Using subsidies to stabilize peer-to-peer ridesharing markets with role assignment

Abstract

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.