# Research on the Impact of Output Adjustment Strategy and Carbon Trading Policy on the Response, Stability and Complexity of Steel Market under the Dynamic Game

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## Abstract

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## 1. Introduction

## 2. Literature Review

#### 2.1. Generation and Development of Carbon Trading Mechanism

_{2}) is the largest, so this transaction is calculated per ton of CO

_{2}equivalent (t CO

_{2}e); thus, it is commonly called “carbon trading”. The United Nations Intergovernmental Panel on Climate Change adopted the United Nations Framework Convention on Climate Change on 9 May 1992. In December 1997, the first additional agreement to the Convention, the Kyoto Protocol (referred to as the Protocol), was adopted in Kyoto, Japan. The “Protocol” regards the market mechanism as a new way to solve the greenhouse gas emission reduction problem represented by CO

_{2}, that is, the CO

_{2}emission rights are regarded as a commodity, thus, forming the trading of CO

_{2}emission rights.

#### 2.2. Literature Review of Carbon Trading Mechanism in the Steel Industry

_{2}emission reduction targets in the US iron and steel sector from 2010 to 2050. Yamazaki [7] examined whether the absolute amount of steel scrap used in Japan increases under an emissions trading scheme using the computable general equilibrium model (CGE model). Kushwaha et al. [8] took Indian steel manufacturers as an example to study the impact of the timing of the implementation of carbon quotas and carbon trading policies on the selection of waste steel collection channels in multiregional issues.

_{2}) from firms participating in Shanghai’s carbon dioxide (CO

_{2}) emissions trading scheme (ETS) to deliver one of the first ex-post evaluations on the co-benefits of China’s ETS.

#### 2.3. The Application of Bounded Rationality in Industrial Sector

#### 2.4. Literature Summary

## 3. Method

#### 3.1. The Establishment and Game Analysis of the Static Output Selection Model under the Carbon Trading Mechanism

_{2}emission reduction and production simultaneously. At this time, enterprise i’s profit function basic form in case K is as follows:

#### 3.2. Scenario Assumptions

- Single carbon trading policy in 2020 (if implemented)

- Mixed carbon trading policy scenario in 2025 (carbon trading and subsidies)

_{0}= 2.3782 and e

_{0}= 2.2197 are discussed, respectively.

- Multiple mixed carbon trading policy implemented in 2030 (carbon trading, subsidies, and CCS)

_{0}= 2.2197 and e

_{0}= 2.0611 are discussed, respectively.

#### 3.3. Establishment of Dynamic Output Selection Model and Analysis of Local Stability

_{i}is taken as the decision variable. The base period profit margin is positive (negative), and the firm will increase (decrease) output in the next period. The product output of enterprise i in period k + 1 is as follows:

_{i}> 0 represents the output adjustment speed of enterprise I, which includes the following:

#### 3.4. Data Sources

_{2}accounting data, this research refers to IPCC2006 [59] and Duan et al. [60].

## 4. Results and Discussions

#### 4.1. The Results of Parameter Fitting

_{0}in the carbon trading mechanism, considering that China has just begun to implement a carbon trading mechanism, the initial carbon emissions benchmark value for the steel industry should not be set too high. After the system matures, the benchmark value setting should be stricter. Combined with related research, it is assumed that the benchmark value for 2020 is the average level of CO

_{2}emission intensity of the steel industry in 2015, which is 2.8210 ton CO

_{2}/ton of steel.

#### 4.2. Empirical Analysis

#### 4.2.1. Single Carbon Trading Policy in 2020 (If Implemented)

- The output adjustment speed of ξ
_{2}, ξ_{5}, ξ_{6}remains unchanged.

_{2}, ξ

_{5}, and ξ

_{6}are all set to 0 at the same time. The steel market stability domain composed of ξ

_{1}, ξ

_{3}, and ξ

_{4}is analyzed. As can be seen in Figure 1, the adjustment coefficient ξ

_{1}range is [0, 3.35], the ξ

_{3}range is [0, 4.00], and the ξ

_{4}range is [0, 5.00], (the ξ value range considered in this section is [0, 5], and the actual situation will not happen if the value is too large or negative, as can be seen below).

_{1}, ξ

_{3}, and ξ

_{4}is basically the same as when the target is 15%.

_{2}, ξ

_{5}, and ξ

_{6}increase from 1.00 to 5.00 (Figure 2), and it can be seen that, as the northeast, southwest, and northwest regions adopt positive production adjustment coefficients at the same time, the stability of the steel market gradually decreases. When ξ

_{2}, ξ

_{5}, and ξ

_{6}are large, the other three regions still have sufficient room for output adjustment.

_{2}, ξ

_{5}, and ξ

_{6}are set to 5 at the same time. The results are shown in Figure 3:

_{1}remains at [0, 1.225], the value range of ξ

_{3}is increased from [0, 1.450] to [0, 1.475], and the value range of ξ

_{4}is increased from [0, 1.825] to [0, 1.850]. Judging from the results, the area of the stability region shows an increasing trend as the target increases. It shows that under the combined effect of the carbon tax and the output adjustment policy of smaller output enterprises, the larger output enterprises’ output adjustment policies will show an increasing trend.

- 2.
- The output adjustment speed of ξ
_{1}, ξ_{3}, ξ_{4}remains unchanged.

_{1}, ξ

_{3}, ξ

_{4}are both set to 0, the steel market stability domain composed of ξ

_{2}, ξ

_{5}, and ξ

_{6}is analyzed. As can be seen in Figure 4, the range of ξ

_{2}is [0, 10.00], ξ

_{5}is [0, 7.50], and ξ

_{6}is [0, 10.00] or even more. The value range of ξ considered in this section is [0, 10].

_{2}, ξ

_{5}, and ξ

_{6}is basically the same as when the target is 15%.

_{1}, ξ

_{3}, and ξ

_{4}simultaneously increase from 0.50 to 2.00. The stability domain is shown in Figure 5, where it can be seen that when North, East, and South Central China adopt positive production adjustment coefficients at the same time, the stability of the steel market gradually decreases. It can be clearly found that when ξ

_{1}, ξ

_{3}, and ξ

_{4}take small positive values, Northeast China, Southwest China, and Northwest China still have greater autonomy in decision-making. However, when ξ

_{1}, ξ

_{3}, and ξ

_{4}gradually increase, the stable area of the entire steel market will shrink sharply. When ξ

_{1}, ξ

_{3}, and ξ

_{4}are 2, the value range of ξ

_{2}, ξ

_{5}, and ξ

_{6}is very small. Obviously, when ξ

_{1}, ξ

_{3}, and ξ

_{4}keep increasing, the market is easily out of balance.

_{1}, ξ

_{3}, and ξ

_{4}take 1.5 at the same time as an example, the results are shown in Figure 6.

_{2}is still maintained at [0, 10] (but through further calculations, the upper limit is increased), the value range of ξ

_{5}is maintained at [0, 3.60], and the value range of ξ

_{6}is increased from [0, 8.60] to [0, 8.80]. Judging from the results, the area of the stability region shows an increasing trend as the target increases. This means that, under the combined effect of the single carbon trading policy and the output adjustment policy of enterprises with larger output, the smaller output enterprises’ output adjustment policies will also increase.

- 3.
- System dynamic characteristics analysis.

_{1}, ξ

_{5}, and the change impacts on system stability (we actually calculated all the results with a reduction target of 15–20%, but due to space limitations, this section uses a reduction target of 20% as an example). The results are shown in Figure 7, Figure 8, Figure 9 and Figure 10.

#### 4.2.2. Mixed Carbon Trading Policy Scenario in 2025: Carbon Trading + Subsidy

_{0}= 2.3782) and Table 10 (e

_{0}= 2.2197).

- 4.
- The output adjustment speed of ξ
_{2}, ξ_{5}, ξ_{6}remains unchanged.

_{0}= 2.3782, emission reduction target is 20%, and ξ

_{2}, ξ

_{5}, and ξ

_{6}take 0 at the same time, the steel market stability domain composed of ξ

_{1}, ξ

_{3}, and ξ

_{4}is analyzed. As can be seen in Figure 11, the adjustment coefficient ξ

_{1}range is [0, 3.50], the ξ

_{3}range is [0, 4.05], and the ξ

_{4}range is [0, 4.75].

_{2}, ξ

_{5}, and ξ

_{6}change from 1.00 to 4.00 (Figure 12), and the stable area gradually decreases. The changing trend of its shape is very similar to that of a single carbon trading policy. However, the difference is that when the values of ξ

_{2}, ξ

_{5}, and ξ

_{6}are large (=4), the area of its stability region has been greatly reduced, but when ξ

_{2}, ξ

_{5}, and ξ

_{6}continue to increase to 5, there is no region left. This shows that with the introduction of the mixed emission reduction policy, the output adjustment policy of enterprises has been compressed, and enterprises with larger output have to carefully consider their next production strategy to prevent the entire steel market from falling into an imbalance.

_{2}, ξ

_{5}, and ξ

_{6}are set to 5 at the same time as an example. This is shown in Figure 13.

_{1}is expanded to [0, 0.075], the value range of ξ

_{3}is expanded to [0, 0.100], and the value range of ξ

_{4}is expanded to [0, 0.125]. This shows that under a mixed emission reduction policy, under the combined effect of the emission reduction policy and the output adjustment policy of an enterprise with a smaller output, as the target gradually increases, the output adjustment policies of enterprises with larger outputs will show an increasing trend.

