Growth of network access technologies in the mobile environment has raised several new issues due to the interference between the available access. Thanks to the currently used access methods such as the orthogonal frequency division multiple access in mobile networks and the long term evolution-advanced systems, the intra-cell interferences are avoided and the quality of service has increased. Nevertheless, the diversity and multiplicity of base stations in the network have left behind a major problem of inter-cell interferences. In this paper, we focus on the optimization of the total throughput of cellular networks using fractional frequency reuse and allowing each mobile user to individually choose its serving base station. We derive analytically the utilities related to the network manager and mobile users and develop a Stackelberg game to obtain the equilibrium. We propose a distributed algorithm that allows the base stations, using a light collaboration, to achieve an efficient utilization of the frequencies, with the optic of maximizing the total system utility. This algorithm is based on stochastic gradient descent which requires some information to be exchanged between neighboring base stations. At user association level, we propose an iterative distributed algorithm based on automata learning algorithm. Both algorithms allow the system to converge to the Stackelberg equilibrium. Furthermore, simulation results carried out based on a realistic network setting show promising results in terms of global utility and convergence issues. In this setting, we include scenarios with a varying number of users and address the problem of robustness and scalability of the proposed approach.