\mathrm{d}-{ \mathrm{C}}_2-\mathrm{g}-\mathrm{h}$	G: $-{\mathrm{C}}_2-2\mathrm{g}-\mathrm{h}$
		P1.$\mathrm{e}+\mathrm{w}+\mathrm{a}+\Delta \mathrm{a}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_3-\Delta {\mathrm{C}}_5$	P1:$-{\mathrm{C}}_5$	P1: $\mathrm{e}+\mathrm{w}-{\mathrm{C}}_3-\Delta {\mathrm{C}}_3-\Delta {\mathrm{C}}_5$	P1:$-{\mathrm{C}}_5$
		P2:$\mathrm{e}-{\mathrm{C}}_5$	P2: $-{\mathrm{C}}_5$	P2: $\mathrm{e}-{\mathrm{C}}_5$	P2: $-{\mathrm{C}}_5$

Note: Where G stands for government, P1 stands for citizens, and P2 stands for other citizens.

, as the government and both citizens maximize their interests as the decision criterion.

Consistent with consensual citizens, the replication dynamic equation for the three parties is

$$\left\{\begin{array}{c}\mathrm{F}\left(\mathrm{x}\right)=\mathrm{x}\left(1-\mathrm{x}\right)\left(\mathrm{h}-{\mathrm{C}}_1-\mathrm{a}\mathrm{y}-\mathrm{a}\mathrm{z}-2\mathrm{y}\Delta \mathrm{a}-2\mathrm{z}\Delta \mathrm{a}-2\mathrm{b}\mathrm{y}\mathrm{z}\right) \\ \mathrm{F}\left({\mathrm{y}}_2\right)={\mathrm{y}}_2\left(1-{ \mathrm{y}}_2\right)(\mathrm{w}+{\mathrm{C}}_5-\Delta {\mathrm{C}}_5-{\mathrm{C}}_3-2\Delta {\mathrm{C}}_3+\left(2\Delta \mathrm{a}+\mathrm{a}+\mathrm{e}\right)\mathrm{x}\\ +\left(\Delta {\mathrm{C}}_5+\mathrm{e}+\Delta \mathrm{e}+\Delta \mathrm{w}+\mathrm{f}-{\mathrm{C}}_4\right)\mathrm{z}+\left(\mathrm{b}-2\mathrm{e}\right)\mathrm{x}\mathrm{z}\\ \mathrm{F}\left(\mathrm{z}\right)=\mathrm{z}\left(1- \mathrm{z}\right)(\mathrm{w}+{\mathrm{C}}_5-\Delta {\mathrm{C}}_5-{\mathrm{C}}_3-2\Delta {\mathrm{C}}_3+\left(2\Delta \mathrm{a}+\mathrm{a}+\mathrm{e}\right)\mathrm{x}\\ +\left(\Delta {\mathrm{C}}_5+\mathrm{e}+\Delta \mathrm{e}+\Delta \mathrm{w}+\mathrm{f}-{\mathrm{C}}_4\right){\mathrm{y}}_2+\left(\mathrm{b}-2\mathrm{e}\right)\mathrm{x}{\mathrm{y}}_2 \end{array}\right.$$

(11)

The same Jacobi matrix was calculated and solved by Matlab, and 16 sets of equilibrium points were obtained in agreement with the consensus-type results, of which eight sets of eigenvalues were opposite to each other and therefore could not reach the steady state. Therefore, the eigenvalues of the remaining eight groups were analyzed and the

Table 6. Table of equilibrium characteristic values of adequate citizen subjects.

