Game Theoretic Analysis of Urban E-Taxi Systems: Equilibria and Efficiency

Yukun Yuan, Yue Zhao, Lin Chen, Shan Lin

Abstract: With increasing deployment of electric vehicles in urban mobility-on-demand systems, electric taxis (e-taxi) drivers need to compete with each other not only for passengers but also for limited charging points due to frequent and time-consuming charging activities. This paper focuses on two crucial research questions in this context: (1) What is the strategy of each e-taxi driver for charging and searching passengers in a non-cooperative environment, and what is the collective system outcome of competing e-taxis? (2) How can the mobility-on-demand service platforms (e.g., Uber and Lyft) push self-interested e-taxi drivers to improve the overall system efficiency. Technically, we study the non-cooperative mobility-on-demand system consisting of e-taxis from a game theoretic perspective. We formulate a mobility-on-demand system with competition among drivers as a stochastic game, analyze the Nash Equilibrium (NE) of the game, and design an approximation algorithm to obtain the NE. Moreover, we show that the NE is not necessarily efficient for the platform and propose a pricing scheme from the platform's perspective which induces the new NE to be efficient. We use a trace-driven simulation to evaluate the design based on datasets consisting of more than 7,000 fuel vehicles and nearly 700 e-taxis, 37 working charging stations, and more than 60,000 passenger trips per day. We show that, compared with the state-of-the-art which optimizes the system efficiency by coordinating e-taxis but is not an equilibrium, the NE achieves a system efficiency of merely 73.5% of that of the cooperative state-of-the-art, and the designed pricing scheme improves the price of anarchy to 95.5 %.