Evolutionary Game Analysis on Local Governments and Airlines’ Behavioral Strategies in China under Carbon Trading

. The reduction of carbon emissions by airlines has become a crucial objective in achieving carbon neutrality. However, due to the existing beneﬁts game between airlines and local governments, reducing carbon emissions in the air transport industry is a complex process. Previous research on reducing carbon emissions in the Chinese air transport industry has been divided on which approach to take. This study investigates the potential contribution of a carbon trading mechanism towards carbon emission reduction. Firstly, evolutionary game theory is employed to analyze the complex interactions between local governments and airlines, with the public will being introduced as a constraint in the proposed model. Secondly, the impact of the carbon trading mechanism on the dynamic evolution process and stakeholders is analyzed. Furthermore, the stability of the proposed evolutionary game model is veriﬁed through empirical analysis. The results show that the carbon trading mechanism plays a signiﬁcant positive role in promoting both parties’ objectives, indicating that it is a feasible method for reducing emissions in China’s air transport industry.


Introduction
The issue of greenhouse gas emissions poses a significant challenge to China's sustainable socioeconomic development. In response, the Chinese government has set ambitious targets to peak carbon dioxide emissions by 2030 and achieve carbon neutrality by 2060 [1]. However, the growing globalisation of the aviation industry presents a significant hurdle to these efforts [2]. Despite the central government's efforts to address environmental concerns through a series of regulations, local governments are struggling to mitigate pollution from the aviation industry due to the strong spatial spillover effects.
The behavior strategies of stakeholders in environmental governance have become a key focus of many academics. Both domestic and international studies have concentrated on the game behavior between subject and object in environmental governance. For instance, Liu H. H. et al. [3] developed a two-stage dynamic game model to describe the interaction between coal and coal-fired power industries. Zu Y. et al. [4] proposed a two-echelon supply chain, consisting of one manufacturer and one supplier, to increase sustainable profits using the Stackelberg differential game. Meanwhile, Kazemi and Hosseinzadeh [5] analyzed the strategic choices of multiple stakeholders in mitigating the greenhouse effect using game theory.
As demonstrated above, it is common to assume that participants are fully rational and that information is absolutely symmetric. But in fact local governments are not always have symmetric information in aviation industry pollution management. At the same time, governments and airlines are often not fully rational due to factors such as information cost, thinking cost and experience [6]. Evolutionary game theory provides a appropriately solved way to the problem that the participants have bounded rationality. In the evolutionary game, the model is upgraded from a deterministic replication dynamic model to a stochastic dynamic model, which utilizes the bounded rationality of participants and incomplete symmetric information [7]. As the result, the evolutionary game model has become an effective instrument for solving environmental problems between government and business.The carbon trading system is considered to be the most effective incentive mechanism [8]. Most of the studies on game mechanisms in carbon trading are based on classical game models. Han Wang et al. [9] adopted the propensity score matching method to realize the win-win situation of environmental in the carbon trading system. Li et al [10] proposed an equilibrium model of a carbon trading scheme and investigated the changes in consumer welfare. Ahn J [11] employed the mixed complementarity problem to study the impact of carbon trading on the electricity market. The above studies did not take into account the interrelation between incomplete information and bounded rationality.
Based on available research results, little attention has been paid to the combination of evolutionary game theory and carbon trading. More importantly, there is a lack of research on the mechanism of the role between government and airlines in carbon trading. This study aims to bridge this gap by examining whether carbon trading can effectively promote carbon emission reduction, with consideration of public preferences. To this end, we develop an evolutionary game model to investigate the behavior of local governments and airlines in carbon trading, taking a group behavior perspective to gain insights into achieving carbon neutrality. Specifically, we explore the relationship between governments and airlines under the constraints of public willingness, as shown in figure 1.
The remainder of this paper is organized as follows: In section 2, an evolutionary game model between local governments and airlines is built. Section 3 presents a case study to review the effectiveness of the approach. The conclusions, research limitations, and opportunities for future research are presented in section 4.

Evolutionary Game Model
This study investigates the workings of various fiscal preferences of local governments towards the airlines derived from an evolutionary game model. Evolutionary game theory offers numerous advantages over traditional game theory. Firstly, it describes the relationship between individual behavior and population behavior without complete competition. Second, the random disturbance components are taken into account by the evolutionary game model. In addition, the model fully considers the impact of carbon trading factors on stakeholder behavior. Table 1. Main parameters and meanings of the model.

Parameters
Description P 0 Environmental benefits by the government when airlines active reduce carbon emissions P 1 Environmental benefits by the government when airlines inactive reduce carbon emissions R 0 Benefits for airlines when they active reduce emissions R 1 Benefits for airlines when they inactive reduce emissions C 0 Cost of government for supervising airlines C 1 Costs of emission reduction for airlines to reduce carbon emissions S Subsidies for airlines to reduce carbon emissions F Fines by government for airlines not implementing emission reduction measures D 0 The impact of airlines will on government D 1 The influence of people's will on airlines D 2 The influence of people's will on government β Free carbon emission level ρ The carbon trading price at carbon trading market A Free carbon allowances E 0 Carbon emissions when airlines reduce emissions E 1 Carbon emissions when airlines do not reduce emissions This study proposes an evolutionary game model to investigate the strategic interaction between local governments and airlines in the carbon trading system. The following assumptions are adopted: (1) There are two stakeholders involved in the game process: local governments and airlines, both of which are bounded rational and make decisions based on limited knowledge and information. The parties adjust their strategies based on feedback from the other party's behavior. (2) Each game agent evolves according to natural law until it reaches a static state. (3) Airlines benefit from an increased reputation when they take active measures to reduce emissions, but such measures entail costs. Failure to reduce emissions will result in lost opportunities for additional benefits. (4) The government regulates airlines through positive incentives, such as timely subsidies, and negative constraints, such as no penalties for negative emissions. However, regulating airlines incurs costs for the government. (5) Failure to subsidize airlines for reducing carbon emissions will result in negative public opinion toward the government, while failure to reduce carbon emissions will decrease airline profitability due to negative public opinion. Ignoring environmental impact leads to negative consequences for both airline profit and government reputation. The illustration of each parameter of evolutionary game model are presented in table 1.