_{0}gradually decreases, that is, the benchmark value in the carbon trading mechanism becomes more and more stringent, in fact, the change rule of the stable region does not change much, except for the difference in area. Take e

_{0}= 2.3782, 2.3148 and 2.2197, ${\xi}_{2}={\xi}_{5}={\xi}_{6}=5$, and the emission reduction target of 25% as an example. Here, ${\xi}_{1}$ remains in the range of [0, 0.075], ${\xi}_{3}$ remains in the range of [0, 0.100], while ${\xi}_{4}$ reduces from [0, 0.125] to [0, 0.100]. It can be foreseen that, when the benchmark value is lower, the stable region may cease to exist.

- 5.
- The output adjustment speed of ξ
_{1}, ξ_{3}, ξ_{4}remains unchanged.

_{0}= 2.3782, the target is 20%, and ξ

_{1}, ξ

_{3}, and ξ

_{4}are taken as 0 at the same time, the steel market stability domain composed of ξ

_{2}, ξ

_{5,}and ξ

_{6}is analyzed. As can be seen in Figure 14, the adjustment coefficient ξ

_{2}range is [0, 9.50], the ξ

_{5}range is [0, 7.40], and the ξ

_{6}range is [0, 10.00] or even more.

_{1}, ξ

_{3}, ξ

_{4}) increases from 0.50 to 2.00.

_{1}, ξ

_{3}, and ξ

_{4}are 1.5, the output adjustment space of the other three regions is as follows: ξ

_{2}is [0, 4.70], ξ

_{5}is [0, 3.70], ξ

_{6}is [0, 9.20]; compared to only a single carbon trading policy scenario (when the target is 20%), its stability area has been greatly reduced. When the values of ξ

_{1}, ξ

_{3}, and ξ

_{4}are larger, it is foreseeable that the moment of system imbalance will be earlier than the situation where there is only a single carbon trading policy scenario (when the target is 20%).

_{1}, ξ

_{3}, and ξ

_{4}take 1.5 at the same time, the value range of ξ

_{2}is maintained at [0, 4.70], the value range of ξ

_{5}is maintained at [0, 3.70], and the value range of ξ

_{6}is increased from [0, 9.20] to [0, 9.30]. When ξ

_{1}, ξ

_{3}, and ξ

_{4}take other smaller values, there is a similar rule. However, when ξ

_{1}, ξ

_{3}, and ξ

_{4}assume larger values at the same time (and there is a stable region), the conclusion is different. When the target is increased from 20% to 25%, ξ

_{1}, ξ

_{3}, and ξ

_{4}are 2, the value range of ξ

_{6}maintained in the interval of [0, 0.90], but the value range of ξ

_{2}is reduced from [0, 0.50] to [0, 0.40], and the value range of ξ

_{2}is reduced from [0, 0.40] to [0, 0.30]. These results are shown in Figure 16 and Figure 17.

_{0}gradually decreases, that is, the benchmark value in the carbon trading mechanism becomes more and more stringent; in fact, the change rule of the stable region does not change much, except for the difference in area. Take e

_{0}= 2.3782, 2.3148 and 2.2197, ${\xi}_{1}={\xi}_{3}={\xi}_{4}=0$ and the emission reduction target of 25% as an example. Here, ${\xi}_{2}$ remains in the range of [0, 9.700], ${\xi}_{6}$ remains in the range of [0, 10.000], while ${\xi}_{5}$ reduces from [0, 7.500] to [0, 7.400]. The changes in ${\xi}_{i}$ are so small that they were almost negligible. Unless e

_{0}is very small, the change is obvious, but that is too extreme.

- 6.
- System dynamic characteristics analysis.

_{0}= 2.3782) as an example for discussion.

#### 4.2.3. Multiple Mixed Carbon Trading Policy Implemented in 2030: Carbon Trading + Subsidy + CCS

_{0}= 2.2197) and Table 14 (e

_{0}= 2.0611).

- 7.
- The output adjustment speed of ξ
_{2}, ξ_{5}, ξ_{6}remains unchanged.

_{0}= 2.2197, the target is 25%, and ξ

_{2}, ξ

_{5}, and ξ

_{6}take 0 at the same time, the steel market stability region consisting of ξ

_{1}, ξ

_{3}, and ξ

_{4}is analyzed. As can be seen in Figure 22, the adjustment coefficient ξ

_{1}range is [0, 3.65], the ξ

_{3}range is [0, 4.15], and theξ

_{4}range is [0, 5.00].

_{2}, ξ

_{5}, and ξ

_{6}change from 1.00 to 4.00 (Figure 23), and the stable area gradually decreases. However, the difference is that when the values of ξ

_{2}, ξ

_{5}, and ξ

_{6}are large (=4), compared to the mixed carbon trading policy scenario (emission reduction target = 25%), the area of its stability region has been greatly reduced. When ξ

_{2}, ξ

_{5}, and ξ

_{6}continue to increase to 5, there is no longer a stable region. This shows that with the introduction of the multiple emission reduction policies, enterprises with larger output have to carefully consider their future production strategies to avoid output adjustment strategies that would spur the entire steel market into an imbalance.

_{2}, ξ

_{5,}and ξ

_{6}are taken as 4 at the same time as an example. This is shown in Figure 24.

_{1}is increased from [0, 0.30] to [0, 0.45], the value range of ξ

_{3}is increased from [0, 0.40] to [0, 0.60], and the value range of ξ

_{4}is increased from [0, 0.45] to [0, 0.70]. This also shows that even if there are more complex mixed emission reduction policies, under the combined effect of emission reduction policies and output adjustment policies for enterprises with smaller output, as the target gradually increases, the output adjustment policies that affect enterprises with a larger output will show an increasing trend.

_{0}gradually decreases, that is, the benchmark value in the carbon trading mechanism becomes more and more stringent, the change rule of the stable region does not change much, except for the difference in area. Take e

_{0}= 2.2197, 2.1563, and 2.0611, ${\xi}_{2}={\xi}_{5}={\xi}_{6}=4$, and an emission reduction target of 30% as an example. Here, ${\xi}_{1}$ reduces from [0, 0.450] to [0, 0.400], ${\xi}_{3}$ reduces from [0, 0.600] to [0, 0.500], while ${\xi}_{4}$ reduces from [0, 0.700] to [0, 0.600]. It can be foreseen that when the benchmark value is lower, the stable region may cease to exist.

- 8.
- The output adjustment speed of ξ
_{1}, ξ_{3}, ξ_{4}remains unchanged.

_{0}= 2.2197, the emission reduction target is 25%, and ξ

_{1}, ξ

_{3}, and ξ

_{4}are taken as 0 at the same time, the steel market stability domain composed of ξ

_{2}, ξ

_{5}, and ξ

_{6}is analyzed. As can be seen in Figure 25, the adjustment coefficient ξ

_{2}range is [0, 8.30], the ξ

_{5}range is [0, 6.30], and the ξ

_{6}range is [0, 10.00] or even more, which is smaller than the scenario of a carbon trading and subsidy policy with a target of 25%. This shows that when the policies become more complex, the production plans of enterprises with smaller output will be affected more obviously.

_{1}, ξ

_{3}, ξ

_{4}) increases from 0.50 to 2.00.

_{1}, ξ

_{3}, and ξ

_{4}are 1.5, the output adjustment space of the other three regions is as follows: ξ

_{2}is [0, 4.40], ξ

_{5}is [0, 3.30], and ξ

_{6}is [0, 6.80]. Compared to the scenario of carbon trading and a subsidy (an emission reduction target of 25%, where ξ

_{2}is [0, 4.70], ξ

_{5}is [0, 3.60], and ξ

_{6}is [0, 9.30]), the area of its stability area has been greatly reduced. However, when the value of ξ

_{1}, ξ

_{3}, and ξ

_{4}is larger (=2), the area of the stability region is bigger than the results of the mixed policy scenario (carbon trading and a subsidy, with a target of 25%). When ξ

_{1}, ξ

_{3}, and ξ

_{4}continue to increase, the system will enter a state of imbalance, but the moment of system imbalance will be later than in the carbon trading and subsidy emission reduction policy scenario (the target is 25%).

_{1}, ξ

_{3}, and ξ

_{4}are 1.5 at the same time, the value range of ξ

_{6}is increased from [0, 6.80] to [0, 6.90], the value range of ξ

_{2}is maintained at [0, 4.40], and the value range of ξ

_{5}is maintained at [0, 3.30]. When ξ

_{1}, ξ

_{3}, ξ

_{4}are other smaller values, there is a similar rule. However, when ξ

_{1}, ξ

_{3}, and ξ

_{4}take on larger values at the same time (and there is a stable region), the conclusion is different. When the target is increased from 25% to 30%, and when ξ

_{1}, ξ

_{3}, and ξ

_{4}are given the value of 2 at the same time, the value range of ξ

_{2}is reduced from [0, 1.10] to [0, 1.00], the value range of ξ

_{5}is reduced from [0, 0.80] to [0, 0.70], and the value range of ξ

_{6}is reduced from [0, 1.70] to [0, 1.40]. These results are shown in Figure 27 and Figure 28.

