  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.
