# Game theory-based Routing for Wireless Sensor Networks: A Comparative Survey
## 3 Game Theory-Based Routing Protocols in WSNs
### Routing Protocol Based on Reputation-Based Game
#### 3.4.1 Game Theory-Based Routing Algorithm (GBRA) Based on Reputation
If node \(i\) is observing node \(j\), the decrease of node \(j\)'s reputation if it deliberately drops data packets is formulated as:  
\[R_{ij}=\frac{R_{ij}}{2}. \tag{44}\]  
If node \(j\) participates in packet forwarding actively rather than dropping packet deliberately, its reputation would increase using the following equation:  
\[R_{ij}=R_{ij}+0.1. \tag{45}\]  
Because node \(i\) is the receiver node and node \(j\) is the sender node, the pay-off function for node \(i\) is expressed as:  
\[U_{i}=\ \xi R_{ij}-\eta E_{c}\ (\xi,\ \eta\in\ [0,\ 1],\ \xi+\eta=1). \tag{46}\]  
The pay-off function for node \(j\) was expressed as:  
\[U_{i}=\ \xi R_{ij}-\eta E_{dest}\ *E_{tot}/E_{rem}.\ (\xi,\ \eta\in\ [0,\ 1],\ \xi+\eta=1). \tag{47}\]As mentioned earlier, there can be a scenario where the neighboring nodes know the route to the destination, or one among them is itself the destination. Figure 7 presents such a scenario in the network. In Figure 7, node \(E\) and \(F\) are the neighboring nodes of the source node \(C\). \(I\) is the destination node. \(C\), after sending a route request (RREQ) message to \(E\) and \(F\), receives back a reply about the optimal route from node \(F\), as it already knows the route. There can also be a scenario where the neighboring node does not know the optimal route to the destination. Figure 8 illustrates this scenario. After receiving RREQ from the source node \(A\), node \(B\) and node \(C\) calculate if \(E_{rem}\) is greater than \(E_{c}\). Furthermore, they compare if the pay-off (calculated using (41)) is greater than zero. If both conditions are satisfied, the neighboring nodes will send ACK messages to the source node. Node \(A\) (source node) calculates its own pay-off using (42) to find out the optimal relay node, as illustrated in Figure 8b. If source node \(A\) determines that node \(B\) is an optimal relay node after pay-off calculation, a new game will start between nodes \(B\) and \(C\). This process continues till it reaches destination node \(I\). Once the destination is reached, the destination node sends back the route to the source for data transmission. Nodes append their IDs when they switch one node for another for a new game. The simulation results demonstrate that the designed protocol performed better than LEACH in terms of prolonging network life time. The reason for this is that the LEACH protocol selects a CH among all the nodes with equal probability and the residual energy of the nodes is not considered during this selection. Furthermore, the distance to the destination during this selection is not considered. This causes early deaths of some nodes, owing to energy wastage for distant transmissions. In the second scenario of the simulation, 20% of malicious nodes were kept in the network. The scheme designed in [43] demonstrated a higher throughput than LEACH. The reason for this is that the malicious nodes were kept aloof from other nodes in the network by reputation mechanism. Technical strengths:  
* Good mechanism to stop packet drops;
* Mechanism to avoid malicious nodes from routing path. Technical weaknesses:
* No technical integration process was mentioned for the watchdog mechanism that was used to monitor the neighboring nodes;
* No mathematical formulation or definition regarding who can be the neighbors of a sending node was presented. Applications:
* Applicable for any data sensitive application that requires continuous information sending. Possible future improvements:
* Network architecture is not well defined. To make the protocol GBRA deployable, it is necessary that the authors clarify the network architecture. Figure 7: Network scenario where the neighboring node knows the optimal route to the destination.