Balancing Point	Eigenvalue 1	Eigenvalue 2	Eigenvalue 3
	Expressions	Expressions	Expressions
(0,0,0)	$\mathrm{h}-{\mathrm{C}}_1$	${\mathrm{C}}_5-\Delta {\mathrm{C}}_5-{\mathrm{C}}_3-2\Delta {\mathrm{C}}_3+\mathrm{w}$	${\mathrm{C}}_5-\Delta {\mathrm{C}}_5-{\mathrm{C}}_3-2\Delta {\mathrm{C}}_3+\mathrm{w}$
(1,0,0)	${ \mathrm{C}}_1-\mathrm{h}$	$\mathrm{a}+{\mathrm{C}}_5-\Delta {\mathrm{C}}_5-{\mathrm{C}}_3+\mathrm{w}+\mathrm{e}+2\Delta \mathrm{a}-2\Delta {\mathrm{C}}_3$	$\mathrm{a}+{\mathrm{C}}_5-\Delta {\mathrm{C}}_5-{\mathrm{C}}_3+\mathrm{w}+\mathrm{e}+2\Delta \mathrm{a}-2\Delta {\mathrm{C}}_3$
(0,1,0)	$\mathrm{h}-{\mathrm{C}}_1-\mathrm{a}-2\Delta \mathrm{a}$	$-{\mathrm{C}}_5+\Delta {\mathrm{C}}_5+{\mathrm{C}}_3-\mathrm{w}+2\Delta {\mathrm{C}}_3$	${\mathrm{C}}_5-{\mathrm{C}}_3-{\mathrm{C}}_4+\mathrm{w}+\mathrm{e}+\mathrm{f}+\Delta \mathrm{e}+\Delta \mathrm{w}-2\Delta {\mathrm{C}}_3$
(0,0,1)	$\mathrm{h}-{\mathrm{C}}_1-\mathrm{a}-2\Delta \mathrm{a}$	$-{\mathrm{C}}_5+\Delta {\mathrm{C}}_5+{\mathrm{C}}_3-\mathrm{w}+2\Delta {\mathrm{C}}_3$	${\mathrm{C}}_5-{\mathrm{C}}_3-{\mathrm{C}}_4+\mathrm{w}+\mathrm{e}+\mathrm{f}+\Delta \mathrm{e}+\Delta \mathrm{w}-2\Delta {\mathrm{C}}_3$
(1,1,0)	$-\mathrm{h}+{\mathrm{C}}_1+\mathrm{a}+2\Delta \mathrm{a}$	$-{\mathrm{C}}_5+{\mathrm{C}}_3+2\Delta {\mathrm{C}}_3-\mathrm{a}-2\Delta \mathrm{a}+\Delta {\mathrm{C}}_5-\mathrm{w}-\mathrm{e}$	$\mathrm{a} +2\Delta \mathrm{a}+ \mathrm{b} -{\mathrm{C}}_3-2\Delta {\mathrm{C}}_3-{\mathrm{C}}_4+{\mathrm{C}}_5+\Delta \mathrm{e}+\Delta \mathrm{w} + \mathrm{f} + \mathrm{w}$
(1,0,1)	$-\mathrm{h}+{\mathrm{C}}_1+\mathrm{a}+2\Delta \mathrm{a}$	$-{\mathrm{C}}_5+{\mathrm{C}}_3+2\Delta {\mathrm{C}}_3-\mathrm{a}-2\Delta \mathrm{a}+\Delta {\mathrm{C}}_5-\mathrm{w}-\mathrm{e}$	$\mathrm{a} +2\Delta \mathrm{a}+ \mathrm{b} -{\mathrm{C}}_3-2\Delta {\mathrm{C}}_3-{\mathrm{C}}_4+{\mathrm{C}}_5+\Delta \mathrm{e}+\Delta \mathrm{w} + \mathrm{f} + \mathrm{w}$
(0,1,1)	$\mathrm{h}-{\mathrm{C}}_1-2\mathrm{a}-2\mathrm{b}-4\Delta \mathrm{a}$	${\mathrm{C}}_3+{\mathrm{C}}_4-{\mathrm{C}}_5-\Delta \mathrm{e} -\Delta \mathrm{w} - \mathrm{e} - \mathrm{f} - \mathrm{w}+2\Delta {\mathrm{C}}_3$	${\mathrm{C}}_3+2\Delta {\mathrm{C}}_3+{\mathrm{C}}_4-{\mathrm{C}}_5-\Delta \mathrm{e} -\Delta \mathrm{w} - \mathrm{e} - \mathrm{f} - \mathrm{w}$
(1,1,1)	$-\mathrm{h}+{\mathrm{C}}_1+2\mathrm{a}+2\mathrm{b}+4\Delta \mathrm{a}$	${\mathrm{C}}_3+2\Delta {\mathrm{C}}_3- \mathrm{b} - \mathrm{a}-2\Delta \mathrm{a}+{ \mathrm{C}}_4-{\mathrm{C}}_5-\Delta \mathrm{e} -\Delta \mathrm{w} - \mathrm{f} - \mathrm{w}$	${\mathrm{C}}_3+2\Delta {\mathrm{C}}_3- \mathrm{b} - \mathrm{a}-2\Delta \mathrm{a}+{ \mathrm{C}}_4-{\mathrm{C}}_5-\Delta \mathrm{e} -\Delta \mathrm{w} - \mathrm{f} - \mathrm{w}$

of eigenvalues was obtained as follows.

