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.

💡 Research Summary

The paper develops a novel bottleneck model that integrates shared autonomous vehicles (SAVs) with conventional private cars (NVs) while explicitly accounting for scale economies and the natural‑monopoly nature of a single SAV operator. Commuters choose both departure time and travel mode to minimize a cost that includes free‑flow travel time, queuing delay at a point‑queue bottleneck, schedule‑delay penalties, and mode‑specific monetary costs (fixed vehicle cost for NVs, fare plus a constant pickup‑waiting cost for SAVs). SAVs generate two technological effects: a capacity effect that increases the bottleneck capacity by a factor 1/κ (0 < κ < 1) and a value‑of‑time (VOT) reduction effect captured by a factor θ (0 < θ < 1). Because fixed costs are spread over the number of SAV users, the average cost per trip falls as adoption rises, creating a feedback loop that can produce multiple equilibria.

Three fare‑setting regimes are examined:

1. Marginal‑cost pricing (MCP) – the operator charges the marginal cost of serving an additional user. This yields the lowest commuter cost and the highest SAV adoption, but the operator cannot recover fixed costs, leading to a chronic deficit.

2. Average‑cost pricing (ACP) – the fare equals the operator’s average cost, guaranteeing financial break‑even. The model shows path dependence: if ACP is introduced when SAV adoption is still low, the resulting high fare suppresses demand, pushing the system into a low‑adoption equilibrium with higher total commuting costs. Conversely, if the market first experiences unregulated monopoly pricing (which may generate a moderate level of adoption) and ACP is later imposed, the system can settle in a high‑adoption equilibrium, preserving the efficiency gains of scale economies while remaining financially viable.

3. Unregulated monopoly pricing – the profit‑maximizing operator sets a fare above marginal cost. This typically reduces SAV usage and raises total social cost relative to MCP, but when the VOT reduction (θ) is small the monopoly outcome can paradoxically be less harmful than MCP because it curtails excessive SAV use that would otherwise generate congestion through the capacity effect.

A key contribution is the identification of a Downs‑Thomson paradox in the SAV context. Under ACP, expanding road capacity (increasing the bottleneck capacity µ) can induce commuters to switch from SAVs back to NVs, lowering SAV utilization, raising the average SAV cost, and ultimately increasing overall commuting costs. Thus, infrastructure expansion alone may worsen system performance when price regulation is present.

Two policy designs are evaluated:

• First‑best policy – combines marginal‑cost pricing with time‑varying congestion tolls. The toll internalizes the external congestion cost, while MCP ensures efficient SAV operation. The policy’s impact depends on the relative strength of the capacity effect versus the VOT effect: when capacity gains dominate, SAV adoption is encouraged; when VOT reductions dominate, the policy can limit SAV use to avoid over‑congestion.

• Second‑best policy – assumes congestion tolls are infeasible and relies solely on fare regulation (typically ACP). By setting a higher fare, the regulator can prevent “excessive” SAV adoption that would otherwise increase total social cost, especially when the VOT effect is strong.

Overall, the analysis demonstrates that promoting SAV adoption is not a panacea; the interaction of scale economies, pricing rules, and infrastructure changes can produce counter‑intuitive outcomes. Effective regulation must align fare structures with the underlying technology characteristics of SAVs to achieve both financial sustainability for the operator and minimal social cost for the commuting public.