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

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.