_{0}gradually decreases, that is, the benchmark value in the carbon trading mechanism becomes more and more stringent, the change rule of the stable region does not change much, except for the difference in area. Take e

_{0}= 2.2197, 2.1563, and 2.0611, ${\xi}_{1}={\xi}_{3}={\xi}_{4}=2$, and an emission reduction target of 30% as an example. The value range of ξ

_{2}is increased from [0, 1.00] to [0, 1.10], the value range of ξ

_{5}is increased from [0, 0.70] to [0, 0.80], and the value range of ξ

_{6}is increased from [0, 1.40] to [0, 1.60]. The changes in ${\xi}_{i}$ are so small that they were almost negligible. Unless e

_{0}is very small, the change is obvious, but that is too extreme.

- 9.
- System dynamic characteristics analysis.

_{0}= 2.2197) as an example for discussion.

#### 4.3. Discussion

_{2}emission reduction targets increases the production adjustment strategy of these regions, that is, they can adopt more flexible production plans. Obviously, under the dual carbon goal, it is most important for steel enterprises in these regions to complete the corresponding emission reduction plans (the requirements of the emission reduction policy combination can be ignored to a certain extent).

_{2}emission reduction policies is more conducive to market stability and the realization of emission reduction goals.

## 5. Conclusions and Recommendations

_{2}emission reduction, which has become a major problem that the steel market must face. There are increasing calls to implement various emission reduction policies, such as carbon trading policies and product subsidy policies, but it is unreasonable to only consider meeting emission reduction targets while ignoring market production stability. In order to examine the comprehensive impact of carbon trading policies and product production adjustment strategies on the steel market, this paper constructs a repeated dynamic game model. This paper introduces a carbon trading mechanism and bounded rationality expectation strategy. Then, this paper analyzes the output selection and market stability of steel oligarchs under multiple emission reduction targets, multiple CO

_{2}emission benchmarks and policies, and further analyzes and compares the dynamic production adjustment and market imbalance conditions of steel oligarchs under various conditions, as well as the corresponding stability regions, bifurcation diagrams, and Lyapunov exponents. This research draws the following conclusions.

- When the steel industry implements a single or mixed carbon trading policy and output adjustment policy, without considering emission reduction targets, the system balance influence of larger output enterprises is much greater than that of smaller output enterprises. When larger output enterprises adopt weak positive adjustment policies, smaller output enterprises will have more autonomy in output planning. However, when large-scale enterprises adopt improper output adjustment policies, such as excessive output, it is more dangerous for small-scale enterprises, which will cause their output adjustment space to shrink sharply. In addition, when multiple firms simultaneously employ dynamic output adjustments, the system is more prone to falling into an imbalanced state;
- When output adjustment policy and a single carbon trading emission reduction policy are combined to act on the steel market, as emission reduction targets are gradually raised, the adjustment policies that enterprises with larger or smaller outputs can implement will show an increasing trend, that is, enterprises can implement more output adjustment policies without causing the system to fall into a state of bifurcation or even chaos;
- If the emission reduction target consistently raised, and the carbon trading policy adds subsidies, CCS, and other mixed emission reduction policies, the enterprises are affected. For enterprises with a larger output, even if a more complex mixed emission reduction policy appears, as the target gradually increases, the output adjustment policies that can be implemented will also show an increasing trend. However, for enterprises with a smaller output, the output adjustment policy will be restricted and affected by more factors, including emission reduction targets. The rule of change is different from that of the single carbon trading scenario, and even occurs that the stability zone shrinks and the output adjustment policies decrease when the emission reduction target is large. This means that enterprises with smaller outputs need to be more cautious in formulating their own production plans to ensure that the enterprises and the entire steel market will not fall into a state of imbalance;
- The selection of the benchmark value will not cause significant changes in the stability region of the steel market. However, it is still recommended that relevant departments should not adopt too aggressive emission reduction targets and benchmarks when considering the implementation of the carbon trading mechanism.

