# Resource Allocation in Wireless Powered IoT System: A Mean Field Stackelberg Game-Based Approach
## 1 Introduction  
Internet of Things (IoT), as the main pattern to link between people and things, has been employed in the logistics for tail after, to build industry IoT environments, and for academia research [1; 2]. Through IoT techniques [3], it is easy for people to access and control the date generated by the sensors, to structure the IoT system. In the IoT system, because the sensors are always battery limited devices [4], one of the main concern faced by the mass sensors is the energy consumption problem. Although the technology of NB-IoT is introduced by 3 GPP to achieve low energy consumption [5], efficient energy utility in the IoT system still a key challenge that is under active research.  
The development of the techniques for energy harvesting and wireless power transfer provides a paradigm to solve the energy efficiency and consumption problems in the IoT system [3; 6]. Through the energy harvesting circuit, the sensors can harvest energy from different energy sources [7], such as sun light, wind, etc. Radio frequency (RF) based wireless power transfer in IoT system [8; 9], which is more reliable and controllable, is also drawn a lot of research interests [10].  
In this paper, we focus on the energy consumption problem in IoT system with RF based wireless power transfer, to achieve optimally resource allocation. We try to use the mean field Stackelberggame theory [11] to solve the resource allocation problem in the wireless powered IoT system, which consists of one HAP and a large number of sensor nodes. The mean field game is firstly inspired by [12; 13], to solve the resource allocation problem with a large number of game players. In this paper, through combining the Stackelberg game and the mean field game, we aim at finding the optimal power control strategies when there is a large number of the sensor nodes. The dynamic characteristics of the battery's energy variation is also considered in the proposed game model. We pay attention to the power control problem, to minimize the utility for both the HAP and the senor nodes. In summary, the key contributions of this paper are as follows:  
* Firstly, we research a wireless powered IoT system, which consists of one hybrid access point (HAP) and \(N\) sensor nodes. The HAP is both the information collection center and the energy source for the sensor nodes.
* Secondly, a mean field Stackelberg game model is proposed to formulate the resource allocation problem in the proposed IoT system. The Stackelberg game is a one-leader-many-followers Stackelberg game. The HAP is the leader, where the sensor nodes are followers. For the mean field game, we use the energy variations as the system state. The objectives for the sensor nodes are to minimize the transmission cost during the energy transfer and information transmission. The objective for the HAP is to control the power level for energy transfer to minimize its utility.
* Finally, the mean field control for both the sensor nodes and the HAP are given based on dynamic programming and the law of large number. The \(\varepsilon\)-Nash equilibriums are also obtained and discussed.  
The paper is organized as follows: Section 2 summarizes the related works. Section 3 gives the system model and problem formulation for the power control problem. Section 4 provides the mean field control of the sensor nodes with \(\varepsilon\)-Nash equilibrium, the mean field control of the HAP with a \(\varepsilon\)-Nash equilibrium. The implementation algorithm are also given in this section. Section 5 is the performance evaluation for both the sensor nodes and the HAP. Finally, the paper is concluded in Section 6.