Informal and Privatized Transit: Incentives, Efficiency and Coordination

Abstract

Informal and privatized transit services, such as minibuses and shared auto-rickshaws, are integral to daily travel in large urban metropolises, providing affordable commutes where a formal public transport system is inadequate and other options are unaffordable. Despite the crucial role that these services play in meeting mobility needs, governments often do not account for these services or their underlying incentives when planning transit systems, which can significantly compromise system efficiency. Against this backdrop, we develop a framework to analyze the incentives underlying informal and privatized transit systems, while proposing mechanisms to guide public transit operation and incentive design when a substantial share of mobility is provided by such profit-driven private operators. We introduce a novel, analytically tractable game-theoretic model of a fully privatized informal transit system with a fixed menu of routes, in which profit-maximizing informal operators (drivers) decide where to provide service and cost-minimizing commuters (riders) decide whether to use these services. Within this framework, we establish tight price of anarchy bounds which demonstrate that decentralized, profit-maximizing driver behavior can lead to bounded yet substantial losses in cumulative driver profit and rider demand served. We further show that these performance losses can be mitigated through targeted interventions, including Stackelberg routing mechanisms in which a modest share of drivers are centrally controlled, reflecting environments where informal operators coexist with public transit, and cross-subsidization schemes that use route-specific tolls or subsidies to incentivize drivers to operate on particular routes. Finally, we reinforce these findings through numerical experiments based on a real-world informal transit system in Nalasopara, India.

Figures (6)

• Figure 1: Depiction of the characteristics of the informal transit system on which minibus drivers service riders on a fixed menu of routes. The left panel depicts the trip characteristics, where, on each trip, a minibus transports $F$ riders from the route’s origin to its destination and then returns empty to the origin to serve additional riders. The middle panel illustrates driver route choice, with each driver selecting one of $n$ routes to operate on based on profitability. The right panel shows the mode choice decision faced by riders who either travel by minibus or take the outside option, such as walking.
• Figure 2: Depiction of the minibus rider demand function when incorporating rider queuing (left) and under a capacity-constrained formulation without rider queuing (right). When rider queuing is incorporated via a Vickrey-style bottleneck model, the minibus rider demand is concave quadratic below a threshold $\Tilde{k}_i^* \leq k_i^*$, and remains flat thereafter. In the special case when the cost difference $S_i = 0$, this rider demand function reduces to the capacity-constrained formulation, where the served minibus rider demand increases linearly with driver supply until the capacity-matching threshold $k_i^*$ at which $\mu_i(x_i) = \lambda_i$, and remains flat thereafter.
• Figure 3: Depiction of the profit ratio (left), rider welfare ratio (center), and equilibrium profit per driver (right) as the number of drivers in the system is varied.
• Figure 4: Profit ratio (left) and rider welfare ratio (right) as the share of centrally controlled drivers $\alpha$ is varied, with the remaining drivers operating as informal or privatized transit operators. We depict three Stackelberg routing algorithms: L-NCF and LPF, which account for the incentives of informal and privatized transit, and a Greedy baseline that does not, reflecting the status-quo and current practice among public transit agencies.
• Figure 5: Depiction of the equilibrium rider waiting time profiles in the regime when the cost difference between the outside option and that of using the minibus without queuing delays satisfies $S_i \geq \Bar{S}(x_i)$ (left) and $S_i < \Bar{S}(x_i)$ (right).

Theorems & Definitions (21)

• Definition 1: The Informal Transit System
• Definition 2: Equilibrium Driver Allocation
• Definition 3: Price of Anarchy
• Proposition 1: Minibus Demand Under Rider Queuing
• Corollary 1: Continuity and Monotonicity of Minibus Rider Demand
• Corollary 2: Continuity and Monotonicity of Per-Driver Profits
• Theorem 1: PoA Upper Bound for Cumulative Driver Profit
• Proposition 2: Tightness of P-PoA Bound
• proof : Proof of Theorem \ref{['thm:poa-driver-profit']}
• proof : Proof of Proposition \ref{['prop:tightness-poa-profit']}