_{2}emissions, and other data. In addition, the characterization of the decision-making process of enterprises, the production game process between enterprises, and the decomposition process of emission reduction targets between the government and enterprises should receive more in-depth and multi-situational discussion, and a more universal theoretical model should be established, so as to be applicable to empirical research in a wider area and a more common industry.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Smale, R.; Hartley, M.; Hepburn, C.; Ward, J.; Grubb, M. The impact of CO
_{2}emissions trading on firm profits and market prices. Clim. Policy**2006**, 6, 31–48. [Google Scholar] [CrossRef] - Allevi, E.; Gnudi, A.; Konnov, I.V.; Oggioni, G. Decomposition method for oligopolistic competitive models with common environmental regulation. Ann. Oper. Res.
**2013**, 268, 441–467. [Google Scholar] [CrossRef] - Boutabba, M.A.; Lardic, S. EU Emissions Trading Scheme, competitiveness and carbon leakage: New evidence from cement and steel industries. Ann. Oper. Res.
**2017**, 255, 47–61. [Google Scholar] [CrossRef] - Stuhlmacher, M.; Patnaik, S.; Streletskiy, D.; Taylor, K. Cap-and-trade and emissions clustering: A spatial-temporal analysis of the European Union Emissions Trading Scheme. J. Environ. Manag.
**2019**, 249, 109352. [Google Scholar] [CrossRef] [PubMed] - Hanclova, J.; Zapletal, F.; Smid, M. On interaction between carbon spot prices and Czech steel industry. Carbon Manag.
**2020**, 11, 121–137. [Google Scholar] [CrossRef] - Karali, N.; Xu, T.F.; Sathaye, J. Reducing energy consumption and CO
_{2}emissions by energy efficiency measures and international trading: A bottom-up modeling for the US iron and steel sector. Appl. Energy**2014**, 120, 133–146. [Google Scholar] [CrossRef] - Yamazaki, M. Effects of CO
_{2}Emissions Trading on Steel Scrap Recycling: A Simulation Analysis Using a Computable General Equilibrium Model. Mater. Trans.**2011**, 52, 498–506. [Google Scholar] [CrossRef] - Kushwaha, S.; Ghosh, A.; Rao, A.K. Collection activity channels selection in a reverse supply chain under a carbon cap-and-trade regulation. J. Clean. Prod.
**2020**, 260, 121034. [Google Scholar] [CrossRef] - Zhu, L.; Zhang, X.B.; Li, Y.; Wang, W.X.; Guo, J. Can an emission trading scheme promote the withdrawal of outdated capacity in energy-intensive sectors? A case study on China’s iron and steel industry. Energy Econ.
**2017**, 63, 332–347. [Google Scholar] - Zhao, Y.B.; Wang, C.; Sun, Y.W.; Liu, X.B. Factors influencing companies’ willingness to pay for carbon emissions: Emission trading schemes in China. Energy Econ.
**2018**, 75, 357–367. [Google Scholar] - Wei, L.; Chen, W.D.; Yang, Y. Decision-makings on the Scrap Iron and Steel Remanufacturing Considering the Introduction of Carbon Emission Reduction Investment. Ind. Eng. Manag.
**2018**, 23, 65–71+79. [Google Scholar] - Liu, X.; Li, Y.; Zhang, D.Y.; Zhu, L. On the Effectiveness of the Abatement Policy Mix: A Case Study of China’s Energy-Intensive Sectors. Energies
**2018**, 11, 559. [Google Scholar] [CrossRef] - Dai, H.C.; Xie, Y.; Liu, J.Y.; Masui, T. Aligning renewable energy targets with carbon emissions trading to achieve China’s INDCs: A general equilibrium assessment. Renew. Sustain. Energy Rev.
**2018**, 82, 4121–4131. [Google Scholar] [CrossRef] - Zeng, B.X.; Zhu, L. Market Power and Technology Diffusion in an Energy-Intensive Sector Covered by an Emissions Trading Scheme. Sustainability
**2019**, 11, 3870. [Google Scholar] [CrossRef] - Lin, W.B.; Gu, A.L.; Liu, B.; Wang, Z.X.; Zhou, L.L. Carbon market, sector competitiveness and carbon leakage: Steel sector case. Progress. Inquisitiones Mutat. Clim.
**2019**, 15, 427–435. [Google Scholar] - Duan, Y.; Han, Z.L.; Zhang, H.; Wang, H.Y. Research on the applicability and impact of CO
_{2}emission reduction policies on China’s steel industry. Int. J. Clim. Chang. Strateg. Manag.**2021**, 13, 352–374. [Google Scholar] [CrossRef] - Zhang, C.; Zhang, X.X. Evolutionary game analysis of air pollution co-investment in emission reductions by steel enterprises under carbon quota trading mechanism. J. Environ. Manag.
**2022**, 317, 115376. [Google Scholar] [CrossRef] [PubMed] - Zhu, B.Z.; Jiang, M.X.; He, K.J.; Chevallier, J.; Xie, R. Allocating CO
_{2}allowances to emitters in China: A multi-objective decision approach. Energy Policy**2018**, 121, 441–451. [Google Scholar] [CrossRef] - Pang, T.; Zhou, S.; Deng, Z.; Duan, M.S. The influence of different allowance allocation methods on China’s economic and sectoral development. Clim. Policy
**2018**, 18, 27–44. [Google Scholar] [CrossRef] - Zhang, Y.L.; Gu, L.Y.; Guo, X. Carbon audit evaluation system and its application in the iron and steel enterprises in China. J. Clean. Prod.
**2020**, 248, 119204. [Google Scholar] [CrossRef] - Jiang, T.Y.; Song, J.C.; Yu, Y. The influencing factors of carbon trading companies applying blockchain technology: Evidence from eight carbon trading pilots in China. Environ. Sci. Pollut. Res.
**2022**, 29, 28624–28636. [Google Scholar] - Wei, P.B.; Cui, H.R.; Gang, M.Q. Scenario analysis of energy conservation and CO
_{2}emissions reduction policies in China’s iron and steel sector. Pol. J. Environ. Stud.**2017**, 26, 2307–2317. [Google Scholar] [CrossRef] - Duan, Y.; Han, Z.L.; Mu, H.L.; Yang, J.; Li, Y.H. Research on the impact of various emission reduction policies on China’s iron and steel industry production and economic level under the carbon trading mechanism. Energies
**2019**, 12, 1624. [Google Scholar] [CrossRef] - Li, Z.L.; Dai, H.C.; Song, J.N.; Sun, L.; Geng, Y.; Lu, K.Y. Assessment of the carbon emissions reduction potential of China’s iron and steel industry based on a simulation analysis. Energy
**2019**, 183, 279–290. [Google Scholar] [CrossRef] - Zhu, X.H.; Zeng, A.Q.; Zhong, M.R.; Huang, J.B.; Qu, H.P. Multiple impacts of environmental regulation on the steel industry in China: A recursive dynamic steel industry chain CGE analysis. J. Clean. Prod.
**2019**, 210, 490–504. [Google Scholar] [CrossRef] - Wang, P.; Dai, H.C.; Ren, S.Y.; Zhao, D.Q.; Masui, T. Achieving Copenhagen target through carbon emission trading: Economic impacts assessment in Guangdong Province of China. Energy
**2015**, 79, 212–227. [Google Scholar] [CrossRef] - Wu, R.; Dai, H.C.; Geng, Y.; Xie, Y.; Mosui, T.; Tian, X. Achieving China’s INDC through carbon cap-and-trade: Insights from Shanghai. Appl. Energy
**2016**, 184, 1114–1122. [Google Scholar] [CrossRef] - Zhang, Y.J.; Shi, W.; Jiang, L. Does China’s carbon emissions trading policy improve the technology innovation of relevant enterprises? Bus. Strategy Environ.
**2020**, 29, 872–885. [Google Scholar] [CrossRef] - Zhang, Y.J.; Wang, W. How does China’s carbon emissions trading (CET) policy affect the investment of CET-covered enterprises? Energy Econ.
**2021**, 98, 105224. [Google Scholar] [CrossRef] - Tan, Q.L.; Liu, L.T.; Zhu, S.L. Study on the benchmark method for national carbon trading in China’s iron and steel industry. Progress. Inquisitiones Mutat. Clim.
**2021**, 17, 590–597. [Google Scholar] - Tan-Soo, J.S.; Li, L.L.; Qin, P.; Zhang, X.B. Do CO
_{2}emissions trading schemes deliver co-benefits? evidence from shanghai. Clim. Policy**2021**, 22, 64–76. [Google Scholar] [CrossRef] - Meinel, U.; Schule, R. The Difficulty of Climate Change Adaptation in Manufacturing Firms: Developing an Action-Theoretical Perspective on the Causality of Adaptive Inaction. Sustainability
**2018**, 10, 569. [Google Scholar] [CrossRef] - Safarzynska, K.; Van den Bergh, J.C.J.M. A higher rebound effect under bounded rationality: Interactions between car mobility and electricity generation. Energy Econ.
**2018**, 74, 179–196. [Google Scholar] - Rezvani, Z.; Hudson, P. How do middle managers really make decisions within the oil and gas industry? Saf. Sci.
**2021**, 139, 105199. [Google Scholar] [CrossRef] - Hammond, S.F.; Gajendran, T.; Savage, D.A.; Maund, K. Unpacking the problems behind the limited green construction adoption: Towards a theoretical model. Eng. Constr. Archit. Manag.
**2021**, 28, 833–844. [Google Scholar] - Ji, W.Z. Study on Outputs Game Models and Chaotic Characters in Electric Power Oligopoly. Ph.D. Thesis, Tianjin University, Tianjin, China, 2008. [Google Scholar]
- Sun, Z.H.; Ma, J.H. Game Model of Dynamically Repeated Price in Domestic Steel Market. J. Xidian Univ.
**2009**, 19, 43–47. [Google Scholar] - Tu, H.L. Research on the Dynamics of the Cournot Dynamical Game Models in the Electricity Market and the Renewable Resource Market. Ph.D. Thesis, Tianjin University, Tianjin, China, 2013. [Google Scholar]
- Dang, J.F.; Hong, I.H. The equilibrium quantity and production strategy in a fuzzy random decision environment: Game approach and case study in glass substrates industries. Int. J. Prod. Econ.
**2013**, 145, 724–732. [Google Scholar] [CrossRef] - Tan, Z.L.; Liang, Z.X. Study on Dynamic Repetition Game Model of Coal Market Price in China. Coal Econ. Res.
**2016**, 36, 45–48. [Google Scholar] - Di, X.; Liu, H.X.; Ban, X.J. Second best toll pricing within the framework of bounded rationality. Transp. Res. Part B Methodol.
**2016**, 83, 74–90. [Google Scholar] - Di, X.; Liu, H.X.; Zhu, S.; Levinson, D.M. Indifference bands for boundedly rational route switching. Transportation
**2017**, 44, 1169–1194. [Google Scholar] [CrossRef] - Liu, L.W. Nonlinear Complex Dynamics of Carbon Emission Reduction Cournot Game with Bounded Rationality. Complexity
**2017**, 2017, 8301630. [Google Scholar] - Yu, Y. Complexity Analysis of Taxi Duopoly Game with Heterogeneous Business Operation Models and Differentiated Products. J. Intell. Fuzzy Syst.
**2017**, 33, 3059–3067. [Google Scholar] - Ding, M.; Qian, Y.; Zhang, J.; He, J.; Yi, J. Defence model based on multistage dynamic game with consideration of bounded rationality against power system cascading failure. Electr. Power Autom. Equip.
**2017**, 37, 69–74+82. [Google Scholar] - Zhang, J.X. Study on Competitive Game Model with Bounded Rationality Enterprise of Emissions Trading. Value Eng.
**2018**, 6, 101–103. [Google Scholar] - Sang, H.Y.; Xie, X.L.; Wang, B. Ship scheme selection based on decision maker’s limited rationality. J. Dalian Marit. Univ.
**2019**, 45, 58–64. [Google Scholar] - Zhang, Y.M.; Chen, W.D.; Mi, Y. Third-party remanufacturing mode selection for competitive closed-loop supply chain based on evolutionary game theory. J. Clean. Prod.
**2020**, 63, 121305. [Google Scholar] - Wu, F. Research on Dynamic and Complexity of Energy-Saving Investment about Multichannel and Multienergy Supply Chain. Complexity
**2020**, 2020, 2409636. [Google Scholar] - Duan, Y.; Han, Z.L.; Mu, H.L.; Yang, J.; Li, Y.H. Research on the Influence of Bounded Rationality and Product Differentiation on the Stability of Steel Industry Market. Discret. Dyn. Nat. Soc.
**2020**, 2020, 1828674. [Google Scholar] - Fan, B.; Guo, T.T.; Xu, R.Z.; Dong, W.Q. Evolutionary Game Research on the Impact of Environmental Regulation on Overcapacity in Coal Industry. Math. Probl. Eng.
**2017**, 2021, 5558112. [Google Scholar] [CrossRef] - Ma, J.H.; Hou, Y.M.; Wang, Z.X.; Yang, W.H. Pricing strategy and coordination of automobile manufacturers based on government intervention and carbon emission reduction. Energy Policy
**2021**, 148, 111919. [Google Scholar] - Huang, Q.Y.; Wang, J.W.; Ye, M.W.; Zhao, S.M.; Si, X. A Study on the Incentive Policy of China’s Prefabricated Residential Buildings Based on Evolutionary Game Theory. Sustainability
**2022**, 14, 1926. [Google Scholar] [CrossRef] - Li, X.J.; Wang, C.; Kassem, M.A.; Liu, Y.S.; Ali, K.N. Study on Green Building Promotion Incentive Strategy Based on Evolutionary Game between Government and Construction Unit. Sustainability
**2022**, 14, 10155. [Google Scholar] [CrossRef] - NBS (National Bureau of Statistics of the People’s Republic of China). China Statistical Yearbook 2005–2017; The Editorial Board of China Statistical Yearbook: Beijing, China, 2005–2017. Available online: http://www.stats.gov.cn/tjsj/ndsj/ (accessed on 2 September 2022).
- NBS (National Bureau of Statistics of the People’s Republic of China). China Industrial Economy Statistical Yearbook 2005–2017; The Editorial Board of China Industrial Economy Statistical Yearbook: Beijing, China, 2005–2017. Available online: https://navi.cnki.net/knavi/yearbooks/YZGJN/detail (accessed on 2 September 2022).
- NBS (National Bureau of Statistics of the People’s Republic of China). China Energy Statistical Yearbook 2005–2017; The Editorial Board of China Energy Statistical Yearbook: Beijing, China, 2005–2017. Available online: https://navi.cnki.net/knavi/yearbooks/YCXME/detail?uniplatform=NZKPT (accessed on 2 September 2022).
- CISA (China Iron and Steel Association). China Steel Yearbook 2005–2017; The Editorial Board of China Steel Yearbook: Beijing, China, 2005–2017. Available online: http://www.csdri.com.cn/periodical (accessed on 2 September 2022).
- IPCC (Intergovernmental Panel on Climate Change). IPCC Guidelines for National Greenhouse Gas Inventories; IPCC: Bracknell, UK, 2006. [Google Scholar]
- Duan, Y.; Mu, H.L.; Li, N. Analysis of the relationship between China’s IPPU CO
_{2}emissions and the industrial economic growth. Sustainability**2016**, 8, 426. [Google Scholar] [CrossRef] - Färe, R.S.; Grosskopf, C.A.; Pasurka, J. Environmental production functions and environmental directional distance functions. Energy
**2007**, 32, 1055–1066. [Google Scholar] [CrossRef] - Lee, J.D.; Park, J.B.; Kim, T.Y. Estimation of the shadow prices of pollutants with production/ environment inefficiency taken into account: A nonparametric directional distance function approach. J. Environ. Manag.
**2002**, 64, 365–375. [Google Scholar] [CrossRef] [PubMed] - Guenno, G.; Tiezzi, S. The Index of Sustainable Economics Welfare (ISEW) for Italy; Fondazione Eni Enrico Mattei: Milano, Italy, 1998. [Google Scholar]

