IoT-based services benefit from cloud which offers a virtually unlimited capabilities, such as storage, processing, and communication. However, the challenges are still open for mobile users to receive computation from the cloud with satisfied quality-of-service (QoS) provisioning. In this paper, we study computation offloading by using edge computing, which is a new paradigm to deliver computation to the edge of pervasive networks nearby mobile users. Without strong incentive in place, however, local edge servers may be reluctant to help offload computation. To stimulate cloud service operator and local edge server owners to participate in computation offloading, we formulate the interactions among cloud service operator and edge server owners as a Stackelberg game to maximize the utilities of cloud service operator and edge server owners by obtaining the optimal payment and computation offloading strategies. Through theoretical analysis, we show that the game is guaranteed to reach a unique Nash equilibrium. We then design two computation offloading algorithms that can quantify their efficiencies in terms of low delay and reduced complexity. Additionally, we extend our work by considering that edge server owners dynamically join or leave computation offloading. Numerical results show that our proposed algorithms perform well in computation offloading and efficiently stimulate edge server owners to make contribution to computation offloading.