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On-demand cloud computing is one of the rapidly evolving technologies that is being widely used in the industries now. With the increase in IoT devices and real-time business analytics requirements, enterprises that ought to scale up and scale down their services have started coming towards on-demand cloud computing service providers. In a cloud data center, a high volume of continuous incoming task requests to physical hosts makes an imbalance in the cloud data center load. Most existing works balance the load by optimizing the algorithm in selecting the optimal host and achieves instantaneous load balancing but with execution inefficiency for tasks when carried out in the long run. Considering the long-term perspective of load balancing, the research paper proposes Stackelberg (leader-follower) game-theoretical model reinforced with the satisfaction factor for selecting the optimal physical host for deploying the tasks arriving at the data center in a balanced way. Stackelberg Game Theoretical Model for Load Balancing (SGMLB) algorithm deploys the tasks on the host in the data center by considering the utilization factor of every individual host, which helps in achieving high resource utilization on an average of 60%. Experimental results show that the Stackelberg equilibrium incorporated with a satisfaction index has been very useful in balancing the loading across the cluster by choosing the optimal hosts. The results show better execution efficiency in terms of the reduced number of task failures by 47%, decreased 'makespan' value by 17%, increased throughput by 6%, and a decreased front-end error rate as compared to the traditional random allocation algorithms and flow-shop scheduling algorithm.