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Fog computing is considered as a promising technology to meet the ever-increasing computation requests from a wide variety of mobile applications. By offloading the computationintensive requests to the fog node or the central cloud, the performance of the applications, such as energy consumption and delay, are able to be significantly enhanced. Meanwhile, utilizing the recent advances of social network and energy harvesting (EH) techniques, the system performance could be further improved. In this paper, we take the social relationships of the EH mobile devices (MDs) into the design of computational offloading scheme in fog computing. With the objective to minimize the social group execution cost, we advocate game theoretic approach and propose a dynamic computation offloading scheme designing the offloading process in fog computing system with EH MDs. Different queue models are applied to model the energy cost and delay performance. It can be seen that the proposed problem can be formulated as a generalized Nash equilibrium problem (GNEP) and we can use exponential penalty function method to transform the original GNEP into a classical Nash equilibrium problem and address it with semi-smooth Newton method with Armijo line search. The simulation results demonstrate the effectiveness of the proposed scheme.Index Terms-Computation offloading, energy consumption, energy harvesting (EH), execution cost, fog computing, generalized Nash equilibrium problem (GNEP), social-aware mobile network.

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