Strategic Remote Estimation

Motivated by the emerging networked applications that involve strategic communication between selfish, rational agents whose objectives are misaligned, this paper studies a strategic variation of the well-known remote estimation problem. The classical remote estimation problem studies the design of a system, consisting of a sensor, an encoder, and a decoder, to observe, transmit and estimate a discrete time stochastic process with minimal transmission energy and estimation error. In order to minimize transmission energy, the encoder makes a real-time (sequential) to send or not to send communication decision based on sensor's observation of the stochastic process. In the variation studied in this paper, the encoder aims to render the estimate at the receiver biased in a particular, statistical manner, hence this consideration transforms the classical remote estimation from a team problem to a game. Specifically, we analyze the problem of sending N samples within a time window of length M. Assuming quadratic distortion measures and affine strategies for sender and receiver, which were shown to be optimal for Gaussian strategic communication, we first determine the optimal sequential transmission policies for this problem in the context of the Stackelberg equilibrium- where the encoder (sensor) is the leader and the decoder (estimator) is the follower- using dynamic programming. We demonstrate the effectiveness of our approach via numerical results.