A Game Theoretic Framework for Power Control in Wireless Sensor Networks

In infrastructure-less sensor networks, efficient usage of energy is very critical because of the limited energy available to the sensor nodes. Among various phenomena that consume energy, radio communication is by far the most demanding one. One of the effective ways to limit unnecessary energy loss is to control the power at which the nodes transmit signals. In this paper, we apply game theory to solve the power control problem in a CDMA-based distributed sensor network. We formulate a noncooperative game under incomplete information and study the existence of Nash equilibrium. With the help of this equilibrium, we devise a distributed algorithm for optimal power control and prove that the system is power stable only if the nodes comply with certain transmit power thresholds. We show that even in a noncooperative scenario, it is in the best interest of the nodes to comply with these thresholds. The power level at which a node should transmit, to maximize its utility, is evaluated. Moreover, we compare the utilities when the nodes are allowed to transmit with discrete and continuous power levels; the performance with discrete levels is upper bounded by the continuous case. We define a distortion metric that gives a quantitative measure of the goodness of having finite power levels and also find those levels that minimize the distortion. Numerical results demonstrate that the proposed algorithm achieves the best possible payoff/utility for the sensor nodes even by consuming less power.