**Figure 1.**The market stability domain (${\xi}_{2}={\xi}_{5}={\xi}_{6}=0$, with an emission reduction target of 15%).

**Figure 2.**The market stability domain (${\xi}_{2}={\xi}_{5}={\xi}_{6}=1~5$, with an emission reduction target of 15%).

**Figure 3.**The market stability domain (${\xi}_{2}={\xi}_{5}={\xi}_{6}=5$; the (

**left**) emission target is 15%, while the (

**right**) is 20%).

**Figure 4.**The market stability domain (${\xi}_{1}={\xi}_{3}={\xi}_{4}=0$, with an emission reduction target of 15%).

**Figure 5.**The market stability domain (${\xi}_{1}={\xi}_{3}={\xi}_{4}=0.5~2$, with an emission reduction target of 15%).

**Figure 6.**The market stability domain (${\xi}_{1}={\xi}_{3}={\xi}_{4}=1.5$, and emission reduction targets of 15% on the (

**left**), and 20% on the (

**right**).

**Figure 7.**The bifurcation diagram of ${\xi}_{1}$ ((

**left**): ${\xi}_{2}~{\xi}_{6}$ = 0, (

**right**): ${\xi}_{2}~{\xi}_{6}$ = 0.4).

**Figure 8.**The bifurcation diagram of ${\xi}_{5}$ ((

**left**): ${\xi}_{1},{\xi}_{2},{\xi}_{3},{\xi}_{4},{\xi}_{6}$ = 0, (

**right**): ${\xi}_{1},{\xi}_{2},{\xi}_{3},{\xi}_{4},{\xi}_{6}$ = 1.5).

**Figure 9.**The Lyapunov exponent diagram ((

**left**): ${\xi}_{2}~{\xi}_{6}$ = 0, (

**right**): ${\xi}_{2}~{\xi}_{6}$ = 0.4).

**Figure 10.**The Lyapunov exponent diagram ((

**left**): ${\xi}_{1},{\xi}_{2},{\xi}_{3},{\xi}_{4},{\xi}_{6}$ = 0, (

**right**): ${\xi}_{1},{\xi}_{2},{\xi}_{3},{\xi}_{4},{\xi}_{6}$ = 1.5).

**Figure 11.**The market stability domain (${\xi}_{2}={\xi}_{5}={\xi}_{6}=0$, with an emission reduction target of 20%, e

_{0}= 2.3782).

**Figure 12.**The market stability domain (${\xi}_{2}={\xi}_{5}={\xi}_{6}=1~4$, with an emission reduction target of 20%).

**Figure 13.**The market stability domain (${\xi}_{2}={\xi}_{5}={\xi}_{6}=5$, with an emission reduction target of 20% on the (

**left**), and 25% on the (

**right**)).

**Figure 14.**The market stability domain (${\xi}_{1}={\xi}_{3}={\xi}_{4}=0$, with an emission reduction target of 20%).

**Figure 15.**The market stability domain (${\xi}_{1}={\xi}_{3}={\xi}_{4}=0.5~2$, with an emission reduction target of 20%).

**Figure 16.**The market stability domain (${\xi}_{1}={\xi}_{3}={\xi}_{4}=1.5$, for the emission reduction target of 20% in 2020 on the (

**left**), 20% in 2025 in the (

**middle**), and 25% on the (

**right**)).

**Figure 17.**The market stability domain (${\xi}_{1}={\xi}_{3}={\xi}_{4}=2$, with an emission reduction target if 20% in 2020 on the (

**left**) 20%, 20% in 2025 in the (

**middle**), and 25% on the (

**right**)).

**Figure 18.**The bifurcation diagram of ${\xi}_{1}$ ((

**left**): ${\xi}_{2}~{\xi}_{6}$ = 0, (

**right**): ${\xi}_{2}~{\xi}_{6}$ = 0.4).

**Figure 19.**The bifurcation diagram of ${\xi}_{5}$ ((

**left**): ${\xi}_{1},{\xi}_{2},{\xi}_{3},{\xi}_{4},{\xi}_{6}$ = 0, (

**right**): ${\xi}_{1},{\xi}_{2},{\xi}_{3},{\xi}_{4},{\xi}_{6}$ = 1.5).

**Figure 20.**The Lyapunov exponent diagram ((

**left**): ${\xi}_{2}~{\xi}_{6}$ = 0, (

**right**): ${\xi}_{2}~{\xi}_{6}$ = 0.4).

**Figure 21.**The Lyapunov exponent diagram ((

**left**): ${\xi}_{1},{\xi}_{2},{\xi}_{3},{\xi}_{4},{\xi}_{6}$ = 0, (

**right**): ${\xi}_{1},{\xi}_{2},{\xi}_{3},{\xi}_{4},{\xi}_{6}$ = 1.5).

**Figure 22.**The market stability domain (${\xi}_{2}={\xi}_{5}={\xi}_{6}=0$, emission reduction target: 25%).

**Figure 23.**The market stability domain (${\xi}_{2}={\xi}_{5}={\xi}_{6}=1~4$, with an emission reduction target of 25%).

**Figure 24.**The market stability domain (${\xi}_{2}={\xi}_{5}={\xi}_{6}=4$, with an emission reduction target of 25% on the (

**left**) 25%, and 30% on the (

**right**)).

**Figure 25.**The market stability domain (${\xi}_{1}={\xi}_{3}={\xi}_{4}=0$, with an emission reduction target of 25%).

**Figure 26.**The market stability domain (${\xi}_{1}={\xi}_{3}={\xi}_{4}=0.5~2$, with an emission reduction target of 25%).

**Figure 27.**The market stability domain (${\xi}_{1}={\xi}_{3}={\xi}_{4}=1.5$, with an emission reduction target of 25% in 2025 on the (

**left**), 25% in 2030 in the (

**middle**) 25%, and 30% on the (

**right**)).

**Figure 28.**The market stability domain (${\xi}_{1}={\xi}_{3}={\xi}_{4}=2$, with an emission reduction target of 25% in 2025 on the (

**left**), 25% in 2030 in the (

**middle**) 25%, and 30% on the (

**right**)).

**Figure 29.**The bifurcation diagram of ${\xi}_{1}$ ((

**left**): ${\xi}_{2}~{\xi}_{6}$ = 0, (

**right**): ${\xi}_{2}~{\xi}_{6}$ = 0.4).

**Figure 30.**The bifurcation diagram of ${\xi}_{5}$ ((

**left**): ${\xi}_{1},{\xi}_{2},{\xi}_{3},{\xi}_{4},{\xi}_{6}$ = 0, (

**right**): ${\xi}_{1},{\xi}_{2},{\xi}_{3},{\xi}_{4},{\xi}_{6}$ = 1.5).

**Figure 31.**The Lyapunov exponent diagram ((

**left**): ${\xi}_{2}~{\xi}_{6}$ = 0, (

**right**): ${\xi}_{2}~{\xi}_{6}$ = 0.4).

**Figure 32.**The Lyapunov exponent diagram ((

**left**): ${\xi}_{1},{\xi}_{2},{\xi}_{3},{\xi}_{4},{\xi}_{6}$ = 0, (

**right**): ${\xi}_{1},{\xi}_{2},{\xi}_{3},{\xi}_{4},{\xi}_{6}$ = 1.5).

Researcher | Main Theory and Model |
---|---|

Game Model | |

Smale et al. [1] | Cournot oligopoly game model |

Allevi et al. [2] | Generalized non-cooperative game |

Wei et al. [11] | Production decision game model |

Zeng and Zhu [14] | Imperfect competition permit market model |

Duan et al. [16,23] | Dynamic game |

Zhang and Zhang [17] | Evolutionary game model |

Equilibrium model | |

Yamazaki [7] | CGE model |

Zhu et al. [9] | Partial equilibrium model |

Liu et al. [12] | Partial equilibrium model |

Dai et al. [13] | CGE model |

Lin et al. [15] | Partial equilibrium model |

Pang et al. [19] | CGE model |

Zhu et al. [25] | CGE model |

Wang et al. [26] | CGE model |

Wu et al. [27] | CGE model |

Programming Model | |

Kushwaha et al. [8] | Mixed-integer linear programming model |

Zhu et al. [18] | Multi-objective decision approach |

Wei et al. [22] | LEAP model |

Analysis model of influencing factors | |

Boutabba and Lardic [3] | Rolling cointegration approach |

Stuhlmacher et al. [4] | Clustering analysis and spatial-temporal analysis |

Hanclova et al. [5] | Dynamic factor augmented vector autoregression (FAVAR) model and Granger causality analysis |

