Power control games between anchor and jammer nodes in wireless localization networks

In this paper, a game theoretic framework is proposed for wireless localization networks that operate in the presence of jammer nodes. In particular, power control games between anchor and jammer nodes are designed for a wireless localization network in which each target node estimates its position based on received signals from anchor nodes while jammer nodes aim to reduce localization performance of target nodes. Two different games are formulated for the considered wireless localization network: In the first game, the average Cramér-Rao lower bound (CRLB) of the target nodes is considered as the performance metric, and it is shown that at least one pure strategy Nash equilibrium exists in the power control game. Also, a method is presented to identify the pure strategy Nash equilibrium, and a sufficient condition is obtained to resolve the uniqueness of the pure Nash equilibrium. In the second game, the worst-case CRLBs for the anchor and jammer nodes are considered, and it is shown that the game admits at least one pure Nash equilibrium. Numerical examples are presented to corroborate the theoretical results.