Stationary Equilibrium Strategies for Bandwidth Scanning

In this paper we investigate the problem of designing a spectrum multi-step scanning strategy to detect an intelligent Invader who wants to utilize spectrum undetected for his/her unapproved purposes. To deal with this problem, we model it as a two stage game, along with specifying an algorithm of scanning the spectrum and evaluating the stationary bandwidth of spectrum to scan. The game is solved explicitly and reveal interesting properties. In particular, we have found a discontinuous dependence of the equilibrium strategies on the network parameters, fine and the Invader’s intention for illegal activity, which can lead even to multi-equilibrium situation. To select a proper equilibrium strategy the best response strategy algorithm can be applied which in the multi-equilibria case always converges for a finite number of iteration, meanwhile for mono-equilibria situation it does not converge, circling around the equilibrium. Also, we have shown that the detection probability and payoffs in some situation can be very sensible to fine and the Invader’s intention to intrude into the network longer, what yields that the network provider has to carefully make a value judgement of fine and estimation of the Intruder’s intentions.