A jammer's dilemma: Where and how to jam

In this paper we introduce a jamming problem in a new scenario where a jammer has to interfere a transmitter's transmission by allocating and configuring correctly the tools employed for jamming. In fact the jammer meets two problems at once: what power to employ to interfere the transmitter's transmission and where to allocate geographically the jamming tools, i.e. to ideally determine the distance between the jammer and the receiver of the transmitter signal. The location problem of jamming tools turns out to be a dilemma. Indeed, on one hand, if the jammer is close to the receiver, he will enlarge the jamming power and then create lots of interference to the transmitter signal. On the other hand, we assume that the receiver can detect the jammer if he is close enough to him. Putting together geographical allocation and power assignment creates a new problem which has interesting features for determining an optimal behavior of the jammer and the transmitter. We study this problem for multi-channel systems in two scenarios: (a) the jammer can choose his power and geographical location simultaneously, (b) he can do it sequentially. We prove that the game has a unique equilibrium and moreover, we describe explicitly this equilibrium, its structure and some properties.