  This paper studies communication scenarios where the transmitter and the
receiver have different objectives due to privacy concerns, in the context of a
variation of the strategic information transfer (SIT) model of Sobel and
Crawford. We first formulate the problem as the minimization of a common
distortion by the transmitter and the receiver subject to a privacy constrained
transmitter. We show the equivalence of this formulation to a Stackelberg
equilibrium of the SIT problem. Assuming an entropy based privacy measure, a
quadratic distortion measure and jointly Gaussian variables, we characterize
the Stackelberg equilibrium. Next, we consider asymptotically optimal
compression at the transmitter which inherently provides some level of privacy,
and study equilibrium conditions. We finally analyze the impact of the presence
of an average power constrained Gaussian communication channel between the
transmitter and the receiver on the equilibrium conditions.
