Research on a Differential Game Considering Endurance and Marketing Effort for eVTOL Under a Subsidy Policy

Abstract

Electric vertical takeoff and landing (eVTOL) represents a novel mode of transportation emerging within the low-altitude economy framework, exhibiting extensive development prospects. As a widely adopted incentive policy, government subsidy constitutes a crucial method for supporting the development of this strategic emerging industry. This paper constructs a differential game model of a supply chain composed of a manufacturer and retailer capable of simultaneously producing and selling eVTOL, considering three scenarios: centralized decision-making and decentralized decision-making with or without cost-sharing. Based on optimal control and differential game theory, the decision-making processes of supply chain members are investigated, and equilibrium strategies under different scenarios are compared and analyzed, with the model’s validity confirmed through numerical simulations. The findings indicate that the subsidy policy exerts a positive impact on the eVTOL supply chain: as the subsidy rates increase, supply chain members are better resourced to invest in endurance and marketing, thereby fostering eVTOL development. Concurrently, a reduction in wholesale and retail prices is observed, rendering eVTOL more affordable and of higher quality for consumers. The competitive structure of the upstream market does not alter this fundamental conclusion. The optimal endurance effort, marketing effort, eVTOL brand goodwill, and demand under the centralized decision-making model are higher than those under the decentralized one. In a certain feasible region, the two-way cost-sharing contract enables the eVTOL supply chain to achieve Pareto improvement, but it does not reach the level of centralized decision-making. This research expands the application of differential game theory in the field of the low-altitude economy, providing a scientific basis for the government to formulate policies and enterprises to distribute products.