The liberalization of the transport market and advancements in real-time information technologies have prospered various shared mobility services, such as ridesourcing and carsharing. The emergence of these services complicates the relationships between them and public transport, as they often compete and cooperate simultaneously. This study develops a game-theoretic model to unveil these interactions using a multi-leader single-follower framework. In this framework, operators set their service rates as leaders, while travelers are assigned to services based on a logit model, which influences the profitability of both operators. The public transport operator may also subsidize travelers who use shared mobility service to access first- or last-mile trips, referring to as the bundle services. We reformulate the resulting nonlinear, nonconvex problem into a standard convex bilevel model by using outer linear approximations and applying KKT conditions to replace the lower-level problem. An iterative algorithm is developed to solve the game-theoretical model, complemented by an optimization-based bound tightening technique to enhance solution efficiency and accuracy. Our findings show that smaller operators, limited by budget constraints, are more likely to cooperate in bundle services for longer distances but tend to compete for shorter distances. In contrast, larger operators strategically alternate between competition and cooperation based on market conditions. Furthermore, well-designed subsidies in the bundle services can incentivize cooperation between shared mobility and public transport, benefiting both operators and travelers.

中文翻译：

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揭示共享出行与公共交通之间的竞争动态：一种博弈论方法


交通市场的自由化和实时信息技术的进步使各种共享出行服务蓬勃发展，例如拼车和汽车共享。这些服务的出现使它们与公共交通之间的关系复杂化，因为它们经常同时竞争和合作。本研究开发了一个博弈论模型，以使用多领导者单追随者框架来揭示这些相互作用。在这个框架中，运营商将他们的服务费率设置为领先者，而旅行者则根据 logit 模型分配给服务，这会影响两家运营商的盈利能力。公共交通运营商还可以补贴使用共享出行服务的旅客进行第一英里或最后一英里的旅行，称为捆绑服务。通过使用外部线性近似并应用 KKT 条件来替换较低级别问题，我们将生成的非线性、非凸问题重新表述为标准的凸双层模型。开发了一种迭代算法来求解博弈论模型，并辅以基于优化的边界紧缩技术，以提高求解效率和准确性。我们的研究结果表明，受预算限制的小型运营商更有可能在较长距离的捆绑服务方面进行合作，但往往会在较短的距离上竞争。相比之下，大型运营商根据市场条件在竞争和合作之间战略性地交替。此外，捆绑服务中精心设计的补贴可以激励共享出行和公共交通之间的合作，使运营商和旅行者都受益。