Strategic Compression and Transmission of Information: Crawford-Sobel Meet Shannon

This paper analyzes the well-known strategic information transmission (SIT) concept of Crawford and Sobel in information economics, from the lens of information theory. SIT differs from the conventional communication paradigms in information theory since it involves different objectives for the encoder and the decoder, which are aware of this mismatch and act accordingly. This leads to a game whose equilibrium solutions are studied here. The problem is modeled as a Stackelberg game-as opposed to the Nash model used in prior work in economics. The transmitter is the leader, and the receiver is the follower. As leader, the transmitter announces an encoding strategy with full commitment, and its distortion measure depends on a private information sequence which is non-causally available --only to the transmitter. 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. Finally, several applications of the results within the broader context of decision theory are presented.