There is no stable point for the strategy combination, so for (1,1,1) to be an ESS point it needs to satisfy:

$$\left\{\begin{array}{c}-\mathrm{h}+{\mathrm{C}}_1+2\mathrm{a}+2\mathrm{b}+4\Delta \mathrm{a}<0\\ {\mathrm{C}}_3+2\Delta {\mathrm{C}}_3-\mathrm{b}-\mathrm{a}-2\Delta \mathrm{a}+{\mathrm{C}}_4-{\mathrm{C}}_5-\Delta \mathrm{e}-\Delta \mathrm{w}-\mathrm{f}-\mathrm{w}<0\end{array}\right.$$

(12)

The equation is consistent with the specific connotation of consensual citizens, so it is not repeated. Both subsidies and costs respond to increases for the adequate citizens compared to the consensual citizens. In general, the government should actively adopt incentive policies to avoid the loss from negligence; the adequate citizens are more likely to implement follow behavior under the government’s incentive and are closely related to the amount of government subsidy. The Nash equilibrium solution of the final evolutionary game is (government: implementation of incentive policies; citizens: follow; other citizens: follow). Based on the results of the evolutionary game analysis above, the following Figure 2 is obtained, and subsequent simulations will be used to examine the validity of this result.

4. Simulation Analysis

4.1. Evolutionary Process Parameter Setting

To provide a more intuitive analysis of the dynamic evolution process between the government and citizens, initial parameter values are first provided. These values are then simulated and analyzed using Python software 3.8. The setting of parameters is required to satisfy the following two points: first, the parameters are of the same magnitude, and all parameters are set within a certain range; second, the parameters are set to satisfy the requirements of the model as well as reality (the requirements of the model are part of the assumptions in the evolutionary game process, and the requirements of reality are based on the realistic situation and combined with the existing scholars’ research content). The probability of three parties is initially set to 0.5 [54], indicating an initial no-choice preference. From the Section 3 the models for consensual and adequate citizens differ only in parameters, and the differences are consistent, so the simulation analysis is only for the more generalized consensual citizens. Combining the existing literature [17,55] with the actual context of this study, the setting of each parameter is simplified, and the sensitivity analysis is used to increase the scientificity and rationality of the parameter settings. The initial values of each parameter were unified in the range of 0–10 and were all greater than zero. In the setting of the parameters, the size of the relevant subject volume of carbon-neutral behavior (government > citizens) is considered. In summary, the initial parameters are set as follows in

Table 7. Parameter initial setting table.

Variables	Initial Value	Variables	Initial Value
$\mathrm{x}$	0.5	g	3
${\mathrm{y}}_1$	0.5	${\mathrm{C}}_3$	2
${\mathrm{y}}_2$	0.5 + α	$\Delta {\mathrm{C}}_3$	1
$\mathrm{z}$	0.5	${\mathrm{C}}_4$	1
${\mathrm{C}}_1$	3	$\mathrm{e}$	1
$\mathrm{h}$	7	$\Delta \mathrm{e}$	1
$\mathrm{a}$	1	${\mathrm{C}}_5$	1
$\Delta \mathrm{a}$	0.5	$\Delta {\mathrm{C}}_5$	0.5
$\mathrm{b}$	0.5	$\mathrm{w}$	0.5
${\mathrm{C}}_2$	1	$\Delta \mathrm{w}$	0.5
d	1	$\mathrm{f}$	0.5
$\Delta \mathrm{d}$	2

.

4.2. Simulation of the Evolutionary Game under the Change of Probability of Three Parties

To determine whether the initial probability values of the three parties affect the final results of the evolutionary game, three sets of probabilities 0.2, 0.5, and 0.8 [56] were therefore selected for simulation, and the final results are shown in Figure 3.

