A duopoly competition problem of shared autonomous vehicles in a multimodal transportation system with government regulation

Shared autonomous vehicles (SAVs) are expected to revolutionize urban mobility. To explore the complex dynamics of competition and cooperation between operators and other traditional transportation modes, this study proposes a tri-level programming model with equilibrium constraints in a multimodal transportation system. At the upper level, the government regulates the fleet size constraints and hub locations for SAVs. The middle level captures the effect of duopoly competition of SAV operators on fleet size and pricing considering the regulation constraints, which is represented as a 2-player noncooperative game with each player maximizing its profit. At the lower level, travelers’ responses to operational strategies are captured by the dynamic activity-travel assignment model in a multimodal transportation system. A hybrid genetic algorithm, involving a hub-based SAV relocation assignment and a route-swapping algorithm for travelers’ path choice at the lower level, is designed to solve the multi-objective programming problem at the middle level with certain government decisions. A numerical example with two SAV operators shows that the operator with higher-quality vehicles charges more but deploys a smaller fleet compared to the competitor deploying lower-cost vehicles. Government regulations can boost fleet utilization but are less effective when not strict.