Competition between the transportation network company and the government with subsidies to public transit riders.

• Cooperative and competitive analysis for a duopoly of TNC and public transit. • TNC can be hurt by a good-intentioned subsidy in areas with high public transit accessibility. • Win-win outcome achieved via subsidy design in areas with low public transit accessibility. The substitution and complement of ride-sourcing services and public transit services greatly affect the mobility and accessibility of a multi-modal transportation system. Since the transportation network company (TNC) (operator of ride-sourcing) concerns the profit and the government (operator of public transit) promotes social welfare, the two policy-makers will both cooperate and compete with each other to enhance their benefits. In this paper, we develop a bi-level game-theoretic approach to model the cooperative and competitive relationship between the TNC and the government. In the upper level, the two policy-makers design a cooperative plan such that the government provides subsidies to public transit riders who use ride-sourcing to solve first- or last-mile problems. In the lower level, they attempt to optimize operational strategies to compete with each other for achieving their objectives. The outcome of the bi-level game depends on passengers' choices among alternative travel modes, which is characterized by an aggregate multi-modal market. Based on the proposed game-theoretic approach, we analytically and numerically examine the impact of the competition with passenger-side subsidies on the multi-modal system, and the existence of optimal strategies that lead to a win–win situation for both the policy-makers. We find that a socially-optimal subsidy level may exist. In areas with high public transit accessibility, a good-intentioned subsidy that boosts first- or last-mile ride-sourcing services can reduce the TNC's profit. Our research highlights the value of a carefully designed subsidy structure that benefits both the TNC (profit) and the society (social welfare), especially in areas with low public transit accessibilities. [ABSTRACT FROM AUTHOR]