# Game theory-based Routing for Wireless Sensor Networks: A Comparative Survey
## 2 Preliminaries
### Games in Routing for WMSNs  
This survey discusses the routing protocols that were published over five years, since 2012. After a comprehensive study of all the protocols published so far, we found three types of games that were used in WSNs for the routing protocol development: cooperative games, noncooperative games, and evolutionary games. A reputation-based game was also used in one of the routing protocols. This falls into the category of cooperative games, however, owing to its distinct features, we discuss it separately. After discussing each type of game in detail, we discuss the implication of each through an example. The aim is to facilitate readers to comprehend each type of game and the methods used to implement them. Certain useful roles of game theory in WSNs are summarized below. _(i) CH selection:_ Cluster-based routing protocols are widely applicable in WSNs. One crucial challenge for this kind of routing is selecting the optimal CH in the setup phase. Introducing a rational decision-making process among the nodes competing to be the CH based on the pay-off function, which considers residual energy level, link quality, etc., can ease the process of CH selection. _(ii) Route discovery excluding the malicious nodes:_ Typically, sensor nodes are required to collaborate with each other for data transmission and each node can be considered a potential routing node. It is possible for malicious nodes to drop packets deliberately in a WSN. Therefore, finding a secure and energy-efficient routing path is a great challenge in WSNs. This kind of problem can be easily countered with reputation-based games. Any kind of deliberate dropping of the data packets will lead to the punishment of the node and its reputation will be decreased in an exponential manner. Nodes with high reputation, energy, and positions closer to the destination will be selected as one-hop routing paths, excluding the malicious nodes. _(iii) Facilitating grouping:_ In many WSNs, grouping is used to facilitate the organization of the node cooperation. Each group contains a leader that is responsible for communicating outside of the group. Let us assume a self-organizing WSN, where a group leader forms and manages the group. The management is performed such that it is beneficial for the other group members; moreover, group members must have the ability to transfer data to the group leader through direct data transmission. In this kind of network, a new node may want to join a group and the group needs to decide whether to accept the node. This kind of group extension scenario may require a complex decision-making process that can be achieved by cooperative game theory. _(iv) Finding an energy and delay-aware route:_ Nodes can decide to play noncooperative games and try to increase their own benefits by choosing the transmission path to the sink node that requires the least energy and delay. _(v) Supporting energy imbalance in WSNs:_ Game theory is especially suitable for supporting energy imbalance among nodes in WSNs. For example, if there are nodes with variant energy levels, it can optimize this energy imbalance with intelligent decision-making processes. Cooperative game theory is a process used to make decisions in strategic settings, where it is necessary to factor the preferences and rational choices of other players into the decision-making process [50]. If there is an added benefit through cooperation, it is favorable to form coalitions for mutual advantage. In cooperative games, we focus on the coalitions that will form the joint actions that groups take and the resulting collective pay-off. When coalitions are formed with more than one action from the action set, we call it a joint action. As coalitions involve more than one player, their pay-offs are considered collective. An advantage of cooperative game theory is that it does not require a precisely defined structure for the actual game. For example, each coalition of nodes in a WSN may exchange information to become CHs consecutively in a clustering routing protocol.