# Resource Allocation in Wireless Powered IoT System: A Mean Field Stackelberg Game-Based Approach
## 4 Game Analysis and Implementation Algorithm
### Mean Field Control Algorithm
(**a**) Power transfer = 50 W; (**b**) power transfer = 100 W; (**c**) power transfer = 150 W; and (**d**) power transfer = 200 W.

## 6 Conclusions

In this paper, we have proposed a Stackelberg mean field game-based model to solve the power control problems in the wireless powered IoT system, to minimize the cost of the information transmission for the sensor nodes, and to minimize the cost of the HAP. In the proposed game model, the relations between the HAP and sensors is analyzed based on the Stackelberg game, and the objective functions are constructed using the mean field game. We consider the energy variations of sensors and HAP as the system state to construct the mean field game model. Then mean filed control for both the sensor nodes and the HAP are analyzed, and \(\epsilon\)-Nash equilibriums are obtained. Based on the simulations results, it can be seen that our proposed model can achieve optimal power control for

Figure 8: Variations of the HAP’s energy. Figure 7: Variations of the mean field term. (**a**) Power transfer = 50 W; (**b**) power transfer = 100 W; (**c**) power transfer = 150 W; and (**d**) power transfer = 200 W.

both the sensor nodes and the HAP. In future work, we will attempt to extend our proposed mean field Stackelberg game-based algorithm, in order to employ it in other kinds of networks, such as smart grid networks [25], M2M networks [26], 5G networks [27; 28], and so on [29]. [PERSON] conceived the draft writing of the manuscript. [PERSON] conceived system model, game analysis and the performance evaluation, he also conceived on the manuscript organization; [PERSON] and [PERSON] conceived to the simulations; [PERSON] conceived to the project management; and all authors contributed to data analysis, simulations, and the writing of this paper. This work is supported by the National Natural Science Foundation of China, No. 61501026, and the National Key R&D Program of China, No.2018 YFB1003905. The authors would like to thank the editor and the anonymous reviewers for their valuable comments and suggestions that improved the quality of this paper. The authors declare no conflicts of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. ## References

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