## 3 Applications of Game Theory in WSN
### Game Theory for Wireless Network Management in WSN
#### 3.1.1 Resource Management--Spectrum Allocation and Bandwidth Allocation  
It is a salient and desirable feature that wireless sensors are deployed in a large number and with a high degree of redundancy. The sensors are therefore mostly manufactured with small size, light weight. Hence the resources, such as power, computation and communication capabilities, that can be embedded onboard the sensor are always limited. Resource management is thus an important consideration while designing a WSN.  
Figure 3: An illustration of the relation between WSN and game theory.  
Impulse Radio-Ultra WideBand (IR-UWB) communication is a strong candidate for short-range biomedical wireless sensor networks (BWSN). [PERSON] _et al_. [35,36] proposed a multiband/ multiuser IR-UWB scheme, which is robust against unknown NarrowBand Interference, by deploying multiband signaling with Forward Error Correction coding and subband scheduling. They defined the problem with an _n_-transmitter Jamming game and find a NE for such a game. Furthermore, they cast the problem of finding the fair sub-band schedule into a multi-objective integer programming problem, and planed to solve it using NBS. [PERSON] _et al_. [130] solved problems such as the optimal coverage of WSN or channel time-sharing in wireless communications inspired by the territory behaviors and mating systems of dragonflies.  
[PERSON] and [PERSON] [2] developed a virtualization framework to separate the network operator (NO) who focuses on wireless resource management and service providers (SP) who targets distinct objectives with different constraints. Within the proposed framework, the authors modeled the interactions among SPs and NO as a stochastic game, each stage of which is played by SPs and is regulated by the NO through the Vickrey-Clarke-Groves (VCG) mechanism. Due to the strong coupling between the future decisions of SPs and lack of global information at each SP, the stochastic game is notoriously hard. They introduced conjectural prices to represent the future congestion levels the end users potentially will experience, via which the future interactions between SPs are decoupled. Then, the policy to play the dynamic rate allocation game becomes selecting the conjectural prices and announcing a strategic value function at each time. They proved that there exists one NE in the conjectural prices and, given the conjectural prices, the SPs have to truthfully reveal their own value function. They further proved that this NE results in efficient rate allocation in virtualized wireless network. [PERSON] _et al_. [131] considered a Markovian dynamical game theoretic setting for distributed transmission control in a WSN. The available spectrum bandwidth is modeled as a Markov chain. A distributed algorithm named correlated Q-learning algorithm was proposed to obtain the correlated equilibrium policies of the system. The problem of sequential estimation and lifetime maximization in a WSN was formulated in a cooperative game theoretic framework in [132,133], which allow the issue of fair resource allocation for sequential estimation task at the \"fusion center\" in a WSN as a solution of a cooperative game.