Pricing schemes are an important smart grid feature to affect typical energy usage behavior of energy users (EUs). However, most existing schemes use the assumption that a buyer pays the same price per unit of energy to all suppliers at any particular time when energy is bought. By contrast, here a discriminate pricing technique using game theory is studied. A cake cutting game is investigated, in which participating EUs in a smart community decide on the price per unit of energy to charge a shared facility controller (SFC) in order to sell surplus energy. The focus is to study fairness criteria to maximize sum benefits to EUs and ensure an envy-free energy trading market. A benefit function is designed that leverages generation of discriminate pricing by each EU, according to the amount of surplus energy that an EU trades with the SFC and the EU's sensitivity to price. It is shown that the game possesses a socially optimal, and hence also Pareto optimal, solution. Further, an algorithm that can be implemented by each EU in a distributed manner to reach the optimal solution is proposed. Numerical case studies are given that demonstrate beneficial properties of the scheme.