# A Game Theoretic Approach for Balancing Energy Consumption in Clustered Wireless Sensor Networks
## 1 Introduction  
A conventional wireless sensor network (WSN) [1] is composed of a mass of tiny, cheap and low-powered sensor nodes with limited sensing, processing and transmitting abilities. After random deployment in a sensing area, these sensor nodes can construct a self-organizing network system automatically through wireless communication [2]. WSNs have been applied in various domains, such as natural disaster relief [3], environmental monitoring [4], biomedical health monitoring [5], military target tracking [6] and smart homes [7], aiming to gather information from the physical environment of interest. WSNs usually are distributed in harsh or hostile environments and work in an unattended way [8]. Sensor nodes in the network are usually powered by batteries with limited capacity, it is hard to recharge or replace the battery after the energy is exhausted. Energy constraints are an essential issue that severely restricts the network lifetime [9]. Since information transmission and receipt exhausts the majority of the energy of sensor nodes [10], an energy-efficient routing scheme need to be adopted to effectively reduce the energy consumption. When designing routing protocols, the major objectives are minimizing energy dissipation of sensor nodes and maximizing the networklifetime [11]. As a more effective way to optimize the network lifetime than other routing schemes, clustering has attracted a lot of attention in the past decade [12; 13; 14]. The idea of clustering is that sensor nodes are clustered into several groups in the network, and each cluster contains one cluster head (CH) node and some normal cluster member (CM) nodes [15]. CMs only transmit the data to their own CHs which have the responsibilities of receiving, aggregating and forwarding these data. Then the communication cost is greatly reduced since only the aggregated data packets need to be forwarded to the base station (BS) over a long distance by CHs. However, the network lifetime can be greatly weakened if a sensor node acts as the CH frequently, since CHs always consume much more energy than normal nodes. Thus, energy consumption must be balanced among sensor nodes to enhance the network lifetime for clustered WSNs. Game theory [16; 17] is a powerful mathematical tool used to analyze and predict the decisions of intelligent rational individuals under conflict situations. It has been widely applied in economics, politics and sociology. Recently, it has been introduced to solve the clustering problem in WSNs by designing energy-balanced CHs optimization mechanisms [18; 19; 20]. Each node is modeled as a rational decision-maker in the network, which has the ability to make decisions based on its own interests. On the one hand, each node abdicates the duty of serving as a CH to other nodes for energy conservation purposes, since a CH has higher energy consumption rate than a normal sensor node; On the other hand, at least one sensor node has to be selected as the CH to provide services for other nodes within a local area. Due to this conflict, game theory is very suitable to make decisions for sensor nodes. Mixed strategies are usually adopted by sensor nodes in game theoretic clustering, such as CROSS [19] and LGCA [20], where each sensor node decides whether being a CH based on a probability. Game theory is used to find an equilibrium solution among the mixed strategies. By playing the clustering game, each sensor node acquires an equilibrium probability to be the CH. And it decides whether to act as the CH according to this probability so that it has no incentives to deviate from the selected strategy as a tradeoff between providing services and saving energy is achieved. However, how to get the equilibrium strategy while maximizing the payoff of each node is rarely addressed to date. In this paper, game theory will be used to model the clustering for WSNs. And we devote to searching for the Nash equilibrium (NE) solution with regards to the combination strategies while maximizing the payoff of each sensor node.