## 3 Applications of Game Theory in WSN
### Game Theory for Wireless Network Management in WSN
#### 3.1.2 Power Management--Energy Saving and Power Control  
In WSN, energy is a limited resource and must be used judiciously. Currently, the energy problem remains one of the major obstacles somehow preventing the complete exploitation of WSN technology. Energy saving and power control strategies should be devised at sensor nodes as well as in the network to prolong the network lifetime. In practice, the Game-theoretical Total Link (GTL) algorithm which sets each node's energy range is usually better than Critical Transmitting Range (CTR) in energy saving according to the topological changing, as shown by [PERSON] _et al_. [122]. [PERSON] _et al_. [123] considered a MAC scheme based on _p_-persistence slotted ALOHA. To determine the value of the attempt probability \(p\), the authors constructed the _p_-persistence slotted ALOHA as a simple non-cooperative game which involves generalized payoffs reflecting energy saving and throughput. They derived an NE in a closed form. [PERSON] _et al_. [27] investigated a cooperative communication scheme for WSN. They modeled the power allocation problem as a two-person bargaining game, and used the Nash Bargaining Solution (NBS) [27,35,36,42,43,44,45,46,47] to achieve a win-win strategy. A distributed optimization framework using GT was used to analyze the power-allocation and rate allocation in WSNs [134]. [PERSON] _et al_. [113] proposed a distributed power control algorithm based on game theory for WSN, and its objectives are formulated toward reducing power consumption, decreasing overhead and increasing network lifetime. The simulation shows that this power control algorithm converges to a NE when decisions are updated according to a better response dynamic. The heterogeneous types of sensors are viewed as intelligent agents interacting with each other locally in a WSN. Sensors in this network interact with each other either in a cooperative way to form coalitions or in a non-cooperative way to deal with conflicts. [PERSON] _et al_. [114] addressed non-cooperative game and cooperative game in a distributed power control algorithm to ensure reliability as well as power efficiency by proposing power allocation algorithms for network formation resulting from both selfish nodes and cooperative nodes. The contribution in [115] has a mechanism for obtaining smooth non-monotonic reaction curves, in contrast to sharp cut-offs with increasing interference that are characteristic of admission control. They [115] provided sufficient conditions for a unique NE under non-monotonic power control (NMPC) algorithm, and view this solution as edan attractive alternative to pricing in wireless networks formed by cooperative nodes. [PERSON] _et al_. [116] presented a game-theoretic treatment of distributed power control in CDMA wireless systems using outage probabilities and proved that the non-cooperative power control game considered admits a unique NE for uniformly strictly convex pricing functions and under some technical assumptions on the SIR threshold levels. [PERSON] _et al_. [117] proposed a power control mechanism based on game theory to reduce power consumption of a WSN. The issue of restrictive energy in WSN was abstractly analyzed, and then the distributed self-adaptive power control algorithm was studied by analyzing the mapping between WSN and the game. The algorithm can reduce power consumption, decrease overhead and increase network lifetime, and converge to a NE when decisions are updated according to a better dynamic response and ensure nice fairness for network. [PERSON] _et al_. [119] presented a novel formulation of the problem of energy misbehavior and develop an analytical framework for quantifying its impact on other nodes. They formulated two versions of the power control problem for WSN with latency constraints arising from duty cycle allocations. In the first version, strategic power optimization, nodes are modeled as rational agents in a power game, who strategically adjust their powers to minimize their own energy.