Before revision:  We capture the decisions of taxi drivers in a game-theoretic model, prove the existence, uniqueness, and global asymptotic stability of Nash equilibrium . We offer a macroscopic view of this equilibrium with laws of thermodynamics.
After revision:  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 of this equilibrium with laws of thermodynamics.