# A Power Control Algorithm Based on Chicken Game Theory in Multi-Hop Networks
## 3 Distributed Chicken Game Algorithm Power Control  
In traditional wireless communication protocols, due to the constraints of their use, their structure is not very flexible. They cannot operate in certain averse conditions and are unable to adapt to dynamic situations. Consequently, this problem causes the system to use spectrum and energy inefficiently. A hybridizing layer design is adaptable, because it means that it has the capability to investigate and reply to variations in the channel. The distributed chicken game algorithm power control (DCGAPC) layer design model can be seen in Figure 3. In this model, the realization of the power control module is in the physical layer, and the module can receive interference messages via an adjacent node table, which is located in the internet layer so that the sending power can be computed. The DCGAPC algorithm is proposed as a cross-layer design method. The power control module includes SNR computing, interference calculations, and power control. Figure 3 shows the hybridizing layer of the proposed method. The SNR computing module calculates and derives a specific transmission distance based on the received signal strength (RSS), which comes from its own physical layer. The native information form is constructed at the network layer. The interference calculation module gets local interference power and transmits it to the interference update module that is located in the network layer. Once the node intends to send a message, the send message processing module, which is located in the networks layer, will find its own native information form and then calculate the sending power with the max payoff. In the next step, the send message processing module calculates and derives the payoff value of the sending power and puts the value to the power control module located in the physical layer. After this power control unit has done its calculations based on  
Figure 3: The distributed chicken game algorithm power control (DCGAPC) layer design model. ID: identification; SNR: signal-to-noise ratio. the DCGAPC algorithm, the wireless communication system sends the message with this calculated power level. When the nodes receive message frames, the SNR computing module determines whether the message is a valid message by calculating the SNR of the received signal. If the message is valid, it can be transmitted to the upper layers to travel between two nodes. If the message is interference, then the nodes will abandon it and operate the interference module to update the information in nodes, which are located in the internet layer. Whenever nodes need to send messages, they calculate the interference of the destiny node based on the adjacent node table and then send the interference to the power control module for calculating. If the power control of nodes in multi-hop networks are considered as a problem using the chicken game, then its basic expression is \(\Gamma=\langle N,A,\{u_{i}\}\rangle\). \(N=\{1,2,\cdots,n\}\) represents the number of all the nodes in the network, and the strategy of the specific node \(i\) is denoted as \(A_{i}=[0,p_{\max}]\). All nodes in the network select their strategies to maximize their gain based on diverse gain function [39]:  
\[\underset{p_{i}\in P_{i}}{\text{max}}u_{i}(p_{i},\textbf{p}_{-i}),i=1,2, \cdots,n \tag{10}\]  
where \(p_{i}\) represents the transmitting power selected by node \(I\) and \(\textbf{p}_{-i}\) denotes the transmitting power selected by other nodes except node \(i\). The quality of wireless networks is often influenced by factors such as signal modulation and coding. The income function can ignore the signal modulation:  
\[u_{i}=\mu\log_{2}(1+SIR_{i})-c(p_{i}) \tag{11}\]  
To state this explicitly, the classical Gauss channel capacity formula is used, where \(\mu\) is the profit coefficient and \(c(p_{i})\) is the price linear functional variable of the sending power:  
\[c(p_{i})=\frac{1}{h_{i}}p_{i} \tag{12}\]  
where \(h_{i}\) is the path gain when the sending power of the node is \(p_{i}\).