# Game theory-based Routing for Wireless Sensor Networks: A Comparative Survey
## 2 Preliminaries
### Routing Metrics  
In the literature, various routing protocols consider different routing metrics to compare their performance with the already established routing protocols. This subsection discusses the different routing metrics adopted by the game theory-based routing protocols. Routing metrics are defined as measures used by routing protocols to make routing decisions [53]. Routing protocols use different routing metrics to choose the best routing path, starting from the source to the destination. The quality of a routing path is indicated by the routing metrics [54]. The routing metrics given below are the ones incorporated by the recent approaches that have used game theory to design routing protocols for WSNs. Sensor nodes are powered using batteries with a small capacity [55]. The deployment of the sensor nodes takes place in a predominantly unattended environment. Hence, energy scavenging is not an option for the sensor nodes in WSNs. Energy consumption is directly related to network lifetime. Therefore, energy consumption is the most important routing metric. To denote energy as a routing metric, two measures are to be considered. One is the path energy and the other is the residual energy of the intermediate nodes. Path energy includes the amount of energy spent for data transmission, starting from the source to the destination. A path cannot be considered efficient if it merely displays the minimal path energy. The residual energy of the intermediate nodes should also be considered. The energy required for data transmission and data reception are also considered. If a protocol is a clustering-based protocol, energy consumption can occur in three cases. They are the transmission and reception of data among the cluster members, cluster heads, and sink node. The packet delivery ratio is the ratio of the number of packets successfully received to the number of total packets sent. Because certain packets may get lost during transmissions, the packet delivery ratio is meaningful with respect to network performance as well as communication reliability. We consider the total number of transmitted data packets and the total number of successfully received data packets in a WSN be \(N_{s}\) and \(N_{r}\), respectively. Then, the packet delivery ratio \(R\) can be represented as \(R=N_{r}/N_{s}\). Note that \((1-R)\) is the packet loss ratio. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Game** & **Key Features** & \begin{tabular}{c} **Comparative** \\ **Characteristics** \\ \end{tabular} & **Routing Metrics** \\ \hline Cooperative & \begin{tabular}{c} Considers preferences and rational \\ choices of other nodes in the routing \\ game of a WSN. \\ \end{tabular} & \begin{tabular}{c} Binding agreements \\ needed for mutual \\ benefit in games \\ designed for routing. \\ \end{tabular} & \begin{tabular}{c} Considers energy and packet \\ delivery ratio as routing \\ metrics. \\ \end{tabular} \\ \hline Noncooperative & \begin{tabular}{c} Considers situation when no two sensor \\ nodes can benefit more by any move \\ after a certain point given that a player \\ sticks to some strategies. \\ \end{tabular} & \begin{tabular}{c} Reaching Nash \\ equilibrium is needed for \\ successful implication. \\ \end{tabular} & \begin{tabular}{c} Considers energy as the \\ main routing metric in most \\ of the protocols. \\ \end{tabular} \\ \hline Evolutionary & \begin{tabular}{c} Does not need to consider the \\ game theory \\ \end{tabular} & \begin{tabular}{c} Evolutionarily stable \\ strategy is needed for the \\ implication of this type \\ of games in routing. \\ \end{tabular} & \begin{tabular}{c} Considers network lifetime \\ as primary routing metric. \\ \end{tabular} \\ \hline Reputation-based & The nodes are cooperative in this type & \
\begin{tabular}{c} Measures the partners’ \\ quality and incentivizes \\ the partners’ behaviors. \\ \end{tabular} &
\begin{tabular}{c} Considers average \\ throughput and network life \\ time in the routing protocol. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}