Stakeholder interactions in Mobility as a Service (MaaS): A unified bi-level optimization framework

Mobility as a Service (MaaS) integrates multiple transport modes within a unified digital platform, yet its implementation requires coordinated decisions among users, transport service providers (TSPs), the MaaS operator, and government authorities. Existing studies typically analyze these stakeholders separately or simplify their interactions, leaving the combined effects of pricing strategies, competition, and public incentives insufficiently understood. This study proposes a bi-level optimization framework that models the economic interactions among MaaS stakeholders in a unified multimodal system. The framework integrates wholesale pricing decisions by TSPs, retail pricing by the MaaS operator, user travel choices, and government incentive mechanisms within a single optimization structure. The framework is demonstrated using an extended Sioux Falls multimodal network, with solutions obtained through a nonlinear iterative optimization procedure that converges to a locally stable equilibrium. The model is evaluated on an extended Sioux Falls multimodal network under multiple policy scenarios combining dynamic pricing and alternative incentive schemes. Results show that MaaS adoption increases from approximately 28% under static pricing without incentives to nearly 40% when dynamic pricing and coordinated incentives are implemented. Importantly, a performance-based incentive scheme achieves adoption levels comparable to fixed subsidies while requiring significantly lower public expenditure. These findings highlight that the design of incentives is more important than the total subsidy amount for achieving efficient and scalable MaaS deployment.