Mobility-as-a-Service (MaaS) systems are two-sided markets, with two mutually exclusive sets of agents, i.e., travelers/users and operators, forming a mobility ecosystem in which multiple operators compete or cooperate to serve customers under a governing platform provider. This study proposes a MaaS platform equilibrium model based on many-to-many assignment games incorporating both fixed-route transit services and mobility-on-demand (MOD) services. The matching problem is formulated as a convex multicommodity flow network design problem under congestion that captures the cost of accessing MOD services. The local stability conditions reflect a generalization of Wardrop's principles that include operators’ decisions. Due to the presence of congestion, the problem may result in non-stable designs, and a subsidy mechanism from the platform is proposed to guarantee local stability. A new exact solution algorithm to the matching problem is proposed based on a branch and bound framework with a Frank-Wolfe algorithm integrated with Lagrangian relaxation and subgradient optimization, which guarantees the optimality of the matching problem but not stability. A heuristic which integrates stability conditions and subsidy design is proposed, which reaches either an optimal MaaS platform equilibrium solution with global stability, or a feasible locally stable solution that may require subsidy. For the heuristic, a worst-case bound and condition for obtaining an exact solution are both identified. Two sets of reproducible numerical experiments are conducted. The first, on a toy network, verifies the model and algorithm, and illustrates the differences local and global stability. The second, on an expanded Sioux Falls network with 82 nodes and 748 links, derives generalizable insights about the model for coopetitive interdependencies between operators sharing the platform, handling congestion effects in MOD services, effects of local stability on investment impacts, and illustrating inequities that may arise under heterogeneous populations.

中文翻译：

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按需移动即服务平台分配游戏，保证稳定的结果


移动即服务（MaaS）系统是双边市场，具有两组相互排斥的代理，即旅行者/用户和运营商，形成一个移动生态系统，其中多个运营商竞争或合作，在治理下为客户提供服务。平台提供商。本研究提出了一种基于多对多分配博弈的 MaaS 平台均衡模型，结合了固定路线交通服务和按需移动 (MOD) 服务。匹配问题被表述为拥塞下的凸多商品流网络设计问题，捕获访问 MOD 服务的成本。局部稳定性条件反映了 Wardrop 原则的概括，其中包括运营商的决策。由于拥塞的存在，该问题可能会导致设计不稳定，因此提出了平台的补贴机制来保证局部稳定性。提出了一种基于分支定界框架的匹配问题精确求解算法，该算法结合拉格朗日松弛和次梯度优化的Frank-Wolfe算法，保证了匹配问题的最优性，但不能保证匹配问题的稳定性。提出了一种集成稳定性条件和补贴设计的启发式方法，它可以达到具有全局稳定性的最优MaaS平台平衡解，或者可能需要补贴的可行的局部稳定解。对于启发式方法，确定最坏情况的边界和获得精确解的条件。进行了两组可重复的数值实验。首先，在玩具网络上验证模型和算法，并说明局部和全局稳定性的差异。 第二个是在具有 82 个节点和 748 个链路的扩展苏福尔斯网络上，得出有关共享平台的运营商之间的合作相互依赖模型的普遍见解，处理 MOD 服务中的拥塞效应，本地稳定性对投资影响的影响，并说明以下不平等：可能会在异质人群中出现。