A bottleneck model with shared autonomous vehicles: Scale economies and price regulations

This study examines how scale economies in the operation of shared autonomous vehicles (SAVs) affect the efficiency of a transportation system where SAVs coexist with normal vehicles (NVs). We develop a bottleneck model where commuters choose their departure times and mode of travel between SAVs and NVs, and analyze equilibria under three SAV fare-setting scenarios: marginal cost pricing, average cost pricing, and unregulated monopoly pricing. Marginal cost pricing reduces commuting costs but results in financial deficits for the service provider. Average cost pricing ensures financial sustainability but has contrasting effects depending on the timing of implementation due to the existence of multiple equilibria: when implemented too early, it discourages adoption of SAVs and increases commuting costs; when introduced after SAV adoption reaches the monopoly equilibrium level, it promotes high adoption and achieves substantial cost reductions without a deficit. We also show that expanding road capacity may increase commuting costs under average cost pricing, demonstrating the Downs--Thomson paradox in transportation systems with SAVs. We next examine two optimal policies that improve social cost, including the operator's profit: the first-best policy that combines marginal cost pricing with congestion tolls, and the second-best policy that relies on fare regulation alone. Our analysis shows that these policies can limit excessive adoption by discouraging overuse of SAVs. This suggests that promoting SAV adoption does not always reduce social cost.