As seen from the figure, the different values of the initial probabilities of the three parties do not affect the final stabilization result (1,1,1), i.e., the government chooses an active incentive policy and both citizens and other citizens choose to follow the carbon-neutral behavior (driven). Comparing the three sets of probability diagrams shows that the higher the initial probability of the three parties, the faster the speed towards the stabilization point, which is (government: implementation of incentive policies; citizens: follow; other citizens: follow).

4.3. Sensitivity Analysis

In the “follow–drive” perspective, a sensitivity analysis of the factors influencing citizens’ carbon-neutral behavior and the costs to the government and citizens is conducted to identify the key factors affecting the evolutionary equilibrium and the speed of evolution. We explore the influence of the government’s negligence loss, citizens’ psychological–physical dual measure of health perception level, and external situational factors on the tripartite evolutionary equilibrium; and consider the evolutionary process of the behavioral choices of the tripartite subjects when the cost decreases.

4.3.1. Options under the Change of Government Negligence Loss

Based on the step size of loss aversion in the literature [57], combined with the data outline of this paper, based on the original initial value of h = 7 for the loss from government negligence, 3, 5, 7, and 9 in the outline 0–10 were selected for sensitivity analysis, and the results obtained are shown in Figure 4.

As seen in the above figure, the greater the loss from government neglect, the more likely it is for the government to adopt an active incentive policy and the faster it will reach the evolutionary equilibrium point. Consequently, the evolutionary speed of both citizens’ choices to follow increases accordingly. This indicates that when government agents actively introduce relevant policies and regulations, the impact on citizens’ carbon-neutral behavior is positive. However, when the loss from government neglect is less than a certain value, the government chooses not to implement incentive policies to save costs, and the evolutionary equilibrium point of citizens remains the same, but the evolutionary speed becomes significantly slower, i.e., the citizens implement carbon-neutral behavior and the speed of reaching the equilibrium point slows down.

4.3.2. Choices under the Altered Psychological–Physical Dual Measure of Health Perception Level

The initial value of the psychological–physical dual measure of health perception level in the citizen only-follow case $\mathrm{w}$ = 0.5, the additional psychological–physical dual measure of health perception level in the follow-and-drive scenario $\Delta \mathrm{w}=0.5$ based on the selection of a scale less than the government 0–5, in steps of 0.5, increasing or decreasing in the same proportion, the results obtained from the simulation are shown in Figure 5.

From the above figure, it can be seen that the higher the citizens’ psychological–physical dual measure of health perception level, the faster the evolution of both citizens’ choice to follow and drive, but at this time the evolution of the government’s choice of active incentive policy slows down. From the practical point of view, when the citizens’ green consciousness, values, etc., are getting higher, the effect of the governmental implementation of incentive policies is relatively weaker.

4.3.3. Choices under the Change of Norms of Citizen Groups

Citizens who do not follow carbon-neutral behaviors in the context of group norms incur an initial external situational loss value of ${ \mathrm{C}}_5$ = 1. For those who follow carbon-neutral behaviors but do not drive other citizens to do the same, an additional external situational loss of $\Delta { \mathrm{C}}_5=0.5$ is incurred. Based on this, a consistent step size of 0.5 is chosen. The simulation results obtained, with proportional increases and decreases, are shown in Figure 6.

As seen in the above figure, the greater the group norm loss of citizens, the faster the evolution of both citizens’ choice to follow and drive, but at this time the evolution of the government’s choice of active incentive policy slows down. From a practical point of view, when carbon-neutral behavior becomes the consensus and the group norm effect is stronger, the group norm loss of citizens who choose not to follow carbon-neutral behavior is higher, and the effect of government incentive policy is relatively weaker currently.

4.3.4. The Choice of Three Parties under the “Cost Reduction” Means

From the game equilibrium in Chapter 3, the cost issue is the most critical factor affecting the choice of the three subjects. Therefore, this subsection considers the cost reduction instrument (the specific method will be developed in detail in the Section 5, i.e., the change of cost reduction on the behavior choice of tripartite subjects. The initial value of the costs spent by the government’s incentive policy ${\mathrm{C}}_1=3$. The initial value of the cost of a consensus-based citizen to follow energy-saving and carbon-reducing behavior ${\mathrm{C}}_3=2$, the initial value of the interpersonal interaction costs required by citizens themselves and other citizens to reach follow and drive ${\mathrm{C}}_4$ = 1, and the evolution is observed to be decreasing in steps of 0.5. Since the interpersonal interaction cost is not likely to be 0, we choose 1, 0.5, and 0.1 to be the three values of ${\mathrm{C}}_4$. The results obtained from the simulation are shown in Figure 7.

