Single-leader multi-follower games for the regulation of two-sided mobility-as-a-service markets

Mobility-as-a-Service (MaaS) is an emerging business model in transportation enabled through mobile internet technologies. A MaaS platform can be viewed as a two-sided market, where travelers and transportation service providers (TSPs) are two groups of interacting agents. We propose an optimization framework for the regulation of two-sided MaaS markets. 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 aims to maximize its profits by optimizing service prices and resource allocation. In response, travelers (resp. TSPs) adjust their participation level in the MaaS platform to minimize their travel costs (resp. maximize their profits). We analyze network effects in the MaaS market and formulate SLMFGs without/with network effects leading to mixed-integer linear/quadratic bilevel programming problems. We propose single-level reformulations based on mathematical programming with equilibrium constraints (MPECs) and prove the equivalence between the solutions obtained using the MPECs and the original bilevel problems. Customized branch-and-bound algorithms based on strong duality reformulations are developed to solve these MPECs. Extensive numerical experiments conducted on large-scale instances generated from realistic mobility data highlight the performance of the proposed algorithms relative to a benchmarking approach, and provide meaningful managerial insights for the regulation of two-sided MaaS markets.