  This paper analyzes the information disclosure problems originated in
economics through the lens of information theory. Such problems are radically
different from the conventional communication paradigms in information theory
since they involve different objectives for the encoder and the decoder, which
are aware of this mismatch and act accordingly. This leads, in our setting, to
a hierarchical communication game, where the transmitter announces an encoding
strategy with full commitment, and its distortion measure depends on a private
information sequence whose realization is available at the transmitter. The
receiver decides on its decoding strategy that minimizes its own distortion
based on the announced encoding map and the statistics. Three problem settings
are considered, focusing on the quadratic distortion measures, and jointly
Gaussian source and private information: compression, communication, and the
simple equilibrium conditions without any compression or communication. The
equilibrium strategies and associated costs are characterized. The analysis is
then extended to the receiver side information setting and the major changes in
the structure of optimal strategies are identified. Finally, an extension of
the results to the broader context of decentralized stochastic control is
presented.
