Recently, the concept of fog computing which aims at providing time-sensitive data services has become popular. In this model, computation is performed at the edge of the network instead of sending vast amounts of data to the cloud. Thus, fog computing provides low latency, location awareness to end users, and improves quality-of-services (QoS). One key feature in this model is the designing of payment plan from network operator (NO) to fog nodes (FN) for the rental of their computing resources, such as computation capacity, spectrum, and transmission power. In this paper, we investigate the problem of how to design the efficient payment plan to maximize the NOs revenue while maintaining FNs incentive to cooperate through the moral hazard model in contract theory. We propose a multi-dimensional contract which considers the FNs characteristics such as location, computation capacity, storage, transmission bandwidth, and etc. First, a contract which pays the FNs by evaluating the resources they have provided from multiple aspects is proposed. Then, the utility maximization problem of the NO is formulated. Furthermore, we use the numerical results to analyze the optimal payment plan, and compare the NOs utility under different payment plans.
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