  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.
