An Analysis of Tripartite Evolutionary Game on Carbon Emission Reduction by Shipping Enterprises under the Goals of Carbon Peaking and Carbon Neutralization
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摘要: 目前水路运输碳减排的演化博弈研究主要聚焦于企业和政府之间，忽视了市场消费者在碳排放减少过程中的影响力。从市场消费者视角出发，引入货主为博弈主体，研究航运企业、政府监管部门及货主的三方博弈过程，可以更全面的揭示航运业碳排放的博弈路径。为平衡航运企业、政府监管部门及货主三方在碳减排过程中的利益冲突，基于演化博弈理论，设定行为主体的行为集、概率组合及博弈行为等相关参数，构建航运公司、政府监管部门及货主之间的三方演化博弈模型及动态复制方程。运用MATLAB仿真工具，求解该模型的12个平衡点，并对平衡点的局部稳定性进行系统分析。通过对三方博弈主体之间的相互作用及演化过程进行数值模拟与仿真分析，研究演化过程中的干扰因素和机制，探讨得出各参数对系统演化结果产生的影响。仿真结果表明：①随着低碳航运技术所产生的收益明显超越传统技术，政府开始采取更加主动的监管策略；②演化博弈过程中，各参与者的策略选择与其初始策略选择的概率密切相关，表明初始策略在策略演化中起到关键引导作用；③货主在政府和航运企业的双重影响下，成为推动航运业碳减排的关键因素；④航运企业对新技术研发的态度与其收益及政府补贴有关，打破传统观念将其只与成本挂钩的观点。研究结果可为航运企业碳减排的政策优化提供参考。Abstract: Currently, the evolutionary game studies on carbon emission reduction in waterway transportation primarily focus on the interaction between enterprises and government, overlooking the impact of market consumers in the carbon reduction process. From the perspective of market consumers and by introducing shippers as game entities, the study of the tripartite game process involving shipping enterprises, regulatory government bodies, and shippers can provide a more comprehensive view of the carbon emission reduction pathways within the shipping industry. To balance the conflicting interests of shipping enterprises, regulatory government bodies, and shippers in the carbon reduction process, an evolutionary game model and dynamic replication equations among the three entities are constructed based on evolutionary game theory. The model is developed with sets of behavioral actions, probability combinations, and game behavior of the involved entities. Using MATLAB simulation tools, 12 equilibrium points of the model are solved, and a systematic analysis of their local stability is conducted. Through numerical simulation and analysis of the interactions and evolutionary processes among the three game entities, the influencing factors and mechanisms during the evolution are investigated. The study aims to explore the impacts of various parameters on the system's evolutionary outcomes. The simulation results indicate: ① As the benefits generated by low-carbon shipping technologies significantly surpass traditional technologies, the government begins to adopt more proactive regulatory strategies; ② During the evolutionary game, the strategy choices of participants are closely related to the probabilities of their initial strategy choices, suggesting that the initial strategies play a crucial guiding role in strategy evolution; ③ Under the dual influence of the government and shipping enterprises, shippers become a critical factor driving carbon emission reduction in the shipping industry; ④ The attitude of shipping enterprises towards new technology development is related to their benefits and government subsidies, challenging the traditional notion that associates it sorely with costs. The findings can provide valuable insights for strategy optimization in carbon emission reduction for shipping enterprises.
