Non-additive network pricing with non-cooperative mobility service providers

This study addresses a mobility network pricing problem in a competitive environment. We consider a multimodal transportation network where the links are operated by multiple profit-maximizing, mobility service providers (MSPs). We take the perspective of a network regulator that aims to increase ridership in a target mobility network by providing non-additive, path-based subsidies to travelers. We model paths’ attractiveness using generalized cost functions that combine path travel time and path cost, and we use linear elastic travel demand functions to capture the proportion of demand served by a path. MSPs are non-cooperative and adjust link fares according to the subsidy policy implemented by the regulator. The goal of the network regulator is to solve a budget-constrained mobility network pricing problem under MSP competition. This game-theoretical framework is modeled as a single-leader multi-follower game (SLMFG) wherein the leader player represents the network regulator and multiple follower players represent the MSPs. We conduct a theoretical analysis of this SLMFG by identifying necessary and sufficient conditions for the existence of solutions to the parameterized generalized Nash equilibrium problem (GNEP) that is played amongst MSPs. We show that this GNEP is jointly convex and we use this property to develop an exact numerical approach to solve the SLMFG based on customized branch-and-bound algorithms. Numerical results reveal the impact of MSP competition in this mobility network pricing problem and shed novel insights into the design of optimal path-based subsidy policies.