Uber Stable: Formulating the Rideshare System as a Stable Matching Problem (2403.13083v1)

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.

• The paper introduces a stable matching formulation by applying the Gale-Shapley deferred acceptance algorithm to rideshare platforms.
• It develops a preference-aware task assignment model that integrates willingness-to-pay, driver preferences, and location factors to optimize revenue and fairness.
• Simulations compare this approach with traditional methods, demonstrating enhanced system efficiency and a more equitable income distribution among drivers.

The paper "Uber Stable: Formulating the Rideshare System as a Stable Matching Problem" explores the complexities of ride-sharing platforms like Uber, Lyft, and DiDi by modeling the bipartite matching problem between riders and drivers through the lens of stable matching theory.

Key Components and Contributions

1. Literature Review:
   • The authors begin with a comprehensive review of the existing literature on ride-sharing platforms.
   • They particularly focus on efforts aimed at enhancing driver satisfaction within the system, stressing the importance of matching quality and equitable income distribution.
2. Algorithmic Approach:
   • The core of the research involves the application of the Gale-Shapley deferred acceptance algorithm, a well-known strategy from stable matching theory.
   • This algorithm addresses a static matching problem over multiple time periods, thereby acknowledging the dynamic nature of ride-sharing environments.
3. Preference-Aware Task Assignment Model:
   • The authors construct a model that integrates several critical factors:
     • Passenger Willingness-to-Pay: Reflecting the economic aspects of rider preferences.
     • Driver Preferences: Capturing individual driver inclinations and priorities.
     • Location Attractiveness: Considering geographic elements and how they influence both rider and driver decisions.
   • The goal is to maximize overall revenue while maintaining a fair distribution of income among drivers.
4. Simulation Testing and Comparative Analysis:
   • Simulations are conducted to observe and compare the performance of the proposed Gale-Shapley algorithm against other algorithms:
     • Random Matching and Closest Neighbor Algorithms: Traditional approaches that are relatively simple.
     • Boston Algorithm: A variant that is also analyzed for performance comparison.
   • Performance metrics include:
     • Total Revenue: Overall income generated by the system.
     • Revenue per Ride: Average income per ride, indicating efficiency.
     • Standard Deviation of Income: A measure of income inequality among drivers.
   • The comparison highlights trends and impacts of prioritizing different factors, such as proximity to passengers versus distance from the city center.
5. Results and Observations:
   • The findings reveal that the Gale-Shapley algorithm can achieve a balance between system efficiency and equitable income distribution better than random matching or closest neighbor algorithms.
   • Prioritizing proximity to passengers generally results in higher total revenue and better driver satisfaction as opposed to merely focusing on central locations.
6. Future Research Directions:
   • The paper underscores the potential for improved dynamic pricing models to enhance both system efficiency and fairness.
   • The authors suggest additional modeling for unconventional driving times, which could provide further insights for optimizing ride-sharing platforms.

Conclusion

The research provides valuable insights into how stable matching theory can be effectively applied to enhance the operational dynamics of ride-sharing platforms. By incorporating both driver and rider preferences and evaluating different priority factors, the paper offers a novel perspective on achieving a balanced, efficient, and fair ride-sharing system. The emphasis on continued exploration in dynamic pricing and time-based modeling indicates a promising future for optimizing these platforms for both economic and social benefits.