VII. CONCLUSIONS
In this paper, we proposed a joint optimization framework in the multi-FN, multi-DSO and multi-DSS scenario for IoT fog computing. In the framework, we first modeled the Stackelberg games to solve the pricing problem of the DSOs and resource purchasing problem of the DSSs. Then a many-tomany matching was proposed between the DSOs and the FNs to deal with the DSO-FN pairing problem. Finally, we applied another many-to-many matching between its paired FNs and serving DSSs to solve the FN-DSS pairing problem within the same DSO. For each stage of the problem, all participants were able to achieve the equilibrium or stable results where no one was able to change its behavior unilaterally for a higher utility. Simulation results showed that all FNs, DSOs and DCOs were able to reach optimal utilities for themselves, and high performance of the proposed framework could be achieved compared with the data services without fog nodes. For the future work, firstly the dynamic computing resource allocation problem can be considered in the three-tier IoT fog network with dynamic Stackelberg game, where each DSO is able to predict its future demands and to rent the computing resources of FNs in advance. Secondly, the analysis of cooperative and competitive behaviors among FNs may provide grouping strategies for FNs to achieve higher revenues. Correspondingly, the effective strategies are required for each DSO to prevent the severe competition for some FNs with other DSOs.