Single-leader multi-follower games for the regulation of two-sided Mobility-as-a-Service markets

Mobility-as-a-Service (MaaS) is emerging mobility trend driven by the concept of "Everything-as-a-Service" and enabled through mobile internet technologies. In the context of economic deregulation, a MaaS system consists of a typical two-sided market, where travelers and transportation service providers (TSPs) are two groups of agents interacting with each other through a MaaS platform. In this study, we propose a modeling and optimization framework for the regulation of two-sided MaaS markets. We consider a double-auction mechanism where travelers submit purchase-bids to accommodate their travel demand via MaaS, and TSPs submit sell-bids to supply mobility resources for the MaaS platform in exchange for payments. We cast this problem as a single-leader multi-follower game (SLMFG) where the leader is the MaaS regulator and two groups of follower problems represent the travelers and the TSPs. The MaaS regulator makes the operating decisions to maximize its profits. In response to the MaaS regulator's decisions, travelers (resp. TSPs) decide the participation levels of joining the MaaS platform to minimize their travel costs (resp. maximize their profits). We formulate SLMFGs without and with network effects leading to mixed-integer linear bilevel programming and mixed-integer quadratic bilevel programming problems, respectively. We propose customized branch-and-bound algorithms based on strong duality reformulations to solve the SLMFGs. Extensive numerical experiments conducted on large scale simulation instances generated from realistic mobility data highlight that the performance of the proposed algorithms is significantly superior to a benchmarking approach and provide meaningful insights for the regulation of two-sided MaaS markets.