Dynamic Incentive Design in Public Transit Subsidization Under Double Moral Hazard: A Continuous-Time Principal-Agent Approach

Public transit subsidization often suffers from a double (or bilateral) moral hazard problem, where both regulators and operators may reduce their efforts due to information asymmetry, thereby compromising service quality despite significant public investment. This paper develops a continuous-time principal-agent model to investigate optimal subsidy contract design under such conditions, where both parties exert costly, unobservable efforts that jointly determine stochastic service outcomes. Using stochastic dynamic programming and exponential utility functions, we derive closed-form solutions for the optimal contracts. Our analysis yields three key findings. First, under standard technical assumptions, the optimal subsidy contract takes a simple linear form based on final service quality, facilitating practical implementation. Second, the contract’s incentive intensity decreases with environmental uncertainty, highlighting a fundamental trade-off between risk-sharing and effort inducement. Third, a unique and mutually agreeable contract emerges as the parties’ risk preferences and productivity levels converge. This study extends the classic principal-agent framework by incorporating bilateral moral hazard in a dynamic setting, offering new theoretical insights into public-sector contract design. For policymakers, the results suggest that performance-based subsidies should be calibrated to account for operational uncertainty, and that regulators are active co-producers of service quality whose own unobservable efforts—distinct from the subsidy itself—are critical to outcomes.The proposed framework provides actionable guidance for designing effective, incentive-compatible subsidies to enhance public transit service delivery.