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

There is a growing need to manage the capacities, allocation, and pricing of mobility services in a Mobility-as-a-Service (MaaS) ecosystem. City agencies need to assess the impact on other mobility operators and travelers when a new company enters the market, or an existing one changes their capacity, routing algorithms, or pricing. At the same time, a new mobility service or change to an existing one can cause travelers to alter routes or switch between companies and services to get where they’re going. This can make certain routes unstable to operate. Policymakers and the MaaS platforms themselves need to maintain an equilibrium while serving the needs of travellers. Up until now, classic traffic assignment models that only emphasize traveler routes were not effective at tracking these complex decisions and their outcomes.

A team at the NYU Tandon School of Engineering, led by Joseph Chow, assistant professor of civil and urban engineering, and Deputy Director of the C2SMART University Transportation Center, proposed a model that can allow travelers to make multimodal, multi-operator trips, resulting in stable cost allocations between competing network operators to provide MaaS for users. Matching multiple links of different traveler paths to multiple operators is a many-to-many assignment game. In such a game, the stability conditions become more complex because they need to be considered from both a user’s path level as well as an operator’s level in serving that user. This new model shows how to derive an optimal assignment flow and corresponding stable outcome space between the operators and the travelers or users.  Theodoros P. Pantelidis and Saeid Rasulkhani, former Ph.D. students under Chow’s guidance (now at American Airlines and Scoop Technologies, respectively), participated.

The research demonstrated the use of the model for handling pricing responses of MaaS operators in technological and capacity changes, government acquisition, consolidation, and firm entry. The model was tested on an illustrative network as well as in a series of comprehensive experiments on the Sioux Falls network to demonstrate its capabilities. They showed it was possible to use stability conditions to link network design decisions and algorithmic policies as well as market dynamics to capture market performance for both operators and users.

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