A Zero-Sum Jamming Game with Incomplete Position Information in Wireless Scenarios

We consider a jamming problem, modeled as a zero-sum game with incomplete information played by a wireless network and a malicious jammer that wants to disrupt communication, in a wireless scenario with distance-dependent loss of the wireless medium. Multiple access is achieved by means of parallel channels, characterized by different propagation parameters. The jammer is unaware of the exact positions of the network nodes, but knows the prior distribution of where they can be located. We investigate the dependence of the equilibria of this game on the actual position of the jammer itself. We conclude that there are regions where the actual gameplay of the jammer at the Nash Equilibrium only consists of pure strategies, and therefore the wireless network can consider itself to be insensitive to the presence of the jammer. This does not mean that the jammer has no effect whatsoever, but if it is known to be physically located in such regions, its damage to the network can be quantified in advance with certainty; on the other hand, there is also no way of counteracting this jammer, and if its presence is not known, the network is not able to distinguish it from background interference.