A many-to-many assignment game and stable outcome algorithm to evaluate collaborative mobility-as-a-service platforms

As Mobility as a Service (MaaS) systems become increasingly popular, travel is changing from unimodal trips to personalized services offered by a platform of mobility operators. Evaluation of MaaS platforms depends on modeling both user route decisions as well as operator service and pricing decisions. We adopt a new paradigm for traffic assignment in a MaaS network of multiple operators using the concept of stable matching to allocate costs and determine prices offered by operators corresponding to user route choices and operator service choices without resorting to nonconvex bilevel programming formulations. Unlike our prior work, the proposed model allows travelers to make multimodal, multi-operator trips, resulting in stable cost allocations between competing network operators to provide MaaS for users. An algorithm is proposed to efficiently generate stability conditions for the stable outcome model. Extensive computational experiments demonstrate the use of the model to handling pricing responses of MaaS operators in technological and capacity changes, government acquisition, consolidation, and firm entry, using the classic Sioux Falls network. The proposed algorithm replicates the same stability conditions as explicit path enumeration while taking only 17 seconds compared to explicit path enumeration timing out over 2 hours.