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 multicommodity flow network design problem under congestion. The local stability conditions reflect a generalization of Wardrop's principles that include operator decisions. A subsidy mechanism from the platform is proposed to guarantee local stability. An exact solution algorithm 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 the optimal MaaS platform equilibrium solution with global stability, or a feasible locally stable solution that may require subsidy. 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 between 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.

翻译：出行即服务（MaaS）系统是双边市场，包含两组互斥的参与者——即旅行者/用户与运营商——形成一个出行生态系统，其中多个运营商在治理平台提供方的管理下相互竞争或合作以服务客户。本研究基于多对多分配博弈，提出了一种MaaS平台均衡模型，该模型整合了固定路线公交服务和按需出行服务。匹配问题被建模为考虑拥堵的多商品流网络设计问题。局部稳定性条件反映了包含运营商决策的Wardrop原理的推广形式。为保障局部稳定性，提出了一种来自平台的补贴机制。基于分支定界框架，结合Frank-Wolfe算法与拉格朗日松弛及次梯度优化，提出了一种精确求解算法，该算法能保证匹配问题的最优性但无法保证稳定性。进一步提出了一种启发式算法，该算法整合了稳定性条件和补贴设计，能够达到具有全局稳定性的最优MaaS平台均衡解，或一个可能需要补贴的可行局部稳定解。同时确定了最坏情况界以及获得精确解的条件。开展了两个可复现的数值实验：第一个实验基于简单网络，验证了模型与算法，并展示了局部稳定性与全局稳定性的差异；第二个实验基于扩展后的Sioux Falls网络（含82个节点和748条边），得出了关于模型在共享平台的运营商间竞合依赖关系、按需出行服务中拥堵效应的处理、局部稳定性对投资影响的作用，以及异质群体下可能产生的不公平现象的普适性洞见。