Mobility Service Providers’ Equilibrium Strategies in Multi-modal Networks

Abstract

Due to the increasing introduction of new mobility solutions in the transport offers, the market equilibrium among Mobility Service Providers (MSPs) has become more complex. The focus of this paper is to develop a novel analytical approach to study competition and/or cooperation between multiple MSPs within a multi-modal network system. We formulate a novel Equilibrium Problem with Equilibrium Constraints (EPEC), where each MSP seeks to maximize their own profits at the upper level. At the lower level, users are divided into classes that capture their heterogeneity in terms of socioeconomic characteristics and activity-travel behaviour. We consider the multi-modal network link costs to be non-separable, therefore the lower-level equilibrium is formulated as a Variational Inequality (VI) problem. A solution approach is proposed and illustrated, based on a relaxation of the Diagonalization method. Finally, we apply the described methodology to a small example to illustrate some key properties of the proposed approach.