Information-Theoretic Approach to Strategic Communication as a Hierarchical Game

Abstract

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 structure of optimal strategies are identified. Finally, an extension of the results to the broader context of decentralized stochastic control is presented.