Network Selection mechanisms play an important role in ensuring quality of service for users in a multi-network environment. These mechanisms handle the selection of an optimal wireless network to satisfy a user request. This paper proposes a radio resource management framework for integrated network selection mechanism control in multi- network environment as an interaction game between the service providers and customers in non-cooperative manner to maximize their rewards. The proposed scheme comprises two steps. The first applies the analytic hierarchy process (AHP) to determine the relative weights of the evaluative criteria according to customer preferences and network condition. The second calculates the payoffs based on the relative weights calculated in the previous step and a utility function evaluation by each wireless network of each customer. Analytical and simulation results demonstrate the effectiveness of proposed model to achieve optimum network utility for the wireless networks along with optimizing the customer's satisfaction. The proposed model is preliminary and its contribution is to create an admission policy that can adapt to different coverage areas of a wireless network and depends on the priority of customers and their requirements.