Model Framework
In this section, we propose an evolutionary game model that balances the interests of both the governments and the airlines, as the former attach importance to environmental factors while the latter prefer operating profitably. The corresponding payoff matrix for both players under different strategies is presented in table 2.
The expected profits of airlines when they choose active reduce emissions and inactive reduce emissions are W 0Y and W 0N , and the average profit is W 0 . The mathematical expressions are shown in Eq. (1) -Eq. (3). (1) The expected profits of local governments when they choose active supervision and inactive supervision are W 1N and W 1N , and the average profit is W 1 .The mathematical expressions are shown in Eq. (4) -Eq. (6).

Evolutionarily Stable Strategy
If the payoff or fitness of a strategy exceeds the average fitness of the group, the strategy will evolve in the group, according to evolutionary game theory. This process is represented by the replicator dynamic function [12]. The equation is where x refers to the proportion of agents of the selected strategy i. By constructing the replicator dynamics function, a two-dimensional dynamic system of the dynamic evolution of the behaviour probability of both sides over time is created, as shown in Eq. (8).
On the basis of Eq. (4), Eq. (5), Eq. (6) and Eq. (8), the replicator dynamics function for governments is given by Eq. (9). As for airlines, their replicator dynamics function can also be obtained in the same way, as shown in Eq. (10).
The government and the airlines form a two-dimensional power system. When the expectations of the two different strategies are equal, the system is in a stable state and appears an equilibrium point. According to the above analysis, there are five equilibrium points in the system when F(x) = dx/dt = 0 and F(y) = dy/dt = 0. In general, local governments and airlines tend to either pursue collusive relationships for economic gain without considering environmental regulation or establish cooperative relationships to improve the local environment. The range of evolutionary games and the distribution of equilibrium points are shown in figure 2.
Considering the ability of Jacobian matrices to provide dynamic equilibrium points for differential [13], the Jacobian matrix was established as shown in Eq. (11).

Analysis of Stability of the Model
It is necessary to determine whether each equilibrium point is stable before case analysis. The point is evolutionarily stable when the Det(J) > 0 and T r(J) < 0,otherwise it is unstable.   Table 3. Determinant and trace of Jacobian matrix at local equilibrium point.

Equilibrium point
Det(J) T r(J) According to the judgment conditions of the evolutionarily stable strategy (ESS) and actual airline operation data, B 3 (0, 0) and B 4 (1, 1) are the equilibrium points of the system stability evolution strategy. The phase diagrams of the evolutionary game is shown as figure 3. No environmental governance by local governments and airlines will be the only evolutionarily stable strategy when the evolutionary game system converges to the equilibrium point . When the evolutionary game system converges to another equilibrium point , local authorities and airlines are more likely to positively cooperate and better manage the environment.

Results Discussion and Analysis
To investigate the impact of the carbon trading mechanism on the evolution of the system, this section utilizes actual production and operational data from airlines and conducts a comparison of simulation results before and after the implementation of carbon trading. Initially, the system evolution process without carbon emission trading is simulated, assuming that the government does not enforce any low carbon regulatory instruments and relies entirely on market economy regulation. All other parameters are held constant, with the carbon penalty Step Probability Figure 4. Systematic evolutionary process without considering carbon trading. Step Probability Airlines Local governments Figure 5. Systematic evolutionary process with considering carbon trading.
F = 40 and carbon subsidy S = 0 set. The simulation results are presented in figure 4, which indicates that at this point, the airlines in the system enter a poor state. This suggests that relying solely on the heavy polluters to meet the carbon reduction target is not feasible. Next, the system evolution process that includes carbon emissions trading is simulated, assuming that the government takes carbon trading measures, and airlines can carry out carbon quota trading in the carbon market. Figure 5 demonstrates that the proportion of active carbon emission reduction of airlines gradually converges to 1, and the system evolves to the equilibrium point B 4 (1, 1) of stable strategy after the intervention of the carbon trading mechanism. These findings highlight the significant positive impact of the carbon trading mechanism on promoting airlines to adopt active carbon emission reduction strategies.

Conclusion
Airlines are under increasing pressure to reduce carbon emissions as a result of both energy consumption concerns and the "double carbon" targets. This study constructs an evolutionary game model of government and airline carbon emission reduction, driven by emissions trading and incorporating public will. The impact of carbon emissions trading on strategic choices made during the game is explored, and the results suggest that the mechanism plays a significant and positive role in promoting active carbon emission reduction by both parties. In particular, airlines exhibit increased enthusiasm for reducing carbon emissions under the carbon trading mechanism. The findings indicate that carbon emissions trading can facilitate mutual coordination between decision-makers at different levels in the air transport industry, thereby enabling participants to make more informed decisions. Nonetheless, some limitations related to this study still exist. While the public will is considered an important factor influencing the strategy choices of the government and airlines, this study focuses solely on their evolution. The evolution of customer relationships with the government or with airlines is not taken into account, despite the complex relationship between these three players in the implementation of prefabrication. Therefore, further in-depth research is needed to fully understand the dynamics of carbon emissions reduction in the air transport industry.