Nowadays, the customer network effects are becoming a central issue for the companies, while the previous studies have been only limited to customer lifetime value and its related models. Therefore, this paper aims to presents a model for calculating customer lifetime value, and simultaneously the network effects are considered. For this purpose, an oligopoly market is considered in which companies compete with each other. The companies individually have a number of buyers and sellers. Interestingly, their policy is based on offering services to their buyers free, and receiving the membership fees from the sellers instead. Customers influence each other, and their wordof-mouth marketing leads to a change in the number of companies' customers. This interaction is also observed among the sellers. In the absence of buyers, the presence of sellers is meaningless. In other words, there is a remarkable proportion between the number of buyers and sellers, which directly affects the companies' profitability. Each company seeks to determine the optimal marketing and pricing policies, considering the effects of the network. By applying differential game theory, the companies are able to receive the market share, advertising, and pricing strategy. The Genetic Algorithm is employed to solve the model. Finally, a numerical example and model validation are provided to demonstrate the proposed model capabilities.