Zhang et al. [20] | Carbon audit theory and the driving force-state-response (DSR) model |

Other Models | |

Karali et al. [6] | Industry sector energy efficiency modeling (ISEEM) |

Zhao et al. [10] | Multiple-bounded discrete choice (MBDC) questionnaire and contingent valuation methods |

Li et al. [24] | Nonlinear environmental economic model based on input–output (I–O) table |

Zhang et al. [28] | Difference-in-differences based propensity score matching methods (PSM-DID) |

Zhang and Wang [29] | Difference-in-differences based propensity score matching methods (PSM-DID) |

Researcher | Industrial Sector |
---|---|

Ji [36] | Electricity industry and electricity market |

Sun and Ma [37] | Steel industry and steel market |

Tu [38] | Power and renewable resources industry |

Dang and Hong [39] | Glass substrates industry |

Tan and Liang [40] | Coal industry and coal market |

Di et al. [41,42] | Transportation planning |

Liu [43] | Carbon trade market |

Yu [44] | Transportation industry |

Ding et al. [45] | Electricity system |

Zhang [46] | Carbon trade market |

Sang, Xie and Wang [47] | Ship-building industry |

Zhang et al. [48] | Remanufacturing industry |

Wu [49] | Electricity market |

Duan et al. [50] | Steel industry |

Fan et al. [51] | Coal industry |

Ma et al. [52] | Vehicle industry |

Huang et al. [53] | Construction industry |

Li et al. [54] | Construction industry |

Notations | Explanations |
---|---|

Q | Steel production |

P | The price of steel |

A | The constant of the market inverse demand curve |

Β | The primary coefficient of the market inverse demand curve |

q_{i} | Steel production of region i |

e_{2015,i} | The region i CO_{2} emission intensity of per ton steel in 2015 |

e_{i} | The region i CO_{2} emission intensity of per ton steel at some stage |

r_{i} | The decline range of CO_{2} emission intensity of per ton steel in region i at some stage |

R | The decline target of national CO_{2} emission intensity of per ton steel at some stage |

MAC | Marginal abatement cost curve in steel industry |

a_{i} | The quadratic coefficient of steel industry’s MAC in region i |

b_{i} | The primary coefficient of steel industry’s MAC in region i |

C_{i} | The cost function of steel industry in region i |

C_{0,i} | The production cost of steel industry in region i |

c_{i} | The cost of base period emission reduction in region i |

e_{0} | CO_{2} emission benchmarks in carbon trading mechanism |

PP | Purchase price of carbon quota |

SP | Selling price of carbon quota |

CQ_{i} | Carbon quota of region i |

W | Social welfare function |

CS | Consumer surplus |

PS | Producer surplus |

D(E) | Total macro external environment loss of CO_{2} emission |

θ | The external loss parameter of CO_{2} |

π_{i} | The profit function of steel industry in region i |

E | The total CO_{2} emissions in steel industry |

ξ_{i} | The adjustment coefficient, rate of output adjustment |

η | The production subsidies |

m | The CO_{2} emission reduced by CCS (carbon capture and storage) demonstration project |

A | The primary coefficient of CCS demonstration project cost curve |

B | The constant of CCS demonstration project cost curve |

S | The total subsidy |

M | The total cost of CCS demonstration project |

Notations | Unit | i = 1 | i = 2 | i = 3 | i = 4 | i = 5 | i = 6 |
---|---|---|---|---|---|---|---|

e_{2015,i} | t CO_{2}/t | 2.3344 | 3.5698 | 2.9040 | 2.8779 | 3.2202 | 4.5864 |

a_{i} | - | 11,661 | 17,208 | 16,932 | 12,952 | 6397.2 | 3485 |

b_{i} | - | −169.76 | 8876.7 | −166.92 | 1483.6 | 502.52 | 421.13 |

c_{i} | Yuan | 2168.2 | 3511.1 | 2165.4 | 3325.1 | 2368.7 | 3814.3 |

C_{0,caseK,i} | Yuan, 2015 | 2833.15 | 4898.47 | 3453.53 | 4153.15 | 3799.03 | 3832.38 |

Yuan, 2020 | 2124.86 | 3918.77 | 2590.15 | 2491.89 | 3609.08 | 3640.76 | |

Yuan, 2025 | 1699.89 | 2743.14 | 2072.12 | 1868.92 | 3067.72 | 3094.64 | |

Yuan, 2030 | 1444.91 | 2194.51 | 1761.30 | 1588.58 | 2454.17 | 2475.71 |

**Table 5.**The equilibrium output E* of each regional enterprise (emission reduction target of 15–20%).

Emission Reduction Target | 15% | 16% | 17% | 18% | 19% | 20% |
---|---|---|---|---|---|---|

q_{1} | 2.5841 | 2.5869 | 2.5900 | 2.5934 | 2.5970 | 2.6009 |

q_{2} | 0.3872 | 0.3856 | 0.3837 | 0.3815 | 0.3791 | 0.3763 |

q_{3} | 2.1673 | 2.1684 | 2.1696 | 2.1708 | 2.1721 | 2.1735 |

q_{4} | 1.7405 | 1.7413 | 1.7422 | 1.7431 | 1.7441 | 1.7452 |

q_{5} | 1.1722 | 1.1725 | 1.1728 | 1.1732 | 1.1737 | 1.1744 |

q_{6} | 0.4915 | 0.4886 | 0.4856 | 0.4826 | 0.4797 | 0.4769 |

Emission Reduction Target | 15% | 16% | 17% | 18% | 19% | 20% |
---|---|---|---|---|---|---|

J_{11} | 1 − 0.5844ξ_{1} | 1 − 0.5852ξ_{1} | 1 − 0.5860ξ_{1} | 1 − 0.5870ξ_{1} | 1 − 0.5880ξ_{1} | 1 − 0.5890ξ_{1} |

J_{12} = J_{13} = J_{14} = J_{15} = J_{16} | −0.2920ξ_{1} | −0.2923ξ_{1} | −0.2927ξ_{1} | −0.2930ξ_{1} | −0.2935ξ_{1} | −0.2929ξ_{1} |

J_{22} | 1 − 0.0880ξ_{2} | 1 − 0.0877ξ_{2} | 1 − 0.0874ξ_{2} | 1 − 0.0871ξ_{2} | 1 − 0.0867ξ_{2} | 1 − 0.0863ξ_{2} |

J_{21} = J_{23} = J_{24} = J_{25} = J_{26} | −0.0438ξ_{2} | −0.0436ξ_{2} | −0.0434ξ_{2} | −0.0431ξ_{2} | −0.0428ξ_{2} | −0.0425ξ_{2} |

J_{33} | 1 − 0.4903ξ_{3} | 1 − 0.4906ξ_{3} | 1 − 0.4910ξ_{3} | 1 − 0.4915ξ_{3} | 1 − 0.4919ξ_{3} | 1 − 0.4924ξ_{3} |

J_{31} = J_{32} = J_{34} = J_{35} = J_{36} | −0.2449ξ_{3} | −0.2450ξ_{3} | −0.2452ξ_{3} | −0.2453ξ_{3} | −0.2455ξ_{3} | −0.2456ξ_{3} |

J_{44} | 1 − 0.3938ξ_{4} | 1 − 0.3941ξ_{4} | 1 − 0.3944ξ_{4} | 1 − 0.3948ξ_{4} | 1 − 0.3952ξ_{4} | 1 − 0.3956ξ_{4} |

J_{41} = J_{42} = J_{43} = J_{45} = J_{46} | −0.1967ξ_{4} | −0.1968ξ_{4} | −0.1969ξ_{4} | −0.1970ξ_{4} | −0.1971ξ_{4} | −0.1972ξ_{4} |

J_{55} | 1 − 0.2654ξ_{5} | 1 − 0.2655ξ_{5} | 1 − 0.2658ξ_{5} | 1 − 0.2660ξ_{5} | 1 − 0.2663ξ_{5} | 1 − 0.2666ξ_{5} |

J_{51} = J_{52} = J_{53} = J_{54} = J_{56} | −0.1325ξ_{5} | −0.1325ξ_{5} | −0.1325ξ_{5} | −0.1326ξ_{5} | −0.1326ξ_{5} | −0.1327ξ_{5} |

J_{66} | 1 − 0.1115ξ_{6} | 1 − 0.1110ξ_{6} | 1 − 0.1105ξ_{6} | 1 − 0.1099ξ_{6} | 1 − 0.1095ξ_{6} | 1 − 0.1090ξ_{6} |

J_{61} = J_{62} = J_{63} = J_{64} = J_{65} | −0.0555ξ_{6} | −0.0552ξ_{6} | −0.0549ξ_{6} | −0.0545ξ_{6} | −0.0542ξ_{6} | −0.0539ξ_{6} |

**Table 7.**The equilibrium output E* of each regional enterprise (emission reduction target of 20–25%, e

_{0}= 2.3782).

