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

TL;DR

This paper develops a bottleneck model with shared autonomous vehicles to study how scale economies and natural monopoly incentives interact with three fare-setting regimes: marginal cost pricing, average cost pricing, and unregulated monopoly pricing. It shows that marginal cost pricing minimizes commuter costs but yields deficits, while average cost pricing can induce multiple equilibria and a Downs--Thomson paradox under capacity expansion; a two-step policy—allow monopoly pricing initially and switch to average cost pricing after reaching a high adoption level—can improve social welfare without deficits. The analysis identifies a capacity-VOT index $\eta=(1-\kappa)/(1-\theta)$ that governs when SAV adoption reduces social costs under first-best and second-best policies, and demonstrates that congestion tolls can be paired with MC pricing to achieve first-best outcomes. Overall, the results highlight that fare regulation and policy timing must align with SAV technology maturity and scale-effect strength to realize welfare gains, and that promoting SAV adoption does not universally reduce social cost.

Abstract

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.

Figures (6)

• Figure 1: Network and normal/autonomous vehicles
• Figure 2: Mode-specific commuting costs and the number of SAV commuters; solid and dashed circles represent the stable and unstable equilibria, respectively. $N=1000$, $\kappa = 0.01$, $\theta = 0.7$, $\beta = 0.4$, $\gamma = 0.4$, $\mu = 0.2$, $t_{f} = 10$, $F_{n} = 100$, $m=100$, $w = 20$, $F_{a}=36000$.
• Figure 3: Downs--Thomson paradox under AC pricing. $N=250$, $\kappa = 0.01$, $\theta = 0.7$, $\beta = 0.4$, $\gamma = 0.4$, $t_{f} = 10$, $F_{n} = 500$, $m=499$, $w = 100$, $F_{a} = 10500$.
• Figure 4: Time-varying congestion tolls in the first-best equilibrium. $N=10000$, $\theta = 0.5$, $\beta = 0.3$, $\gamma = 2.0$, $\mu = 1$, $t_{f} = 2$, $F_{n} = 500$, $m=800$, $w = 200$.
• Figure 5: Contour plot of the social cost. $N=10000$, $\theta = 0.5$, $\beta = 0.3$, $\gamma = 2.0$, $\mu = 20$, $t_{f} = 2$, $F_{n} = 300$, $m=210$, $w=100$, $F_{a} = 50000$.

Theorems & Definitions (31)

• Lemma 1: Van_den_Berg2016-mv
• Proposition 1
• Proposition 2
• Proposition 3
• Proof 1
• Proposition 4
• Theorem 1
• Theorem 2
• Lemma 2
• Proof 2