This is the first paper to address the topology structure of Job Edge-Fog interconnection network in the perspective of network creation game. A two level network creation game model is given, in which the first level is similar to the traditional network creation game with total length objective to other nodes. The second level adopts two types of cost functions, one is created based on the Jackson-Wolinsky type of distance based utility, another is created based on the Network-Only Cost in the IoT literature. We show the performance of this two level game (Price of Anarchy). This work discloses how the selfish strategies of each individual device can influence the global topology structure of the job edge-fog interconnection network and provides theoretical foundations of the IoT infrastructure construction. A significant advantage of this framework is that it can avoid solving the traditional expensive and impractical quadratic assignment problem, which was the typical framework to study this task. Furthermore, it can control the systematic performance based only on one or two cost parameters of the job edge-fog networks, independently and in a distributed way.
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