# Game theory-based Routing for Wireless Sensor Networks: A Comparative Survey
## 3 Game Theory-Based Routing Protocols in WSNs
### Routing Protocols Based on Noncooperative Games
#### 3.2.6 Game Theory-based Energy-efficient Routing Algorithm (GERA)  
Energy consumption is a critical concern for WSNs and clustering techniques are popular for reducing energy consumption via lessening the number of transmissions to the sink node. Usually, routing protocols based on clusters have a CH in each cluster. Selecting a CH in a cluster is a difficult task and should be handled carefully, as selecting a node with a lower energy level as the CH may result in network malfunction. In their paper, [PERSON] et al. [33] designed a game theory-based energy-efficient routing algorithm (GERA). It is a clustering algorithm that adopts game theory, in which CHs are optimally selected based on a utility function of the node. The cluster formation process relies on a cost function. The designed routing scheme consists of three phases: CH selection, cluster formation, and data transmission. CHs are optimally selected using game theory. Before this process, all the nodes in the network gather local information of their neighboring nodes and broadcast a \"hello\" message. The nodes in the network are aware of the number of neighbors who had received the \"hello\" packets. The \"hello\" message consists of information like the location of the node, node energy level, and node's existence. The CH election game is defined as:  
\[CG=\langle N,\ S,\ U\rangle, \tag{23}\]  
where \(N\) is a set of players (sensor nodes in this case), \(S\) is a set of available strategies, and \(U\) is the utility function. The strategy set consists of two elements. Thus, the strategy set, \(S=\{AVOW,\ DISAVOW\}=\{A,\ DA\}\). \(DISAVOW\) refers to the strategy of not declaring a node as a CH and \(AVOW\) presents the strategy of a node being declared as a CH. As mentioned earlier, assuming \(N\) players are taking part in a clustering game, the utility function of any player \(i\) could be defined as:  
\[U(S_{i})=\left\{ \begin{array}{l}G-E_{A}\ if\ S_{i}=A,\\ G-E_{DA}\ if\ S_{j}=A\ where\ i\
eq j,\\ 0\ if\ S_{j}=0\ for\ all\ j\in N,\end{array} \right. \tag{24}\]where \(U(S_{i})\) is the utility function of the node \(i\), \(G\) is the gain obtained by each node during packet forwarding to the sink node, \(E_{A}\) is the energy consumed by the CH in forwarding the aggregated data to the sink node, and \(E_{DA}\) is the amount of energy consumed by the CM to transmit the data to the CH. After certain nodes have declared themselves as CHs, they do not participate in the CH election process and the probability of these nodes being CH in the upcoming round is set to zero. The nodes that do not become CHs send a request message to the nearby identified CH. Based on the already enrolled cluster members, the CH could either send a _JOIN_ACC_ message that allows a requesting node to be a cluster member or it could send a _REQ-REJ_ message to reject a requesting node from being a cluster member. The CHs directly transmit the data packets to the sink nodes in the data transmission phase of the routing protocol. The routing metrics considered in this protocol are energy consumption and packet delivery ratio. In this protocol, the total energy consumption of a node is defined as the amount of energy consumed by a node while performing its role in routing. It is the summation of the energy required for sensing the data, aggregating the data, and transmitting the data in [33]. In this protocol, the packet delivery ratio is considered as packets delivered by the node in the network for a certain number of rounds. The GERA claims superiority over the density-based energy-efficient game-theoretic routing algorithm [67] and low-energy adaptive clustering hierarchy (LEACH) [68] routing protocols based on these parameters. Technical strengths:  
* Energy is well conserved by preventing the nodes that were CHs in the previous round from being CHs in the ongoing round;
* Energy consumption was considered for both data transmission and reception.