The recent development of Electric Vehicles (EV) rises many questions in the research community. A Charging Point Operator (CPO), responsible for a given public Charging Station ({\color{blue} CS}) management aims to maximize her/his profit. The objective of this study is to help a CPO to design her/his pricing policy. The user's reaction to the pricing policy on the decision of joining or not the CS is modeled.

The CPO wants to find the optimal pricing in order to maximize the long-run expected profit, which depends on the expected number of EV user joining and the expected revenue of the CPO per EV. The pricing is a constant piece-wise function of the parking duration.

In our work, inspired from the rich literature of queueing games [Hassin et al. 2003], an analytical formulation of the objective function is provided, which depends on the probability that an arriving EV joins the CS. Uniqueness of the optimal pricing in order to maximize the charging station operator's benefit is proved. A sensitivity analysis of the solution is also provided.