As seen in the above three sets of graphs, the reduction of cost does not affect the final choice of the three parties, but it affects the speed of evolution of the three parties. The lower the cost, the faster the evolution of citizens’ choices followed by both parties, and the evolution of government-imposed incentives increases, i.e., the time required for the three parties to reach the final stable equilibrium point becomes shorter, and there is mutual influenceability. Therefore, the cost reduction means is the most direct and effective factor influencing citizens’ carbon-neutral behavior for both consensual and adequate citizens.

5. Discussion

Government incentive subsidies have a positive effect on the carbon-neutral follow behavior of two types of citizens (consensual citizens and adequate citizens), and the larger the amount of subsidy, the more actively citizens follow and drive carbon-neutral behavior. Similar conclusions were obtained by Hong et al. (2019), who explored the influence of psychological factors on citizens’ energy-saving behavior from the perspective of government subsidies. This study demonstrates that citizens’ attitudes towards energy conservation and environmental responsibility have a significant positive impact on energy conservation behavior. However, values do not have a significant positive impact on energy conservation behavior. Additionally, subsidy policies play a critical role in promoting energy conservation behavior and have significant positive moderating effects on attitudes and energy conservation behavior. However, they have a negative moderating effect on the relationship between environmental responsibility and energy conservation behavior [58]. This suggests that subsidized incentives are an effective way for the government to implement them but require high costs and are prone to disruptions in citizen behavior without subsidies.

Therefore, it is crucial for the government to take a citizen-centric approach and use incentive subsidies to explore in-depth the psychological and physiological factors that influence citizens’ perception levels of health (such as psychological empowerment, physical perceptions, etc.) related to carbon-neutral behavior. This exploration should also consider cost scenarios, policy scenarios, and group norms, among other factors, to ensure citizens’ spontaneous compliance with carbon-neutral behaviors and to mobilize their active participation. Physiological and psychological health are the prerequisites for citizens to follow carbon-neutral behaviors, and when citizens are conscious and government subsidies are combined, a low-carbon scenario is expected. Cao Xiang and Gao Yu used a quasi-natural experiment to discuss whether pilot low-carbon city policies effectively promote green lifestyles among urban citizens. The results show that the pilot low-carbon city policy significantly increased the green lifestyle of urban citizens, mainly by increasing the supply of green products in the pilot cities instead of significantly increasing their awareness of green consumption. However, the study also points out that there is a time lag in this policy effect [59]. Odland et al. (2023) considered the support for specific policy types related to citizen behavior and found that a majority of homeowners supported voluntary policies, such as subsidy policies for low-carbon heating technology, while support for mandatory policies, such as carbon taxes or renewable natural gas mandates, was relatively low [60]. Golla et al. (2022) used a multi-objective evolutionary algorithm to determine household sustainable residential energy technology investments based on individual preferences. The study found that the government should carefully consider the preferences of objects within the community and that government subsidies can offset residents’ inertial investment decisions [61].

Cost reduction is the most effective way to boost the carbon-neutral behavior of multiple subjects. From the perspective of government subjects, the exploration of how to define the carbon-neutral behavior of citizens and how to carry out differential subsidies is an effective means to reduce costs. Further, government spending on creating a low-carbon atmosphere in society and promoting carbon-neutral knowledge and education can fundamentally improve citizens’ intrinsic behaviors. The realization of this initiative can also gradually reduce the number of subsidies or even eliminate them. Consistent with this study, Cheng et al. (2020) considered the utility of policy advancement and studied the utility misalignment of low-carbon living policy advancement. The results indicate that increasing the proportion of environmental benefits to citizens, government efforts and subsidies, and reducing the cost of implementing green and low-carbon lifestyles for citizens can reduce policy utility mismatches [62].

