Stochastic assignment games for Mobility-as-a-Service markets

2025-12-22

AI Summary

This paper addresses fare optimization in multimodal mobility markets—such as Mobility-as-a-Service (MaaS) platforms—under incomplete information. We propose the first modeling paradigm embedding a stochastic many-to-many assignment game within a Stackelberg framework, where the MaaS platform acts as leader and heterogeneous users and operators as followers. Methodologically, we integrate stochastic game theory, bilevel optimization, and a coalition Logit model to define a core solution incorporating expected payoffs, and design a provably convergent iterative equilibrium algorithm. Our key contribution lies in unifying, for the first time, the stochasticity and strategic behavior inherent in both user route choice and operator supply response—enabling simultaneous platform revenue maximization and supply-demand co-governance. Extensive validation via two real-world case studies demonstrates the model’s effectiveness and robustness in fare optimization and coordinated regulation of public transport services.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We study the stochastic assignment game and extend it to model multimodal mobility markets with a regulator or a Mobility-as-a-Service (MaaS) platform. We start by presenting general forms of one-to-one and many-to-many stochastic assignment games. Optimality conditions are discussed. The core of stochastic assignment games is defined, with expected payoffs of sellers and buyers in stochastic assignment games as payoffs from a hypothetical "ideal matching" that represent sellers' and buyers' expectations under imperfect information. To apply stochastic assignment games to the urban mobility markets, we extend the general stochastic many-to-many assignment game into a stochastic Stackelberg game to model MaaS systems, where the platform is the leader, and users and operators are the followers. The platform sets fares to maximize revenue. Users and operator react to the fare settings to form a stochastic many-to-many assignment game considering both fixed-route services and Mobility-on-Demand (MOD). The Stackelberg game is formulated as a bilevel problem. The lower level is the stochastic many-to-many assignment game between users and operators, shown to yield a coalitional logit model. The upper-level problem is a fare adjustment problem maximizing revenue. An iterative balancing algorithm is proposed to solve the lower-level problem exactly. The bilevel problem is solved through an iterative fare adjusting heuristic, whose solution is shown to be equivalent to the bilevel problem with an additional condition when it converges. Two case studies are conducted. The model can be applied to design MaaS fares maximizing income of the platform while anticipating the selfish behavior and heterogeneity of users and operators. Public agencies can also use the model to manage multimodal transportation systems.

Problem

• Models stochastic assignment games for Mobility-as-a-Service markets with a regulator.
• Extends to a Stackelberg game to optimize platform fares and user-operator interactions.
• Solves bilevel problem to design fares maximizing revenue while anticipating selfish behaviors.

Innovation

• Extends stochastic assignment games to model MaaS markets
• Formulates MaaS as a bilevel Stackelberg game with fare optimization
• Proposes iterative balancing algorithm to solve stochastic assignment game