Competitive charging station pricing for plug-in electric vehicles

This paper considers the problem of charging station pricing and station selection of plug-in electric vehicles (PEVs). Every PEV needs to select a charging station by considering the charging prices, waiting times, and travel distances. Each charging station optimizes its charging price based on the prediction of the PEVs' charging station selection decisions, in an attempt to maximize its profit. To obtain insights of such a highly coupled system, we consider a one-dimensional system with two charging stations and Poisson arriving PEVs. We propose a multi-leader-multi-follower Stackelberg game model, in which the charging stations (leaders) announce their charging prices in Stage I, and the PEVs (followers) make their charging station selections in Stage II. We show that there always exists a unique charging station selection equilibrium in Stage II, and such equilibrium depends on the price difference between the charging stations. We then characterize the sufficient conditions for the existence and uniqueness of the pricing equilibrium in Stage I. Unfortunately, it is hard to compute the pricing equilibrium in closed form. To overcome this challenge, we develop a low-complexity algorithm that efficiently computes the pricing equilibrium and the subgame perfect equilibrium of our Stackelberg game with no information exchange.