# Game theory-based Routing for Wireless Sensor Networks: A Comparative Survey
## 3 Game Theory-Based Routing Protocols in WSNs
### Routing Protocols Based on Cooperative Games
#### 3.1.2 Assignment Game Approach  
Future generation wireless networking is expected to be quite challenging as the number of devices will drastically increase, making the WSN paradigm more energy constrained. To deal with this problem, the authors in [34] addressed the reduction of energy consumption of the energy-constrained wireless devices through the cooperative relaying of nodes in heterogeneous networks using game theory. In [34], mobile users were considered coalition forming agents and encompassed multiple relays and sources. Devices pooled their resources like battery and antenna and relayed to each other for minimizing energy expenditure collectively. The problem was designed as an assignment game and it addressed the optimal method of identifying relays. They derived the core solution of the game. Furthermore, the process of conflict avoidance through this solution was elaborated. Subsequently, the authors of [34] defined a characteristic function along with the utility function to evaluate the amount of energy saving of the relaying nodes. The scheme focused on a two-hop relaying system. Figure 3 presents a radio access network (RAN) that denotes a long-term evolution or WiFi network. The RAN considered in this scheme served multiple-user equipment (UE) that included mobile phones, sensors, and machines. The UE employed technologies for both short and long ranges of communication. The devices were assumed to be within the coverage of RAN, with different channel qualities. There are three ways that UEs can send their traffic to the RAN. They can send it through direct communication over a conventional cellular link or through short-range relaying link. Alternatively, communication can take place in two hops. The first hop is short-ranged and takes place between the source and relay. The second hop is long-ranged and takes place mainly between the relay and the RAN. The bounded ellipsoidal area in Figure 3 is the RAN's coverage area subjected to path loss and shadowing. In the mentioned ellipsoidal area, \(S_{1}\) remains in the deep shadowing area and \(S_{2}\), despite having good channel quality, suffers from low battery level. Both \(S_{1}\) and \(S_{2}\) can commence scanning their neighborhood using their short-range interface. For the mentioned scenario in Figure 3, \(S_{1}\) will be able to identify \(R_{1}\) and \(S_{2}\) will be able to identify \(R_{2}\) within their short-range coverage. Subsequently, \(S_{1}\) and \(S_{2}\) could start sending their traffic via relay nodes to the RAN. \(S_{3}\) was assumed to have both good battery level and channel quality. Consequently, it could send directly to the RAN. Authors of [34] also assumed that the information gathered by the UEs could be shared with each other and they could periodically sense and communicate. There were two scenarios where coalitions could be formed among the nodes. A UE could join a nearby coalition after discovering it or certain UEs close to each other could create a new coalition by clinging to a certain profitable group strategy. The UEs were also responsible for acquiring information about the data rate and transmission power  
Figure 3: Coalitional short-range relaying. of the short-range and long-range links. This information could later be transferred to the RAN by the UEs. After receiving this necessary information from all the UEs, the RAN solved the problem of relay selection. Nodes were then informed by the RAN about their cooperative patterns. The main concept of this routing scheme was in designing a coalitional relay selection game, in which the UEs built coalitions to pool their resources and relay packets for each other to decrease the overall energy consumption. A simple example of coalition formation consisted of two players. To design a characteristic function for this, the utility function was formulated as a weighted function of the energy saving process and battery life extension of UEs.