A dynamic transmitter-jammer game with asymmetric information

We consider a jamming attack on a transmitter-receiver pair, in which the transmitter wants to transmit the state of an i.i.d. Gaussian process across an unsecured communication channel to the receiver while minimizing its cost functional. The transmitter decides whether or not to transmit the current state of the random process. The jammer disrupts the transmission on the channel strategically in order to increase the total cost to the transmitter, but can do this only a limited number of times over the entire horizon. The jammer only detects whether or not a transmission is happening over the channel, but does not observe the state of the random process being transmitted. This leads to a dynamic zero-sum game with asymmetric information between the transmitter and the jammer. We prove that the saddle-point strategy of the transmitter is threshold-based and that under certain conditions, the jammer plays a mixed strategy.