Optimum versus Nash-equilibrium in taxi ridesharing

In recent years, Transportation Network Companies (TNC) such as Uber and Lyft have embraced ridesharing: a passenger who requests a ride may decide to save money in exchange for the inconvenience of sharing the ride with someone else and incurring a delay. When matching passengers, these services attempt to optimize cost savings. But a possible scenario is that while passenger A is matched to passenger B, if matched to passenger C then both A and C would have saved more money. This leads to the concept of “fairness” in ridesharing, which consists of finding the Nash equilibrium in a ridesharing plan. In this paper we compare the optimum plan (i.e., benefit maximized at a global level) and the fair plan in both static and dynamic contexts. We show that in contrast to the theoretical indications, the fair plan is almost optimum. Furthermore, the fairness concept may help attract more passengers to rideshare and thus further reduce vehicle miles traveled. If social preferences are included in the total benefit, we demonstrate that the optimum ridesharing plan may be unboundedly and predominantly unfair in a sense that will be formalized in this paper.