On Communication Scheduling and Remote Estimation in the Presence of an Adversary as a Nonzero-sum Game

In this paper, we consider a nonzero-sum dynamic game that arises in a remote sensing system with a sensor, an encoder, a decoder, and adversarial intervention. At each time step, the sensor makes a measurement on the state of a stochastic process, and then it decides whether to transmit the measurement or not. If the sensor decides to transmit the measurement, it sends the measurement to the encoder, which then transmits an encoded message to the decoder over an additive noise channel. The decoder generates a real-time estimate on the state of the stochastic process. In this scenario, the cost associated with the remote sensing system consists of a charge for the transmissions made by the sensor, a charge for the encoding power consumed by the encoder, and a charge for the estimation error caused by the decoder. The components of the remote sensing system have the common objective of minimizing this cost. On the other hand, the additive channel noise is generated by an adversary, which is charged the power of the noise and is rewarded the error of the estimated state. Under some technical assumptions, we obtain a Nash equilibrium solution to this nonzero-sum dynamic game.