LTE (Long Term Evolution) networks support a wide range of voice, data and video services. LTE networks are designed to deliver high rates of transmission, low latency and higher spectral efficiency than the current generation of 3G networks. However, due to the limited radio resources, it is important to take advantage of these resources efficiently. This way, an appropriate strategy to resource allocation gains utmost importance for the requirements of QoS (Quality of Service) to be achieved. This paper proposes a Resource Allocation Scheme in two layers that combines game theory and the Proportional Fair Scheduler, aiming at improving performance and justice in the distribution of radio resources. The results of the study of the performance based on modeling and simulation are satisfactory.