Peer-to-peer (P2P) ridesharing is a form of shared-use mobility that has emerged in recent decades as a result of enabling of the sharing economy, and the advancement of new technologies that allow for easy and fast communication between individuals. A P2P ridesharing system provides a platform to match a group of drivers, who use their personal vehicles to travel, with their peer riders who are in need of transportation. P2P ridesharing systems are traditionally categorized as two-side markets, with two mutually exclusive sets of agents, i.e., riders and drivers. Fixing the roles of participants a priori, however, could come at an opportunity cost of missed social welfare/revenue for the system. Consequently, this paper proposes a new market game, and its corresponding mathematical formulation, that outputs matching, role assignment, and pricing. We investigate the stability properties of this market game, and present a mathematical formulation that yields a stable outcome if one exists. Furthermore, we propose a Lagrangian relaxation algorithm to obtain a stable solution for large-scale games with empty cores through subsidizing the system. Using numerical experiments, we demonstrate the benefits of the proposed methodology, and its advantages over previously proposed methods for stabilizing non-bipartite graphs.

点对点（P2P）乘车共享是共享使用移动性的一种形式，由于共享经济的实现以及新技术的发展，这种共享使用移动性已在最近几十年出现，可实现个人之间的便捷通信。P2P乘车共享系统提供了一个平台，可将一群使用私家车旅行的驾驶员与需要运输的同伴驾驶员配对。P2P乘车共享系统传统上分为两类市场，有两组互斥的代理，即骑手和驾驶员。但是，先验地确定参与者的角色可能会以错过该系统的社会福利/收入为代价。因此，本文提出了一种新的市场博弈及其相应的数学公式，可以输出匹配，角色分配和定价。我们研究了这种市场博弈的稳定性，并提出了一种数学公式，如果存在的话，它将产生稳定的结果。此外，我们提出了一种Lagrangian松弛算法，通过对系统进行补贴，可以获得具有空核的大型游戏的稳定解。使用数值实验，我们证明了所提出的方法的优点，以及它相对于以前提出的用于稳定非二分图的方法的优点。