Repositioning, Ride-matching, and Abandonment in On-demand Ride-hailing Platforms: A Mean Field Game Approach

TL;DR

A novel two-matching-radius nearest-neighbor dispatch algorithm is proposed that eliminates undesirable equilibria and ensures a unique mean field equilibrium for multi-region systems and reduces customer abandonment, minimizes waiting times for both customers and drivers, and improves overall platform efficiency.

Abstract

The on-demand ride-hailing industry has experienced rapid growth, transforming transportation norms worldwide. Despite improvements in efficiency over traditional taxi services, significant challenges remain, including drivers' strategic repositioning behavior, customer abandonment, and inefficiencies in dispatch algorithms. To address these issues, we introduce a comprehensive mean field game model that systematically analyzes the dynamics of ride-hailing platforms by incorporating driver repositioning across multiple regions, customer abandonment behavior, and platform dispatch algorithms. Using this framework, we identify all possible mean field equilibria as the Karush-Kuhn-Tucker (KKT) points of an associated optimization problem. Our analysis reveals the emergence of multiple equilibria, including the inefficient "Wild Goose Chase" one, characterized by drivers pursuing distant requests, leading to suboptimal system performance. To mitigate these inefficiencies, we propose a novel two-matching-radius nearest-neighbor dispatch algorithm that eliminates undesirable equilibria and ensures a unique mean field equilibrium for multi-region systems. The algorithm dynamically adjusts matching radii based on driver supply rates, optimizing pick-up times and waiting times for drivers while maximizing request completion rates. Numerical experiments and simulation results show that our proposed algorithm reduces customer abandonment, minimizes waiting times for both customers and drivers, and improves overall platform efficiency.

Figures (3)

• Figure 1: Two-matching-radius Nearest-neighbor Dispatch: (a). an arriving customer is immediately matched with the closest idle driver within matching radius $R_c$ and (b). an arrival driver is immediately matched with the closest waiting customer within matching radius $R_d$.
• Figure 2: The LHS of \ref{['eq:ne_oneregion']} as a function of the driver supply rate $x$. We set the matching radius $R_c$ and $R_d$ to be the same. In this figure, the matching radius values, from left to right, are 1 km, 2 km, 3 km, and 4 km. We can observe that for larger matching radii ($R=2,3,4$ km) and a driver density near 25, there can be up to three equilibria. Additionally, the efficiency loss in the inefficient equilibrium is approximately $5\%-10\%$.
• Figure 3: Figure showing driver density as a function of driver supply rate (RHS of \ref{['eq:ne_oneregion']}), with various customer arrival rates and matching radii, compared to the proposed dynamic optimal matching radius \ref{['eq:dynamic_radii']}. Panels from left to right represent low, medium, and high demand scenarios with customer arrival rates of $1$, $2$, $3$ pass/(min$\cdot$km$^2$), respectively. The proposed dynamic optimal matching radius (highlighted by the red color) outperforms all fixed radii, and under this dynamic scheme, driver density strictly increases with the driver supply rate, ensuring a unique equilibrium.

Theorems & Definitions (10)

• definition 1
• proposition 1
• theorem 1
• corollary 1
• corollary 2
• proposition 2
• proposition 3
• corollary 3
• proposition 4: Optimal Radii Design
• theorem 2: Monotone Sojourn Time