A game-theoretic approach for pricing policy under urban rail mixed passenger–freight transport

This study develops a tripartite game-theoretic model to analyze subsidy and pricing policies for urban rail mixed passenger–freight transport. We formalize the critical dual externality trade-off that policymakers must confront: subsidies designed to capture environmental benefits from emission reductions may simultaneously exacerbate negative passenger externalities from crowding and discomfort. Integrating Nash equilibrium, Stackelberg, and Nash bargaining games, we demonstrate that cooperative governance enables Pareto improvements for all stakeholders, but these gains are strictly bounded. Crucially, successful cooperation is viable only within a defined effective cooperation zone, whose boundaries are determined by the trade-off between passenger sensitivity to freight traffic and the government’s valuation of environmental benefits. Empirical analysis calibrated with Sydney Metro data confirms that system performance depends critically on this balance. Our findings provide policymakers with a structured framework for designing multi-stakeholder strategies, underscoring that the success of metro-based urban logistics hinges on explicitly quantifying and managing the dual externality trade-off.