On-demand Mobility-as-a-Service platform assignment games with guaranteed stable outcomes

Mobility-as-a-Service (MaaS) systems are two-sided markets, with two mutually exclusive sets of agents, i.e., travelers/users and operators, forming a mobility ecosystem in which multiple operators compete or cooperate to serve customers under a governing platform provider. This study proposes a MaaS platform equilibrium model based on many-to-many assignment games incorporating both fixed-route transit services and mobility-on-demand (MOD) services. The matching problem is formulated as a multicommodity flow network design problem under congestion. The local stability conditions reflect a generalization of Wardrop's principles that include operator decisions. A subsidy mechanism from the platform is proposed to guarantee local stability. An exact solution algorithm is proposed based on a branch and bound framework with a Frank-Wolfe algorithm integrated with Lagrangian relaxation and subgradient optimization, which guarantees the optimality of the matching problem but not stability. A heuristic which integrates stability conditions and subsidy design is proposed, which reaches either the optimal MaaS platform equilibrium solution with global stability, or a feasible locally stable solution that may require subsidy. A worst-case bound and condition for obtaining an exact solution are both identified. Two sets of reproducible numerical experiments are conducted. The first, on a toy network, verifies the model and algorithm, and illustrates the differences between local and global stability. The second, on an expanded Sioux Falls network with 82 nodes and 748 links, derives generalizable insights about the model for coopetitive interdependencies between operators sharing the platform, handling congestion effects in MOD services, effects of local stability on investment impacts, and illustrating inequities that may arise under heterogeneous populations.