Emission Reduction Target | 20% | 21% | 22% | 23% | 24% | 25% |
---|---|---|---|---|---|---|

q_{1} | 2.4863 | 2.4900 | 2.4942 | 2.4985 | 2.5033 | 2.5088 |

q_{2} | 0.9253 | 0.9209 | 0.9160 | 0.9107 | 0.9049 | 0.8984 |

q_{3} | 2.1506 | 2.1517 | 2.1526 | 2.1535 | 2.1543 | 2.1548 |

q_{4} | 1.8143 | 1.8149 | 1.8154 | 1.8158 | 1.8161 | 1.8161 |

q_{5} | 1.1706 | 1.1710 | 1.1715 | 1.1720 | 1.1725 | 1.1729 |

q_{6} | 0.4702 | 0.4673 | 0.4646 | 0.4623 | 0.4602 | 0.4583 |

**Table 8.**The equilibrium output E* of each regional enterprise (emission reduction target of 20–25%, e

_{0}= 2.2197).

Emission Reduction Target | 20% | 21% | 22% | 23% | 24% | 25% |
---|---|---|---|---|---|---|

q_{1} | 2.4806 | 2.4836 | 2.4866 | 2.4902 | 2.4942 | 2.4987 |

q_{2} | 0.9263 | 0.9220 | 0.9173 | 0.9121 | 0.9063 | 0.9000 |

q_{3} | 2.1516 | 2.1527 | 2.1539 | 2.1549 | 2.1558 | 2.1565 |

q_{4} | 1.8152 | 1.8160 | 1.8167 | 1.8173 | 1.8176 | 1.8179 |

q_{5} | 1.1715 | 1.1721 | 1.1728 | 1.1734 | 1.1740 | 1.1746 |

q_{6} | 0.4711 | 0.4684 | 0.4659 | 0.4637 | 0.4617 | 0.4600 |

Emission Reduction Target | 20% | 21% | 22% | 23% | 24% | 25% |
---|---|---|---|---|---|---|

J_{11} | 1 − 0.5619ξ_{1} | 1 − 0.5627ξ_{1} | 1 − 0.5637ξ_{1} | 1 − 0.5647ξ_{1} | 1 − 0.5657ξ_{1} | 1 − 0.5670ξ_{1} |

J_{12} = J_{13} = J_{14} = J_{15} = J_{16} | −0.2810ξ_{1} | −0.2814ξ_{1} | −0.2818ξ_{1} | −0.2823ξ_{1} | −0.2829ξ_{1} | −0.2835ξ_{1} |

J_{22} | 1 − 0.2091ξ_{2} | 1 − 0.2081ξ_{2} | 1 − 0.2070ξ_{2} | 1 − 0.2058ξ_{2} | 1 − 0.2045ξ_{2} | 1 − 0.2030ξ_{2} |

J_{21} = J_{23} = J_{24} = J_{25} = J_{26} | −0.1046ξ_{2} | −0.1041ξ_{2} | −0.1035ξ_{2} | −0.1029ξ_{2} | −0.1023ξ_{2} | −0.1015ξ_{2} |

J_{33} | 1 − 0.4863ξ_{3} | 1 − 0.4863ξ_{3} | 1 − 0.4865ξ_{3} | 1 − 0.4867ξ_{3} | 1 − 0.4869ξ_{3} | 1 − 0.4870ξ_{3} |

J_{31} = J_{32} = J_{34} = J_{35} = J_{36} | −0.2430ξ_{3} | −0.2431ξ_{3} | −0.2432ξ_{3} | −0.2433ξ_{3} | −0.2434ξ_{3} | −0.2435ξ_{3} |

J_{44} | 1 − 0.4100ξ_{4} | 1 − 0.4102ξ_{4} | 1 − 0.4103ξ_{4} | 1 − 0.4104ξ_{4} | 1 − 0.4104ξ_{4} | 1 − 0.4104ξ_{4} |

J_{41} = J_{42} = J_{43} = J_{45} = J_{46} | −0.2050ξ_{4} | −0.2051ξ_{4} | −0.2051ξ_{4} | −0.2052ξ_{4} | −0.2052ξ_{4} | −0.2052ξ_{4} |

J_{55} | 1 − 0.2646ξ_{5} | 1 − 0.2647ξ_{5} | 1 − 0.2648ξ_{5} | 1 − 0.2649ξ_{5} | 1 − 0.2650ξ_{5} | 1 − 0.2651ξ_{5} |

J_{51} = J_{52} = J_{53} = J_{54} = J_{56} | −0.1323ξ_{5} | −0.1323ξ_{5} | −0.1324ξ_{5} | −0.1324ξ_{5} | −0.1325ξ_{5} | −0.1325ξ_{5} |

J_{66} | 1 − 0.1063ξ_{6} | 1 − 0.1056ξ_{6} | 1 − 0.1050ξ_{6} | 1 − 0.1045ξ_{6} | 1 − 0.1040ξ_{6} | 1 − 0.1036ξ_{6} |

J_{61} = J_{62} = J_{63} = J_{64} = J_{65} | −0.0531ξ_{6} | −0.0528ξ_{6} | −0.0525ξ_{6} | −0.0522ξ_{6} | −0.0520ξ_{6} | −0.0518ξ_{6} |

Emission Reduction Target | 20% | 21% | 22% | 23% | 24% | 25% |
---|---|---|---|---|---|---|

J_{11} | 1 − 0.5606ξ_{1} | 1 − 0.5613ξ_{1} | 1 − 0.5620ξ_{1} | 1 − 0.5628ξ_{1} | 1 − 0.5637ξ_{1} | 1 − 0.5647ξ_{1} |

J_{12} = J_{13} = J_{14} = J_{15} = J_{16} | −0.2803ξ_{1} | −0.2806ξ_{1} | −0.2810ξ_{1} | −0.2814ξ_{1} | −0.2818ξ_{1} | −0.2823ξ_{1} |

J_{22} | 1 − 0.2093ξ_{2} | 1 − 0.2084ξ_{2} | 1 − 0.2073ξ_{2} | 1 − 0.2061ξ_{2} | 1 − 0.2048ξ_{2} | 1 − 0.2034ξ_{2} |

J_{21} = J_{23} = J_{24} = J_{25} = J_{26} | −0.1047ξ_{2} | −0.1042ξ_{2} | −0.1037ξ_{2} | −0.1031ξ_{2} | −0.1024ξ_{2} | −0.1017ξ_{2} |

J_{33} | 1 − 0.4863ξ_{3} | 1 − 0.4865ξ_{3} | 1 − 0.4868ξ_{3} | 1 − 0.4870ξ_{3} | 1 − 0.4872ξ_{3} | 1 − 0.4874ξ_{3} |

J_{31} = J_{32} = J_{34} = J_{35} = J_{36} | −0.2431ξ_{3} | −0.2433ξ_{3} | −0.2434ξ_{3} | −0.2435ξ_{3} | −0.2436ξ_{3} | −0.2437ξ_{3} |

J_{44} | 1 − 0.4102ξ_{4} | 1 − 0.4104ξ_{4} | 1 − 0.4106ξ_{4} | 1 − 0.4107ξ_{4} | 1 − 0.4108ξ_{4} | 1 − 0.4108ξ_{4} |

J_{41} = J_{42} = J_{43} = J_{45} = J_{46} | −0.2051ξ_{4} | −0.2052ξ_{4} | −0.2053ξ_{4} | −0.2054ξ_{4} | −0.2054ξ_{4} | −0.2054ξ_{4} |

J_{55} | 1 − 0.2648ξ_{5} | 1 − 0.2649ξ_{5} | 1 − 0.2650ξ_{5} | 1 − 0.2652ξ_{5} | 1 − 0.2653ξ_{5} | 1 − 0.2655ξ_{5} |

J_{51} = J_{52} = J_{53} = J_{54} = J_{56} | −0.1324ξ_{5} | −0.1324ξ_{5} | −0.1325ξ_{5} | −0.1326ξ_{5} | −0.1327ξ_{5} | −0.1327ξ_{5} |

J_{66} | 1 − 0.1065ξ_{6} | 1 − 0.1059ξ_{6} | 1 − 0.1053ξ_{6} | 1 − 0.1048ξ_{6} | 1 − 0.1043ξ_{6} | 1 − 0.1040ξ_{6} |

J_{61} = J_{62} = J_{63} = J_{64} = J_{65} | −0.0532ξ_{6} | −0.0529ξ_{6} | −0.0527ξ_{6} | −0.0524ξ_{6} | −0.0522ξ_{6} | −0.0520ξ_{6} |

**Table 11.**The equilibrium output E* of each regional enterprise (emission reduction target: 25–30%, e

_{0}= 2.2197).

