This study models a Mobility-as-a-Service (MaaS) system as a multi-leader-multi-follower game that captures the complex interactions among the MaaS platform, service operators, and travelers. We consider a coopetitive setting where the MaaS platform purchases service capacity from service operators and sells multi-modal trips to travelers following an origin-destination-based pricing scheme; meanwhile, service operators use their remaining capacities to serve single-modal trips. As followers, travelers make both mode choices, including whether to use MaaS, and route choices in the multi-modal transportation network, subject to prices and congestion. Inspired by the dual formulation for traffic assignment problems, we propose a novel single-level variational inequality (VI) formulation by introducing a virtual traffic operator, along with the MaaS platform and multiple service operators. A key advantage of the proposed VI formulation is that it supports parallel solution procedures and thus enables large-scale applications. We prove that an equilibrium solution always exists given the negotiated wholesale price of service capacity. Numerical experiments on a small network further demonstrate that the wholesale price can be tailored to align with varying system-wide objectives. The proposed MaaS system demonstrates potential for creating a "win-win-win" outcome -- service operators and travelers are better off compared to the "without MaaS" scenario, meanwhile the MaaS platform remains profitable. Such a Pareto-improving regime can be explicitly specified with the wholesale capacity price. Similar conclusions are drawn from the experiment of an extended multi-modal Sioux Falls network, which also validates the scalability of the proposed model and solution algorithm.

翻译：本研究将出行即服务(MaaS)系统建模为多领导者-多跟随者博弈，以刻画MaaS平台、服务运营商和出行者之间的复杂交互。我们考虑一种竞合场景：MaaS平台依据基于起讫点的定价方案向服务运营商购买服务容量并向出行者销售多模式出行服务；同时，服务运营商利用其剩余容量提供单模式出行服务。作为跟随者，出行者在价格和拥堵约束下，既进行模式选择（包括是否使用MaaS），又在多模式交通网络中进行路径选择。受交通分配问题对偶表述的启发，我们通过引入虚拟交通运营商，与MaaS平台及多个服务运营商共同构建了一种新颖的单层变分不等式(VI)表述。该VI表述的关键优势在于支持并行求解流程，从而适用于大规模应用。我们证明在给定服务容量协商批发价格的前提下，均衡解始终存在。小型网络的数值实验进一步表明，批发价格可根据不同系统目标进行定制调整。所提出的MaaS系统展现出创造"三方共赢"结果的潜力——与"无MaaS"情景相比，服务运营商和出行者均获得更优效益，同时MaaS平台保持盈利。这种帕累托改进机制可通过容量批发价格明确设定。扩展的多模式Sioux Falls网络实验得出相似结论，同时验证了所提模型与求解算法的可扩展性。