In recent years, global mobile data traffic has seen an unprecedented increase. This is due to worldwide usage of smart devices, availability of fast internet connections, and the popularity of social media. The Mobile Network Operators (MNOs) are, therefore, facing problems in handling this huge traffic flow. Each type of traffic, including real-time video, audio, and text has its own Quality of Services (QoS) requirements which, if not met, may cause a sufficient loss of profit. Offloading of these traffics can be made more efficient so that values of QoS parameters are enhanced. In this work, we propose an incentive-based game-theoretic frame work for downloading data. The download of each type of data will get an incentive determined by the two-stage Stackelberg game. We model the communication among single Mobile Base Station (MBS) and multiple Access Points (APs) in a crowded metropolitan environment. The leader offers an economic incentive based on the traffic type and followers respond to the incentive and offload traffic accordingly. The model optimizes strategies of both the MBS and APs in order to make the best use of their utilities. For the analysis, we have used a combination of analytical and experimental methods. The numerical outcome characterized a direct process of the best possible offloading ratio and legalized the efficiency of the proposed game. Optimal incentives and optimal offloading was the achievement of our proposed game-theoretic approach. We have implemented the model in MATLAB, and the experimental results show a maximum payoff was achieved and the proposed scheme achieved Nash Equilibria.