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Due to the technological advancement in cellular networks, massive data traffic appends to the existing digital technologies. These emerging digital technologies face quality of service (QoS) challenges, particularly when it comes to maintaining the tradeoffs between customers and service providers. The cellular service providers are trying to meet the needs of end users by handling four substantially different types of data, i.e., Real Time, Video, Audio, and Text, with each type having its own requirements. To achieves an efficient QoS, different incentive-based algorithms were proposed. However, these schemes do not ensure a fair distribution of profit among the mobile network operator and access points. Furthermore, these schemes do not provide efficient QoS to the end user and cannot ensure a fair distribution of channels in crowning time. We propose an incentive-based scheme using game theory and two-stage Stackelberg approach for integrated data, offloading the decision-making process in a heterogeneous network. A single mobile base station and some integrated access points in a crowded metropolitan area are modeled in our proposed scheme. This station offers an economic incentive based on traffic types, and access points compete with each other to earn incentives for offload traffic. A mathematical game is derived to analyze the real-world scenario through simulation. The experimental method is applied to validate the numerical outcomes by comparing the results with other models.