Attacker Detection Game in Wireless Networks with Channel Uncertainty

Identification and isolation of attackers in a distributed system is a challenging problem. This problem is even more aggravated in a wireless network because the unreliable channel makes the actions of the users (nodes) hidden from each other. Therefore, legitimate users can only construct a belief about a potential attacker through monitoring and observation. In this paper, we use game theory to study the interactions between regular and attacker nodes in a wireless network. We model the attacker node detection process as a Bayesian game with imperfect information and show that a mixed strategy perfect Bayesian Nash Equilibrium is attainable. Further, we show how an attacker node can construct a nested belief system to predict the belief held by a regular node. By employing the nested belief system, a Markov Perfect Bayes-Nash Equilibrium is reached and the equilibrium postpones the detection of the attacker node. Simulation results and their discussions are provided to illustrate the properties of the derived equilibria.