From the perspective of cost reduction of citizen subjects, there are many ways to implement carbon-neutral behaviors, such as green travel, green consumption, energy-saving behaviors, etc. Citizens can choose to follow low-cost carbon-neutral behaviors. Yue et al. (2013) classify energy-saving behaviors into use-reduction behaviors, energy-efficiency improvement behaviors, and interpersonal promotion of energy-saving behaviors based on the analysis of rooting theory [63]. Energy reduction behavior refers to the behavior of reducing energy use by changing daily energy use habits without sacrificing the quality of energy use; energy efficiency improvement behavior refers to the behavior of reducing energy use by investing in energy-efficient products or equipment and improving energy efficiency; interpersonal promotion behavior refers to the behavior of promoting energy conservation in others through active interpersonal activities based on one’s commitment to energy conservation.

In addition, Rainisio et al. (2022) also confirmed the key role of self-efficacy in energy-saving behavior through a study by Lombardi [64]. The high cost of carbon sequestration for adequate citizens can be reduced through the joint efforts of individuals and enterprises, such as Alipay’s Ant Forest “Internet + Tree Planting” model, which enables citizens to sequester carbon at “zero cost” [55]. Therefore, a government-enterprise platform can be built to facilitate the implementation of the project on one side and assist on the other side to achieve a win–win situation for society. From the viewpoint of the cost of citizens’ following, government propaganda and Internet information interaction will greatly reduce the interpersonal cost of citizens’ following.

In general, citizens need both external situational factors and internal psychological factors to follow and drive carbon-neutral behavior. The government should actively promote education to enhance citizens’ sense of environmental responsibility and green personality. Improving the corresponding policy incentive means that it can cooperate with enterprises to reduce the objective cost of citizens, so as to achieve the reduction of government environmental governance costs. The differences between the Section 5 of this study and previous research are summarized in

Table 8. Discussion of selected studies.

Study Factors	Psychological–Physical Dual Measure of Health Perception Level		Outer Situational Factors			Categories
	Psychological Empowerment Perception	Physiological Perception	Cost Scenarios	Policy Scenarios	Group Norms	Categories of Citizens
Our study	√	√	√	√	√	√
Rainisio et al. (2022) [64]						√
Hong et al. (2019) [58]	√		√	√
Cao Xiang, Gao Yu (2021) [59]	√			√
Cheng et al. (2020) [62]			√	√
Odland et al. (2023) [60]	√	√	√	√
Yue et al. (2013) [63]	√	√
Golla et al. (2022) [61]		√	√	√
Zhang Wenrui, Zhang Zhiguang (2022) [55]			√

.

6. Conclusions and Recommendations

6.1. Conclusions

Based on the evolutionary game, this study analyzes the interaction of carbon-neutral citizenship behavior and extends the meaning of behavioral intervention from a single individual to multiple parties, constructing a collaborative and interactive carbon-neutral citizenship behavior “follow–drive” guidance mechanism. By systematically simulating the formation and stabilization process of carbon-neutral citizenship behavior under different influencing factors, the following conclusions are drawn.

(1)

The final evolutionary equilibrium point of consensual citizens and adequate citizens is the same. Both types of citizens are more likely to follow the government’s incentive policy, and follow behavior is closely related to the amount of government subsidy. At this point, the Nash equilibrium solution of the evolutionary game is that the government implements the incentive policy, citizens follow the carbon-neutral behavior and lead other citizens to follow the carbon-neutral behavior, i.e., the follow–drive behavior is established.

(2)

When the initial probability value of the three parties changes, it will not affect the final evolutionary equilibrium point, i.e., the government chooses an active incentive policy, and both citizens and other citizens choose to follow and drive the carbon-neutral behavior; when the initial probability of the three parties is larger, the time for the three parties to reach stability is correspondingly shorter.

(3)

The greater the loss from government negligence, the higher the likelihood of the government adopting positive incentive policies, leading to a shorter time required to achieve stability. Consequently, it is more likely that both types of citizens will choose to follow and drive other citizens’ carbon-neutral behaviors. This reflects the positive impact of governmental entities’ active policies and regulations on citizens’ carbon-neutral behaviors.

