The rapidly developing cloud computing and virtualization techniques provide mobile devices with battery energy saving opportunities by allowing them to offload computation and execute applications remotely. A mobile device should judiciously decide whether to offload computation and which portion of application should be offloaded to the cloud. In this paper, we consider a mobile cloud computing (MCC) interaction system consisting of multiple mobile devices and the cloud computing facilities. We provide a nested two stage game formulation for the MCC interaction system. In the first stage, each mobile device determines the portion of its service requests for remote processing in the cloud. In the second stage, the cloud computing facilities allocate a portion of its total resources for service request processing depending on the request arrival rate from all the mobile devices. The objective of each mobile device is to minimize its power consumption as well as the service request response time. The objective of the cloud computing controller is to maximize its own profit. Based on the backward induction principle, we derive the optimal or near-optimal strategy for all the mobile devices as well as the cloud computing controller in the nested two stage game using convex optimization technique. Experimental results demonstrate the effectiveness of the proposed nested two stage game-based optimization framework on the MCC interaction system. The mobile devices can achieve simultaneous reduction in average power consumption and average service request response time, by 21.8% and 31.9%, respectively, compared with baseline methods.