# Game theory-based Routing for Wireless Sensor Networks: A Comparative Survey
## 3 Game Theory-Based Routing Protocols in WSNs
### Routing Protocols Based on Evolutionary Games
#### 3.3.4 Evolutionary Routing Game for Energy Balance in WSN (ERG)  
Finding out a desirable route in a WSN is always challenging. Some disparate routes may frequently suffer from congestion and exhaust fast. Since all the nodes in the network will act upon saving energy, choosing one good route suddenly by many nodes may result in faster energy depletion in such routes. As a result, network lifetime may be shortened. [PERSON] et al. analyzed this issue in [45]and proposed an evolutionary routing game (ERG) for balancing energy in WSNs. They modeled the routing problem as an evolutionary anti-coordination routing game.  
The authors of [45] derived an evolutionary stable strategy for the proposed ERG. Also, the replicator dynamics of the formulated evolutionary game were derived. The proposed anti-coordination routing game had a set of \(N\) homogeneous sensors (players). They were randomly distributed in a certain area. Each player must choose a path for data packets. The set of next hops were presented as \(R\). The path of each packet was controlled independently by rational players so that the cost of transmission and latency was minimized. Each hop in the route had a specific cost \(C_{r}\), that was related to the distance between transmitter and receiver. Sensor nodes in the network were rational and non-cooperative. In the proposed model [45], the cost (C) of forwarding a packet consisted of two parts: the energy needed to transmit a data packet and the other is the energy required for receiving the packet. Therefore, the total cost is calculated as:  
\[C=C_{tx}(d)+C_{rx}, \tag{41}\]  
where \(C_{tx}(d)\) is the cost of transmitting the packet over a distance \(d\), and \(C_{rx}\) is the cost of receiving the packet. The evolutionary routing game in [45] is presented as:  
\[G=\langle R,S,U\rangle, \tag{42}\]  
where \(R\) is the set of next available hops, \(S=\{S_{t}|r\in R\}\) is the strategy space denoting the set of actions that the players can alternatively choose. \(U\) is the pay-off function. The pay-off function is defined as follows:  
\[U(s_{r},s_{t})=\left\{\begin{array}{ll}\big{(}\frac{1}{C_{rx}},\ \frac{1}{C_{tx}}\big{)}when \ r\
eq t,\ v\in[A,B]\\ (0,0)\ when\ r=t\end{array}\right.\ G=\langle R,S,U\rangle, \tag{43}\]  
where \(C_{rx}\) is the transmission cost of the packet through hop \(r\), that belongs to population either \(A\) or \(B\). \(t\) is another alternative hop other than \(r\). Therefore, \(C_{rt}\) is the transmission cost of the packet through hop \(t\). The authors provided a reasonable amount of simulation results that proved the feasibility of implying evolutionary game theory [45]. Unfortunately, the proposed scheme was not compared with any other state-of-the-art protocols.  
Technical strengths:  
* Pure strategy Nash equilibrium and replicator dynamics of the evolutionary game were explained and formulated comprehensively. Players can not only learn strategies but also can modify it. Technical weaknesses:
* One-hop transmission among nodes are discouraged by imposing lower pay-off. Multi-hop transmissions can be energy consuming.
* Applications:
* Any kind of energy-efficient multi-hop data transmission for WSNs. Possible future improvements:
* Some experimental results involving network lifetime could be added.