(4)

The higher the level of citizens’ psychological–physical health perceptions, the shorter the time to reach the stabilization point where both citizens choose to follow and motivate other citizens to be carbon-neutral, but the longer the time to reach the stabilization point where the government chooses to provide positive incentives. The greater the loss of group norms among citizens, the more likely it is that both citizens will choose to follow and motivate other citizens to be carbon-neutral, but the longer it takes to reach the stabilization point at which the government chooses active incentives. From a practical point of view, when citizens’ green consciousness and values are getting higher, the effect of governmental incentive policy is relatively weaker; when carbon-neutral behavior becomes a consensus and the group norm effect is stronger, citizens will suffer from group norm loss if they do not follow carbon-neutral behavior, and the effect of governmental incentive policy is relatively weaker at this time.

(5)

The reduction of cost does not affect the final choice of the three parties, but it will affect the time to reach the final stabilization point of the three parties. When the cost of each type is lower, both citizens are more likely to choose to follow and drive carbon-neutral behavior, and the government is more likely to implement incentive policies, and there is some mutual influence.

6.2. Recommendations

Based on the findings above, the following feasibility recommendations are made to government departments.

(1)

The promotion and facilitation of carbon-neutral behavior should establish a systematic long-term incentive mechanism and innovative institutional design (the government’s incentive behavior has a positive impact on citizens’ carbon-neutral behavior) so that the public’s green behavior can be effectively and normally guided. In the areas of low-carbon product certification, third-party certification of carbon emissions, and energy contract management, the government’s involvement in market activities should be limited to a strict extent. Moreover, social supervision and severe punishment are necessary to cultivate and maintain third-party credibility. Furthermore, the incentive mechanism for low-carbon development should be improved.

(2)

Public participation is an important part of low-carbon policymaking. Focusing on the role of individual citizens’ carbon-neutral behavior, the government should deeply analyze the factors influencing urban citizens’ carbon-neutral citizenship behavior, such as the psychological–physical dual health perception level of citizens, group norms, green consciousness, and values mentioned in the above findings. By studying the driving mechanism of carbon-neutral citizen behavior, the policy booster effect can be brought into play to promote individual willingness to be carbon-neutral, so that urban citizens can implement carbon neutrality voluntarily, consciously and spontaneously. The state should also shift its strategic focus to the demand side, popularize low-carbon knowledge and policies through various channels such as information disclosure, policy advocacy, product carbon labeling, and hearings; advocate low-carbon production and life, raise the low-carbon awareness of all people, and continuously promote green consumption. Making green consumption a positive choice for citizens has become a sure way to alleviate energy problems and achieve carbon peaking and carbon neutrality.

(3)

The government should promote the active participation of the whole society in the social governance process of low-carbon development, break the barriers between the government, enterprises, citizens and other subjects involved in the carbon-neutral behavior, play an important role of each subject, and cooperate with each other to achieve a positive social interaction. It is necessary to establish a mechanism for enterprises and the public to participate in climate change, build a low-carbon governance system and platform, play the role of public and media supervision, create a low-carbon development atmosphere in society, and further improve the psychological health perception of citizens so that the physiological health perception of citizens will also be improved in the long run.

6.3. Limitations and Future Prospects

The limitations of the article are mainly reflected in the fact that the parameters of citizens’ carbon-neutral behavior are still not well set. Although most of the findings of existing scholars have been considered, there are still some influencing factors that are difficult to quantify, which will be analyzed and explored in the subsequent studies.

In terms of future prospects, how to design the simulation subject, behavior rules and simulation process in the model accurately and rationally is the main direction for further research on citizens’ carbon-neutral behavior. Based on the evolutionary game and simulation, the decision law of carbon-neutral behavior of urban citizens under the role of policy adjustment and control can be explored. When constructing the simulation model, the preferences of citizens’ decision-making, the knowledge gap between interacting objects and the preference-matching degree during social interaction should be taken into account; different individual strategy evolution rules should be established to examine the effects of parameters such as benefits, costs and norms on the emergence pattern of citizens’ group decision-making. In addition, combining the theoretical model policy, questionnaire analysis results, experimental process and computer simulation conclusions on the influence mechanism of carbon-neutral citizen behavior of urban citizens in China, and drawing on foreign policy experience to analyze and evaluate the current carbon-neutral citizen behavior guidance policy system in China according to the characteristics of energy consumption, travel patterns and lifestyles of urban citizens in China, to propose policy recommendations and establish a more scientific carbon-neutral citizen behavior guidance policy system for urban citizens will be the key direction of future research.