Research on the new energy transformation strategy of the automobile industry based on differential game

Xiaojuan Li; JinZhou He; Zhenfei Zhan; Shanshan Li; Yechao Cheng; Zhengzhi Ma; Zufeng Zhang; Xiaojuan Li; JinZhou He; Zhenfei Zhan; Shanshan Li; Yechao Cheng; Zhengzhi Ma; Zufeng Zhang

doi:10.3934/jimo.2026137

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 8: 3835-3863. doi: 10.3934/jimo.2026137

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Research article

Research on the new energy transformation strategy of the automobile industry based on differential game

1.
Department of Mechanical and Vehicle Engineering, Chongqing Jiaotong University, Chongqing, Chongqing Municipality, China
2.
Chongqing Chang'an Industry (Group) Co., Ltd., Chongqing, N/A, China
3.
School of Management Science and Real Estate, Chongqing University, Chongqing, Chongqing Municipality, China

Received: 29 April 2026 Revised: 06 July 2026 Accepted: 14 July 2026 Published: 21 July 2026
91A05, 91A10, 91A25

In this study, we examined new-energy vehicle (NEV) transformation strategies in low-NEV-penetration automobile markets. We developed a tripartite differential game model involving traditional internal-combustion-engine vehicle (ICE vehicle) manufacturers, new-energy vehicle (NEV) enterprises, and local governments. The model compared Nash non-cooperative, government-led Stackelberg, and cooperative decision-making structures to derive equilibrium effort levels, subsidy policies, stakeholder utilities, and transformation trajectories. The results showed that government cost-sharing subsidies increased the transformation efforts of ICE vehicle manufacturers and NEV enterprises, while the Stackelberg structure improved outcomes relative to the Nash benchmark through government-led cost sharing. Cooperative decision-making generated the highest stakeholder utilities, aggregate ecosystem utility, and new-energy transformation level index. Numerical simulation, sensitivity analysis of revenue-sharing coefficients, and the Changan Automobile case were consistent with the theoretical results. This study provides a dynamic framework for designing cost-sharing subsidy, revenue-sharing, and coordination mechanisms during the low-penetration stage of automotive new-energy transformation.
- industrial transformation,
- government subsidies,
- differential games,
- cooperation,
- Hamilton-Jacobi-Bellman equation
Citation: Xiaojuan Li, JinZhou He, Zhenfei Zhan, Shanshan Li, Yechao Cheng, Zhengzhi Ma, Zufeng Zhang. Research on the new energy transformation strategy of the automobile industry based on differential game[J]. Journal of Industrial and Management Optimization, 2026, 22(8): 3835-3863. doi: 10.3934/jimo.2026137

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Abstract

In this study, we examined new-energy vehicle (NEV) transformation strategies in low-NEV-penetration automobile markets. We developed a tripartite differential game model involving traditional internal-combustion-engine vehicle (ICE vehicle) manufacturers, new-energy vehicle (NEV) enterprises, and local governments. The model compared Nash non-cooperative, government-led Stackelberg, and cooperative decision-making structures to derive equilibrium effort levels, subsidy policies, stakeholder utilities, and transformation trajectories. The results showed that government cost-sharing subsidies increased the transformation efforts of ICE vehicle manufacturers and NEV enterprises, while the Stackelberg structure improved outcomes relative to the Nash benchmark through government-led cost sharing. Cooperative decision-making generated the highest stakeholder utilities, aggregate ecosystem utility, and new-energy transformation level index. Numerical simulation, sensitivity analysis of revenue-sharing coefficients, and the Changan Automobile case were consistent with the theoretical results. This study provides a dynamic framework for designing cost-sharing subsidy, revenue-sharing, and coordination mechanisms during the low-penetration stage of automotive new-energy transformation.

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