Abstract: Since the “double carbon” was established, environmental protection and energy transition have received widespread attention from all walks of life. New energy vehicles (NEV), which use clean energy instead of traditional fuels and have low energy consumption, little environmental pollution, and minimal ecological damage, have become a significant trend in the growth of the automobile industry. When compared to the usage of gasoline vehicles (GV), the adoption of NEV is accelerating thanks to the robust national policy thrust. However, the GV industry is an important pillar industry of the national economy. Therefore, finding a solution to the pressing issue of how to achieve the coordinated growth of the automotive industry under the energy transformation while balancing the game between economic expansion and energy conservation and emission reduction is imperative. The two premises in the short-term game, the hypotheses of rational economic man and market complete information, are difficult to exist in the real economy and society. Hence, some scholars have incorporated bounded rationality into the field of economics, revealing complex dynamic phenomena that economic theories cannot explain. In a single game, it is difficult for all parties to arrive at a stable market equilibrium because of the bounded rationality. It is necessary to carry out long-term repeated games. Currently, little literature on long-term repeated game in the automobile industry takes into account the impact of production competition on market stability, or addresses how to maintain the smooth transition of energy transformation in the automobile industry.
Based on the practical issues, this study first constructs a short-term game model for duopoly automakers that produce NEV and GV respectively under the dual credit policy. Next, it discusses the production and environmental protection strategies of automakers. Further, the nonlinear dynamic system model under the dynamic adjustment of production and environmental protection level is established, and the long-term repeated game behavior of automakers is analyzed based on the complex system theory. Finally, combined with the actual case, values are assigned to the model. The influences of product substitution coefficient, low-carbon preference of consumers and credits trading price on the production and environmental protection level of automakers are compared under the two scenarios of cooperation and non-cooperation. The system’s dynamic properties are characterized by the chaotic bifurcation and the largest Lyapunov exponents, and the decision variable adjustment approach is explored.
The results show that: (1)The product substitution coefficient, consumer’s low-carbon preference and credits trading price have a positive promoting effect on the production of NEV, while negatively inhibiting that of GV. In addition, consumer’s low-carbon preference has a significant role in improving the environmental protection level. (2)The manufacturing strategy of automakers will become unstable and ultimately descend into a state of chaos with an increase in the adjustment speed of production and environmental protection level. Therefore, in order to ensure a good market order, automakers should treat market competition rationally and limit the adjustment speed within a reasonable range. In addition, the range of NEV production adjustment is wider than that of GV, indicating that consumers are more sensitive to GV production adjustment. (3)The increase in substitution coefficient and credits trading price will narrow the stable region of the automakers’ production strategy. It is necessary to take measures to control the chaotic behavior of manufacturers, such as delayed feedback control methods. (4)The excessive adjustment strategy of the automakers always hurts their own profit and benefit, while increasing the profit of their rivals. Once in a state of chaos, the market is unstable, and it is difficult for either automaker to make a profit. This research expands the application of nonlinear analysis method of complex system theory, which has very important practical significance and reference value for the optimal strategies of automakers and the policy formulation of government.

Key words: dual credit policy, automakers, nonlinear dynamic system, complex dynamic behavior, chaotic bifurcation

摘要： 针对分别生产新能源汽车(NEV)和汽油车(GV)的双寡头汽车制造商,在双积分政策下首先构建了短期博弈模型,探讨了制造商的生产与环保策略;然后基于复杂系统理论建立了产量和环保水平动态调整下的非线性动力学系统模型,分析了制造商的长期重复博弈行为。研究表明:(1)产品替代系数、消费者低碳偏好及积分交易价格与NEV产量正相关,与GV产量负相关。消费者低碳偏好对NEV环保水平具有正向促进作用。(2)产量和环保水平的调整速度对制造商均衡策略有很大的影响,可能会出现混沌等复杂现象。(3)替代系数和积分价格的增大会缩小制造商生产策略的稳定区域。(4)过度的调整策略往往损害了自身的利润,却给竞争对手带来利益。

关键词: 双积分政策, 汽车制造商, 非线性动力学系统, 复杂动态行为, 混沌分岔