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.

拼车服务和公共交通服务的替代和补充极大地影响了多式联运系统的流动性和可达性。由于交通网络公司（TNC）（拼车运营商）关注利润，政府（公共交通运营商）推动社会公益，因此，两个决策者将相互合作和竞争，以提高各自的利益。在本文中，我们开发了一种双层博弈论方法来模拟跨国公司与政府之间的合作和竞争关系。在上层，两位政策制定者设计了一项合作计划，政府为使用拼车服务解决第一英里或最后一英里问题的公共交通乘客提供补贴。在较低的级别，他们试图优化运营策略以相互竞争以实现其目标。双层博弈的结果取决于乘客在替代出行方式中的选择，其特点是聚合多模式市场。基于所提出的博弈论方法，我们分析和数值研究了乘客侧补贴的竞争对多模式系统的影响，以及导致政策和政策双赢的最优策略的存在。制造商。我们发现可能存在社会最优的补贴水平。在公共交通可达性高的地区，善意的补贴会促进第一英里或最后一英里的乘车采购服务，可能会降低 TNC 的利润。