# A Power Control Algorithm Based on Chicken Game Theory in Multi-Hop Networks
## 4 Simulation Analyses  
In order to use the power control proposed in this article, the adjacent node form (Table 1) has to be established in order to record the identification (ID) of the nodes, interference of adjacent nodes, and the gain. The algorithm proposed in this paper should work as follows: First, every node writes the local interference power value into the HELLO message and then broadcasts it to its neighbors. Once a node receives a HELLO message, it computes the income according to Equation (11) and updates its neighboring node's information table. When a mobile port needs to transmit information, the node checks the native form and then chooses the maximum income for calculating the sending power \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Nodes ID** & **Distance** & **Interference** & **Gain** \\ \hline ID1 & d\({}_{i1}\) & p\({}_{i}^{1}\)infer & u\({}_{i1}\) \\ ID2 & d\({}_{i2}\) & p\({}_{i}^{2}\)infer & u\({}_{i2}\) \\ ID3 & d\({}_{i3}\) & p\({}_{i}^{1}\)infer & u\({}_{i3}\) \\... &... &... &... \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Adjacent node table. based on Equation (8) in order to send the information. Virtually, Equation (11) is computed according to Equation (12), and the transmit power is calculated from Equation (8) based on Equations (1)-(9). The Algorithm 1 can be written as below:  
```
1:Initialize the local table. 2:FUNCTION INIT (0
3:if {t = 0 Then P\({}_{\text{i}}\) = P\({}_{\text{max}}\); P\({}_{\text{infer}}\) = 0;
4:Initialize (native_form);
5:endif;}
6:update the local table once system get a new message. 7:FUNCTION Deal Message (HI/HELLO)
8:if 1 get HELLO Then update(native_form); Endif;}
9:determine whether system need to transmit the message according to evaluate the cost from native form. 10:FUNCTION Send Message (M)
11:if i transmits M Then u < = find_payoff(native_form);
12:Pi < = calculate_trans_power(u);
13:If M = message then add_infer_area (P\({}_{\text{infer}}\));
14:Endif;
15:Endif;}
```  
**Algorithm 1** Power control  
In the simulation test, there are three ways used to control power:  
1. Maximum energy power control algorithm (MAXPCA), by which all the nodes in the networks choose the highest transmission power;
2. Minimum energy power control algorithm (MINPCA), by which all the nodes in the networks choose the lowest sending power;
3. Distributed chicken game algorithm to power control (DCGAPC), which is the method proposed in this article. The factors for the numerical computation simulation test can be seen in Table 2.  
In all figures, the Monte-Carlo computation process was used to calculate the numerical simulation results. All data were computed using the C programming language, and then, these numerical data were drawn into a statistical curve using professional tools, such as MATLAB and Microsoft VISIO. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters (Unit)** & **Values** \\ \hline Simulation area (m\({}^{2}\)) & \(500\times 500\) \\ Figure of the nodes & 50 \\ Communications protocol & CSMA/CA (Carrier Sense multiple Access/Collision Avoidance) \\ Route protocol & Flooding \\ Bandwidth (Mbps) & 2 \\ Required BER (Bit Error Ratio) & \(10^{-2}\) \\ The max sending power of the node(mw) & 2.5 \\ The max coverage radius of the node(m) & 230 \\ SNR(dB) & 13 \\ Path decay parameter & \(\alpha\) = 3–4 \\ Standard deviation of the shadowing loss & \(\sigma\) = 4–10 dB \\ Number of paths & L = 16 \\ Power delay profile & Exponential \\ Decay factor & \(\gamma\) = 0–10 dB \\ Environmental noise (dBm) & \(-\)120 \\ DCGAPC (s/packet) & 0.01–2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Computation conditions. During the test of the performance of the routing method, the following performance parameters in the simulation experiment were also investigated:  
1. Reachability--ratio of the figures of the correct messages received compared to the figure of the actual messages received. 2. Average latency--how long it takes for a broadcast message to be sent from the source node to all nodes in the network. 3.