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图 2 三方博弈行为策略示意图
Figure 2. Schematic diagram of the behavioral strategies of the tripartite game
图 6 政府补贴对博弈主体演化影响
Figure 6. Impact of government subsidies on the evolution of game players
表 1 博弈具体参数及其含义
Table 1. Specific parameters and meaning of the game
参数 含义 YF 航运企业研发减排技术的成本 CS 航运企业使用传统固有技术获得的收益 DS 航运企业使用低碳技术获得的收益 BT 航运企业使用低碳技术获得的政府补贴 QS 航运企业使用低碳技术给政府带来的潜在收益 SS 政府调控下非低碳船舶运输收取碳税，导致的航运企业营业收入损失 α 航运企业让利给货主的资金占政府的补贴比例 β 货主分摊航运企业燃料税的比例 ZC 政府采取调控策略时付出的人力、物力、财力等成本 ZS 政府将承担企业使用非低碳方式运输导致的环境损失 HS1 货主选择使用低碳技术航运企业运输的预期收益 HS2 货主选择使用其他运输方式的预期收益 
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表 2 企业、政府和货主的行为策略组合及收益矩阵
Table 2. Behavioral strategy combinations and benefit matrices for firms, governments and shippers
行为策略组合 航运公司收益 政府收益 承运人收益 $\left(C_1, T_1, J 1\right)$ $\tau_1=Y F+D S+(1-\alpha) B T$ $\tau_2=C S-B T-Z C$ $\tau_3=H S 1+\alpha B T$ $\left(C_1, T_1, J_2\right)$ $\tau_1=Y F+D S+B T$ $\tau_2=C S-B T-Z C-Z S+\beta S S$ $\tau_3=H S 2-\beta S S$ $\left(C_1, T_2, J_1\right)$ $\tau_1=Y F+D S$ $\tau_2=C S$ $\tau_3=H S 1$ $\left(C_1, T_2, J_2\right)$ $\tau_1=Y F+D S$ $\tau_2=C S$ $\tau_3=H S 2$ $\left(C_2, T_1, J_1\right)$ $\tau_1=C S-(1-\beta) S S$ $\tau_2=Z C-Z S-\alpha B T+(1-\beta) S S$ $\tau_3=H S 1+\alpha B T$ $\left(C_2, T_1, J_2\right)$ $\tau_1=C S-(1-\beta) S S$ $\tau_2=Z C-Z S+S S$ $\tau_3=H S 2-\beta S S$ $\left(C_2, T_2, J_1\right)$ $\tau_1=C S$ $\tau_2=Z S$ $\tau_3=H S 1$ $\left(C_2, T_2, J_2\right)$ $\tau_1=C S$ $\tau_2=-Z S$ $\tau_3=H S 2$
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表 3 特征值
Table 3. Eigenvalues
均衡点 Jαcobiαn矩阵特征值 稳定性结论 $\lambda_1、\lambda_2、\lambda_3$ D1(0，0，0) $H S 1-H S 2, Z C-C S, D S-C S-Y F$ 不稳定点 D2(0，0，1) $H S 2-H S 1, D S-C S-Y F, S S \beta+Z C-S S-B T \alpha$ ESS D3(0，1，0) $C S-Z C, H S 1-H S 2+B T \alpha+C S \beta, D S-C S \beta-Y F+B T$ 不稳定点 D4(1，0，0) $H S 1-H S 2, C S-D S+Y F, B T+S S+Z C-C S \beta$ 不稳定点 D5(1，1，1) $H S 2-H S 1-B T A-C S \beta, S S-Z C-B T A-S S \beta, B T+D S-Y F-B T \alpha-C S \beta$ ESS D6(1，1，0) $Y F-D S-B T+C S \beta, H S 1-H S 2+B T A+C S \beta, C S \beta-S S-Z C-B T$ 不稳定点 D7(1，0，1) $H S 2-H S 1, B T+Z C, C S-D S+Y F$ 不稳定点 D8(1，1，1) $-B T-Z C, H S 2-H S 1-B T \alpha-C S \beta, \quad Y F-D S-B T+B T \alpha-S S \beta$ ESS $\begin{aligned} & \boldsymbol{D} 9(1, \quad-(H S 1-H S 2) /(B T \alpha+S S \beta) \\ & (B T+Z C+Z S-S S \beta) /(Z S-S S \beta)\end{aligned}$ $f 1, \operatorname{CSSS}^2 \beta^2-D S S S^2 \beta^2+S S^2 Y F \beta^2, 6 H S^2 S S^2 Z C Z S \beta^2+2 B T S S^2 Z C \alpha \beta^2+$ $2 \mathrm{~B} T S^2 Z \mathrm{C} \alpha \beta^2+2 \mathrm{~B}^2 S S Z S^2 \alpha \beta-2 \mathrm{~B} T^2 S S^2 Z S \alpha \beta-2 \mathrm{~B} T^2$ 不稳定点 $\begin{aligned} & \boldsymbol{D} 10(-(Z C-S S+B T \alpha+S S \beta) /(B T+S S-B T \alpha- \\ & S S \beta), (Y F+C S-D S) /(B T+S S-B T \alpha-S S \beta), 1)\end{aligned}$ $f 2, g 2, h 2$ 不稳定点 $\begin{aligned} & \boldsymbol{D} 11((S S-Z C) /(B T+S S+Z S-S S \beta), \\ & (Y F+C S-D S) /(B T+S S-S S \beta), 0)\end{aligned}$ $f 3, g 3, h 3$ 不稳定点 $\boldsymbol{D} 12(0, -(H S 1-H S 2+S S \beta) /(B T a)$, $(S S-Z C) /(B T \alpha+S S \beta))$ $f 4, g 4, h 4$ 不稳定点
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