Anarchy and Fairness in Ride-Sharing System

Ride-sharing platforms have become increasingly popular. The platforms act as "matchmaker" for a two sided market --- people who would like to pay for a short-distance travel and people who offer to drive them around to get paid. Currently, drivers serving in the platform have autonomy on whether or not they participate in it at any given moment. Such autonomous behaviors may, however, not be beneficial to the platforms and the riders, and, consequently the drivers themselves. In this thesis we examine two problems regarding ride-sharing platforms. The first is optimal policies for empty-car relocations; the second is whether simple pricing can replace origin-based pricing when platforms have control over the relocations of empty cars. To address the first problem, we model the ride-sharing system as a finite-state discrete fluid model. We focus on designing relocation policy for empty cars. We study the steady state distribution of mass drivers under any chosen strategy, and establish the existence and uniqueness of the steady state. We then develop a constructive framework to design a dynamic relocation policy. We prove that the constructive dynamic relocation policy enjoys many desirable properties. The simulations based on both synthetic and real data shows that our constructive relocation policy outperforms other policies in terms of some quantitative metrics. Our constructive approach provides a flexible framework to suit many types of objectives, such as efficiency, fairness, and as well as combinations of objectives. To address the second problem, we refine our model to: (1) take account the effect of price on the two-sided ride-sharing market; and (2) use infinite horizon average-reward Markov Model for strategic drivers' relocation decision process. We show in a simple three-region case that the drivers' optimal strategy may not be aligned with the request of rides. This can occur when passenger-less drivers relocate to regions that are already saturated when there are still regions with unfilled demand. Allowing the platform to control empty rides can remedy this situation. We also show that this control is beneficial not only to the platforms and the drivers, but also to the passengers.