Information-Theoretic Approach to Strategic Communication as a Hierarchical Game

TL;DR

This paper applies information theory to analyze hierarchical communication games involving strategic information disclosure, characterizing equilibrium strategies and costs in various settings including Gaussian sources and decentralized control.

Contribution

It introduces a novel information-theoretic framework for hierarchical strategic communication, analyzing equilibrium strategies in Gaussian and decentralized settings.

Findings

Equilibrium strategies are characterized for Gaussian sources.

Major structural changes in strategies are identified with receiver side information.

Extensions to decentralized stochastic control are proposed.

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