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Bibliographic Details
Main Authors: Yao, Rui, Ma, Xinyu, Zhang, Kenan
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2601.19880
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author Yao, Rui
Ma, Xinyu
Zhang, Kenan
author_facet Yao, Rui
Ma, Xinyu
Zhang, Kenan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_19880
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Mobility-as-a-service (MaaS) system as a multi-leader-multi-follower game: A single-level variational inequality (VI) formulation
Yao, Rui
Ma, Xinyu
Zhang, Kenan
General Economics
Economics
Computer Science and Game Theory
Optimization and Control
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.
title Mobility-as-a-service (MaaS) system as a multi-leader-multi-follower game: A single-level variational inequality (VI) formulation
topic General Economics
Economics
Computer Science and Game Theory
Optimization and Control
url https://arxiv.org/abs/2601.19880