Stable Matching of Users in a Ridesharing Model

A ridesharing system is a transport mode where two or more users share the same vehicle and divide the trip's expenses based on similar routes and itineraries. Popular ridesharing systems, such as Uber, Flinc, and Lyft, define a matching among users based only on the coincidence of routes. However, these systems do not guarantee a stable matching (i.e., a matching in which no user prefers another different from the assigned one). In this work, a new ridesharing system model is proposed, including three types of trips: identical, inclusive, and partial. This model is used to introduce a new algorithm to address the stable matching problem for ridesharing systems. Finally, a set of experimental simulations of the proposed algorithm is conducted. Experimental results show that the proposed algorithm always produces a stable matching.