Uber Stable: Formulating the Rideshare System as a Stable Matching Problem

TL;DR

The research underscores the importance of continued exploration in areas such as dynamic pricing models and additional modeling for unconventional driving times to further enhance the findings on the effectiveness and fairness of ride-sharing platforms.

Abstract

Peer-to-peer ride-sharing platforms like Uber, Lyft, and DiDi have revolutionized the transportation industry and labor market. At its essence, these systems tackle the bipartite matching problem between two populations: riders and drivers. This research paper comprises two main components: an initial literature review of existing ride-sharing platforms and efforts to enhance driver satisfaction, and the development of a novel algorithm implemented through simulation testing to allow us to make our own observations. The core algorithm utilized is the Gale-Shapley deferred acceptance algorithm, applied to a static matching problem over multiple time periods. In this simulation, we construct a preference-aware task assignment model, considering both overall revenue maximization and individual preference satisfaction. Specifically, the algorithm design incorporates factors such as passenger willingness-to-pay, driver preferences, and location attractiveness, with an overarching goal of achieving equitable income distribution for drivers while maintaining overall system efficiency. Through simulation, the paper compares the performance of the proposed algorithm with random matching and closest neighbor algorithms, looking at metrics such as total revenue, revenue per ride, and standard deviation to identify trends and impacts of shifting priorities. Additionally, the DA algorithm is compared to the Boston algorithm, and the paper explores the effect of prioritizing proximity to passengers versus distance from city center. Ultimately, the research underscores the importance of continued exploration in areas such as dynamic pricing models and additional modeling for unconventional driving times to further enhance the findings on the effectiveness and fairness of ride-sharing platforms.

Figures (10)

• Figure 1: Mean income per driver vs. number of agents. In the randomly matched algorithm, we see that mean income stays around the same at $600 per driver, which is as expected, since the ratio of drivers and passengers stay 1-to-1. In contrast, we see that the Boston matching algorithm demonstrates greater variability with increased number of agents, since given the instability, there is increased capacity for the algorithm to output suboptimal matchings between drivers and passengers, where passengers may not give input on better wait times, which may imply better allocation. Then, we see that the closeness and DA matching algorithms are better equipped to capture greater revenue as agents increase. These results demonstrate that proximity is a driver of revenue, and the DA algorithm builds on this revenue driver by further considering of profit and city-center-clustering.
• Figure 2: Revenue per ride vs. number of agents. Here, we see that, despite significantly better revenue performance for closeness matching and DA, we see that the the closeness matching and random matching algorithms maintain relatively similar per-ride revenue.
• Figure 3: Standard deviation of income per driver vs. number of agents. As expected, standard deviation of driver income of the non-random algorithms increase with the increased number of agents, while the random algorithms maintains around the same variability.
• Figure 4: Total revenue of system vs. number of agents. This graph further supports our findings in previous figures, which demonstrate that the DA algorithm best capitalizes on more agents' preferences to maximize revenue for drivers. We also continue to see that the Boston matching algorithm demonstrates higher variability due to instability.
• Figure 5: Total revenue based on fairness vs. number of agents. Interestingly, we find that our hypothetically fair algorithm (DA with driver income taken into consideration for preference ordering) achieves higher aggregate revenue compared to the vanilla DA algorithm. This result would suggest that equitable income distribution not only has positive implications on the labor market and sustainable business practices, but also increases welfare and revenue generation. Still, we may have to do further work to confirm the drivers for this revenue-driving equity.