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Driven by the growing popularity of mobile applications, mobile cloud computing has been envisioned as a promising approach to enhance computation capability of mobile devices and reduce the energy consumptions. In this paper, we investigate the problem of multi-user computation offloading for mobile cloud computing under dynamic environment, wherein mobile users become active or inactive dynamically, and the wireless channels for mobile users to offload computation vary randomly. As mobile users are self-interested and selfish in offloading computation tasks to the mobile cloud, we formulate the mobile users' offloading decision process under dynamic environment as a stochastic game. We prove that the formulated stochastic game is equivalent to a weighted potential game which has at least one Nash Equilibrium (NE). We quantify the efficiency of the NE, and further propose a multi-agent stochastic …