Drivers learn city-scale dynamic equilibrium

Abstract

Understanding driver behavior in on-demand mobility services is crucial for designing efficient and sustainable transport models. Drivers' delivery strategy is well understood, but their search strategy and learning process still lack an empirically validated model. Here we provide a game-theoretic model of driver search strategy and learning dynamics, interpret the collective outcome in a thermodynamic framework, and verify its various implications empirically. We capture driver search strategies in a multi-market oligopoly model, which has a unique Nash equilibrium and is globally asymptotically stable. The equilibrium can therefore be obtained via heuristic learning rules where drivers pursue the incentive gradient or simply imitate others. To help understand city-scale phenomena, we offer a macroscopic view with the laws of thermodynamics. With 870 million trips of over 50k drivers in New York City, we show that the equilibrium well explains the spatiotemporal patterns of driver search behavior, and estimate an empirical constitutive relation. We find that new drivers learn the equilibrium within a year, and those who stay longer learn better. The collective response to new competition is also as predicted. Among empirical studies of driver strategy in on-demand services, our work examines the longest period, the most trips, and is the largest for taxi industry.

Multi-market Oligopoly of Equal Capacity

“…The strict concavity or convexity requirement is easy to satisfy as well. For example, [35] shows that the expected revenue as a function of vehicle supply on a street segment is increasing, strictly concave, and smooth. Given this assumption, it is easy to see that p x (s x ) = u x /s x is (decreasing) non-increasing.…”

“…Fish abundance differs spatially at the fishery, so the fishermen can strategize on their allocation of time at different locations. Another example is the taxi industry, where drivers search on a street network for passengers [34,35]. For such a multimarket oligopoly, we study its Nash equilibrium of the static game, its stability under dynamic processes, and its economic efficiency.…”