Emission Reduction Target | 25% | 26% | 27% | 28% | 29% | 30% |
---|---|---|---|---|---|---|

q_{1} | 2.3949 | 2.3999 | 2.4049 | 2.4106 | 2.4182 | 2.4230 |

q_{2} | 1.0483 | 1.0413 | 1.0341 | 1.0263 | 1.0300 | 1.0216 |

q_{3} | 2.1003 | 2.1007 | 2.1009 | 2.1009 | 2.1130 | 2.1131 |

q_{4} | 1.7343 | 1.7342 | 1.7339 | 1.7334 | 1.7451 | 1.7447 |

q_{5} | 1.3864 | 1.3869 | 1.3875 | 1.3880 | 1.3686 | 1.3700 |

q_{6} | 0.6749 | 0.6739 | 0.6734 | 0.6731 | 0.6534 | 0.6550 |

**Table 12.**The equilibrium output E* of each regional enterprise (emission reduction target of 25–30%, e

_{0}= 2.0611).

Emission Reduction Target | 25% | 26% | 27% | 28% | 29% | 30% |
---|---|---|---|---|---|---|

q_{1} | 2.3840 | 2.3879 | 2.3921 | 2.3963 | 2.4012 | 2.4065 |

q_{2} | 1.0499 | 1.0433 | 1.0361 | 1.0286 | 1.0205 | 1.0119 |

q_{3} | 2.1022 | 2.1027 | 2.1030 | 2.1033 | 2.1033 | 2.1030 |

q_{4} | 1.7361 | 1.7362 | 1.7360 | 1.7358 | 1.7353 | 1.7346 |

q_{5} | 1.3882 | 1.3890 | 1.3896 | 1.3904 | 1.3911 | 1.3917 |

q_{6} | 0.6767 | 0.6759 | 0.6755 | 0.6755 | 0.6759 | 0.6767 |

Emission Reduction Target | 25% | 26% | 27% | 28% | 29% | 30% |
---|---|---|---|---|---|---|

J_{11} | 1 − 0.5413ξ_{1} | 1 − 0.5424ξ_{1} | 1 − 0.5435ξ_{1} | 1 − 0.5448ξ_{1} | 1 − 0.5465ξ_{1} | 1 − 0.5476ξ_{1} |

J_{12} = J_{13} = J_{14} = J_{15} = J_{16} | −0.2706ξ_{1} | −0.2712ξ_{1} | −0.2718ξ_{1} | −0.2724ξ_{1} | −0.2733ξ_{1} | −0.2738ξ_{1} |

J_{22} | 1 − 0.2369ξ_{2} | 1 − 0.2353ξ_{2} | 1 − 0.2337ξ_{2} | 1 − 0.2319ξ_{2} | 1 − 0.2328ξ_{2} | 1 − 0.2309ξ_{2} |

J_{21} = J_{23} = J_{24} = J_{25} = J_{26} | −0.1185ξ_{2} | −0.1177ξ_{2} | −0.1169ξ_{2} | −0.1160ξ_{2} | −0.1164ξ_{2} | −0.1154ξ_{2} |

J_{33} | 1 − 0.4747ξ_{3} | 1 − 0.4747ξ_{3} | 1 − 0.4748ξ_{3} | 1 − 0.4748ξ_{3} | 1 − 0.4775ξ_{3} | 1 − 0.4776ξ_{3} |

J_{31} = J_{32} = J_{34} = J_{35} = J_{36} | −0.2373ξ_{3} | −0.2374ξ_{3} | −0.2374ξ_{3} | −0.2374ξ_{3} | −0.2388ξ_{3} | −0.2388ξ_{3} |

J_{44} | 1 − 0.3920ξ_{4} | 1 − 0.3919ξ_{4} | 1 − 0.3919ξ_{4} | 1 − 0.3918ξ_{4} | 1 − 0.3944ξ_{4} | 1 − 0.3943ξ_{4} |

J_{41} = J_{42} = J_{43} = J_{45} = J_{46} | −0.1960ξ_{4} | −0.1960ξ_{4} | −0.1959ξ_{4} | −0.1959ξ_{4} | −0.1972ξ_{4} | −0.1971ξ_{4} |

J_{55} | 1 − 0.3133ξ_{5} | 1 − 0.3134ξ_{5} | 1 − 0.3136ξ_{5} | 1 − 0.3137ξ_{5} | 1 − 0.3093ξ_{5} | 1 − 0.3096ξ_{5} |

J_{51} = J_{52} = J_{53} = J_{54} = J_{56} | −0.1567ξ_{5} | −0.1567ξ_{5} | −0.1568ξ_{5} | −0.1568ξ_{5} | −0.1547ξ_{5} | −0.1548ξ_{5} |

J_{66} | 1 − 0.1525ξ_{6} | 1 − 0.1523ξ_{6} | 1 − 0.1522ξ_{6} | 1 − 0.1521ξ_{6} | 1 − 0.1477ξ_{6} | 1 − 0.1480ξ_{6} |

J_{61} = J_{62} = J_{63} = J_{64} = J_{65} | −0.0763ξ_{6} | −0.0761ξ_{6} | −0.0761ξ_{6} | −0.0761ξ_{6} | −0.0738ξ_{6} | −0.0740ξ_{6} |

Emission Reduction Target | 25% | 26% | 27% | 28% | 29% | 30% |
---|---|---|---|---|---|---|

J_{11} | 1 − 0.5388ξ_{1} | 1 − 0.5397ξ_{1} | 1 − 0.5406ξ_{1} | 1 − 0.5416ξ_{1} | 1 − 0.5427ξ_{1} | 1 − 0.5439ξ_{1} |

J_{12} = J_{13} = J_{14} = J_{15} = J_{16} | −0.2694ξ_{1} | −0.2698ξ_{1} | −0.2703ξ_{1} | −0.2708ξ_{1} | −0.2713ξ_{1} | −0.2719ξ_{1} |

J_{22} | 1 − 0.2373ξ_{2} | 1 − 0.2358ξ_{2} | 1 − 0.2342ξ_{2} | 1 − 0.2325ξ_{2} | 1 − 0.2306ξ_{2} | 1 − 0.2287ξ_{2} |

J_{21} = J_{23} = J_{24} = J_{25} = J_{26} | −0.1186ξ_{2} | −0.1179ξ_{2} | −0.1171ξ_{2} | −0.1162ξ_{2} | −0.1153ξ_{2} | −0.1143ξ_{2} |

J_{33} | 1 − 0.4751ξ_{3} | 1 − 0.4752ξ_{3} | 1 − 0.4753ξ_{3} | 1 − 0.4753ξ_{3} | 1 − 0.4753ξ_{3} | 1 − 0.4753ξ_{3} |

J_{31} = J_{32} = J_{34} = J_{35} = J_{36} | −0.2375ξ_{3} | −0.2376ξ_{3} | −0.2376ξ_{3} | −0.2377ξ_{3} | −0.2377ξ_{3} | −0.2376ξ_{3} |

J_{44} | 1 − 0.3924ξ_{4} | 1 − 0.3924ξ_{4} | 1 − 0.3923ξ_{4} | 1 − 0.3923ξ_{4} | 1 − 0.3922ξ_{4} | 1 − 0.3920ξ_{4} |

J_{41} = J_{42} = J_{43} = J_{45} = J_{46} | −0.1962ξ_{4} | −0.1962ξ_{4} | −0.1962ξ_{4} | −0.1962ξ_{4} | −0.1961ξ_{4} | −0.1960ξ_{4} |

J_{55} | 1 − 0.3137ξ_{5} | 1 − 0.3139ξ_{5} | 1 − 0.3141ξ_{5} | 1 − 0.3142ξ_{5} | 1 − 0.3144ξ_{5} | 1 − 0.3145ξ_{5} |

J_{51} = J_{52} = J_{53} = J_{54} = J_{56} | −0.1569ξ_{5} | −0.1570ξ_{5} | −0.1570ξ_{5} | −0.1571ξ_{5} | −0.1572ξ_{5} | −0.1573ξ_{5} |

J_{66} | 1 − 0.1529ξ_{6} | 1 − 0.1528ξ_{6} | 1 − 0.1527ξ_{6} | 1 − 0.1527ξ_{6} | 1 − 0.1528ξ_{6} | 1 − 0.1529ξ_{6} |

J_{61} = J_{62} = J_{63} = J_{64} = J_{65} | −0.0765ξ_{6} | −0.0764ξ_{6} | −0.0763ξ_{6} | −0.0763ξ_{6} | −0.0764ξ_{6} | −0.0765ξ_{6} |

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## Share and Cite

**MDPI and ACS Style**

Li, D.; Di, Q.; Mu, H.; Han, Z.; Wang, H.; Duan, Y.
Research on the Impact of Output Adjustment Strategy and Carbon Trading Policy on the Response, Stability and Complexity of Steel Market under the Dynamic Game. *Sustainability* **2022**, *14*, 12205.
https://doi.org/10.3390/su141912205

**AMA Style**

Li D, Di Q, Mu H, Han Z, Wang H, Duan Y.
Research on the Impact of Output Adjustment Strategy and Carbon Trading Policy on the Response, Stability and Complexity of Steel Market under the Dynamic Game. *Sustainability*. 2022; 14(19):12205.
https://doi.org/10.3390/su141912205

**Chicago/Turabian Style**

Li, Di, Qianbin Di, Hailin Mu, Zenglin Han, Hongye Wang, and Ye Duan.
2022. "Research on the Impact of Output Adjustment Strategy and Carbon Trading Policy on the Response, Stability and Complexity of Steel Market under the Dynamic Game" *Sustainability* 14, no. 19: 12205.
https://doi.org/10.3390/su141912205