This study addresses a mobility network pricing problem in a competitive environment. We consider a multimodal transportation network where the links are operated by multiple profit-maximizing, mobility service providers (MSPs). We take the perspective of a network regulator that aims to increase ridership in a target mobility network by providing non-additive, path-based subsidies to travelers. We model paths’ attractiveness using generalized cost functions that combine path travel time and path cost, and we use linear elastic travel demand functions to capture the proportion of demand served by a path. MSPs are non-cooperative and adjust link fares according to the subsidy policy implemented by the regulator. The goal of the network regulator is to solve a budget-constrained mobility network pricing problem under MSP competition. This game-theoretical framework is modeled as a single-leader multi-follower game (SLMFG) wherein the leader player represents the network regulator and multiple follower players represent the MSPs. We conduct a theoretical analysis of this SLMFG by identifying necessary and sufficient conditions for the existence of solutions to the parameterized generalized Nash equilibrium problem (GNEP) that is played amongst MSPs. We show that this GNEP is jointly convex and we use this property to develop an exact numerical approach to solve the SLMFG based on customized branch-and-bound algorithms. Numerical results reveal the impact of MSP competition in this mobility network pricing problem and shed novel insights into the design of optimal path-based subsidy policies.

中文翻译：

---

与非合作移动服务提供商的非附加网络定价


本研究解决了竞争环境中的移动网络定价问题。我们考虑一个多式联运网络，其中的链接由多个利润最大化的移动服务提供商（MSP）运营。我们从网络监管者的角度出发，旨在通过向旅行者提供非附加的、基于路径的补贴来增加目标出行网络的乘客量。我们使用结合路径旅行时间和路径成本的广义成本函数对路径的吸引力进行建模，并使用线性弹性旅行需求函数来捕获路径所服务的需求比例。 MSP不合作，根据监管机构实施的补贴政策调整线路票价。网络监管机构的目标是解决 MSP 竞争下预算受限的移动网络定价问题。该博弈论框架被建模为单领导者多追随者博弈（SLMFG），其中领导者玩家代表网络监管者，多个追随者玩家代表 MSP。我们通过确定 MSP 之间的参数化广义纳什均衡问题 (GNEP) 解存在的必要和充分条件，对该 SLMFG 进行理论分析。我们证明了这个 GNEP 是联合凸的，并且我们利用这个特性开发了一种精确的数值方法来求解基于定制的分支定界算法的 SLMFG。数值结果揭示了 MSP 竞争对移动网络定价问题的影响，并为基于最优路径的补贴政策的设计提供了新的见解。